FAQ and corrections in this comment! (video Q&A will be on the second channel!) 1) This is the first time I'm using the A/B split thumbnail tool. because I was kinda lost - I just think waves on strings are really cool. If anybody has good title/thumbnail ideas, I'm all ears lol. 2) Real Q&A coming soon - after there are Qs to A...
@@GabeSullice It already does if you count IR. If you mean visible light - No, it would melt way before that. And probably lose resonance way before melting because of softening.
@@AlphaPhoenixChannel Thumbnail idea: INFINITE WAVES??? In red with you (just your head) doing a click bait face on the bottom right confused looking up trying to find the top and a wave dwarfing you in the background. There is a red arrow pointing off screen to the top of the wave. Directs the viewers eyes to the wave, and makes them wonder what's so special at the top.
I wouldn't necessarily say it's "overused." In fact, I think the opposite is true. People think superposition is magic because it's only really used in the context of quantum weirdness, but many different things in physics obey the superposition principle. Waves, forces, fields.
Superposition itself is just a boring, but useful tool. The WHY (why can you just add two waves?) is way more interesting because it leads you to the simplifying assumptions discussed in this video.
For my entire life this was known as "linearity". A more precise: passing something through linear function does not change how things are added. In Math language f(A + B) = f(A) + f(B). I do not understand why we need another term (and I know this property holds for some definitely not linear functions, so I guess "linear" might be misleading), but what is crazy, is how simple this property is and how often explanation of superposition is made so complicated, that you have no idea what people are talking about.
@IlluminatiBG linearity and superposition are not quite the same thing. As you said, linearity can be described as f(a) + f(b) = f(a+b). That's not what superposition is. If you wanted to put it into mathematical notation that way, superposition would be much more akin to h(a) = f(a) + g(a). The superposition principle says that for certain quantities if there are two (or more) sources of that quantity at the same position the value you get when you measure that quantity at that location is the sum of the values for all sources. The big difference between the two is that the measured function (h in my example) *need not be the same* as either of the original source functions (f and g). This is why two traveling waves can add together to form a superposition which is a standing wave.
As an instrument maker this is super cool. One thing I would add is there are two types of nodes. Really, a node just means a spot where a certain property is zero or minimal, so there are many depending on what property you are interested in but two are usually important. The node you mention at 4:18 is a velocity node where the movement or velocity is zero. However this spot also represents a stress/pressure anti-node, where the internal tension in the string is maximal. This is similar to pressure anti-nodes in a woodwind instrument where the air isn't moving because it is being squished from both sides evenly, but the pressure changes are highest.
in transmission lines, an electrical node is a currents antinode... with a standing wave induced, the electric node can reach potentials so high the insulation breaks down. and 1/4 wave from there, the current so high the conductor fuses and melts...
That part near the end where you mentioned "Knowing when your model is about to break" is a whole entire video (or series) in itself. I'd love to deep dive that point applied to models of the universe or climate or even traffic or holiday shopping. A lot of people distrust scientific models because they have a limit where the model breaks down, but the accuracy of a model up to that limit isn't linear, and it's that accuracy and knowing those limits that allows us to do things like predict the future (e.g. meteorology) with astounding precision.
Yes! This is why statistics is so important. The models predict things with infinite precision, so you need statistical analysis of real-world data to assess how valid the model is under given parameters.
Please don't say infinite until weve seen infinity Statistics is and will always be a "stereotype" - it's a way to draw pictures of shapes - minimal insight will be gained from this approach I LOVE this approach for now BOTH are true - Life is Quantum There's No Ledge in Knowledge - keep jumping
@@BracaPhoto They are using the word infinite correctly here. You can't "see" infinity - it's a mathematical concept that means that, for any number, there is always a number bigger than it. In the case of a mathematical model, you can always keep calculating more digits of precision. As an example, say you calculate the model out to 10 digits. That's just when you choose to stop. You can continue to 11 digits, 12, 13, and so on. There is never a number of digits N for which there isn't another number N+1 that you could continue to. That's the definition of infinite. Keep in mind that they are also using the word "precision" for it's mathematical meaning. Precision simply means the number of digits we have in the number - how little we leave out. That doesn't mean the model is perfectly "accurate" - the value calculated need not match the value you would observe in the real world. People often use these words interchangeably without realizing they mean two distinctly different things. Like it or not, statistics is how we summarize our knowledge of the world. We can't see everything happening for all of eternity. We can't measure it to infinite precision. We only have moments in time measured to some fixed precision. These are representations of the real world (think Plato's shadows on the cave wall), but they nonetheless are a result of the things that happen in the real world. Without a way to know exactly how the real things come to be, we can only create models - ideas - of what's happening based on our observations. This is statistics - combining all of the discrete observations we have to form an idea that could explain what we have observed. The insight that is gained is that we move from individual observations to an overall understanding of the whole by combining those observations and finding the set of possible relationships that would agree with those observations. The more observations we have, the fewer models we are left with that agree, bringing us ever closer to the true behaviour. It has nothing to do with pictures or shapes. Please understand that without a thorough understanding of what statistics is and how it's used, you can't make a fair judgment of it. Just like you said, you are making a stereotype out of statistics - you think of it based on your own observations while not seeing the whole picture. Those who work with statistics every day have many more observations and as a result have a much better picture of what it is. Keep an open mind and keep learning - don't assume that you know all there is to know about a subject, whether that's about life or just about statistics. Otherwise, you make the same error that you are telling others to avoid.
@reverse_engineered ok i do think i might have a new understanding ... so we can keep adding imaginary concepts together... I LOVE MATH for that very reason - it allows is to "Picture" infinity Sorry for joking about statistics "painting pictures" - I just LOVE a good Graph and a Laugh 😃 Math is sooooo precise but is it precision if the timing is off? Time is the joke - I'll wait for it Plancks "h" is the real 🔑 I suppose - Good luck picturing it
@reverse_engineered you spent a whole page to explain what I already said 🙄 I LOVE MATH 2 It let's us paint "pictures" just like you said - Infinity symbols - don't be embarrassed- it's just a mistake Peace
How glad are you that Mythbusters is finally available on TH-cam? Personally, I would even pay money to buy a complete series on dvd's. I'm just glad it's finally available!
@@runforitman I've seen a few episodes of "mythbusters abridged" on youtube. (although they might have been taken down by now) and after taking out the fluff, those episodes are like 5 minutes, lol. I don't blame @BeefIngot for not being able to watch em anymore.
Excellent video! Another fun example: the change in resonant frequency as tension increases is easily observed with a guitar string which is strummed too aggressively, especially the lower-pitched strings. Playing a string too hard results in its pitch going sharp and then returning to its proper pitch as the amplitude decays.
@@AlphaPhoenixChannelanother music related phenomenon - the harmonics of a plucked string are not quite integer multiples. The higher harmonics are sharp because of the stiffness of the string. This is especially noticeable in the thick bass strings of a piano. This also affects that way that pianos are tuned, which is as much an art as a science.
It hasn't happened too often and only in buildings with the right construction, usually older wooden dance halls, but during some gigs where my bass is locked in with the drums and put through a decent PA system, I've sometimes felt the stage resonate beneath my feet. And the stage is attached is attached to the floor and of course the walls so you can actually get the whole building throbbing. It's an extremely visceral feeling with the shifting volume of air but also little puffs of dust coming of the tops of rafters provide visual evidence. Also I'm totally putting a slo-mo camera on my bottom B string now. Great video, cheers.
This made me realise that's probably the awe-inspiring effect they go for with those building-spanning pipe organs, having that happen back before electricity was widespread and buildings just didn't move without wind or calamity would have been quite something. Now I wanna try amped up drone music in a cathedral...
I was playing drums, near the bass rig, last week. The bassist was using a 1000w amp, with the preamp turned down, and 2 15" + 2 12" cabinets (yeah...overkill). He began to play and I felt a literal "gut wrenching", sickening, pressure through my whole body. I asked him to stop and change something (anything) on his settings because I assumed I was in exactly the wrong spot in a "standing wave". He did and the effect disappeared. Now I wonder where I was in that wave...a node, crest, mid-rise/fall....??? It felt as if my body was resonating with the wave and soaking up too much energy from the amp.
I never had this happen, it's always struggling to understand something, I manage to grasp it and then someone posts a video clearly explaining the basics of it that weren't explained at all that I had to spend hours looking for
@@AmorDeae Same 😅. This video was actually not perfectly timed for me either. I actually learned about resonance in strings 2 months ago, but since my final exam in roughly 45 days will most likely include resonance, I think it still counts 🤓. The video did add something new that our teacher didn't mention though, the struggles of trying to match the theory with reality 👀. And I have to agree, I've found so many videos after learning about a subject in school (college), barely passing the subject and perfectly understanding the subject with a 20-40 minutes video by a "random" guy on youtube 😅.
For my applied physics bachelor, we did string resonance experiments as well. We would put alternating current on a tensioned copper wire and make it vibrate by placing a magnet next to the wire
I was actually surprised regarding the derivation of Einstein field equtions. Lots of dancing around with the geometry on a sphere. Nothing complicated, easy to mess up due to a blunder in basic geometry. What I love about physics: no politics envolved (unlike hystory or gender studies). Physisists find a way to say "we can bring politics in the field, but then your nuke fails to launch your tank wouldn't start moving". Good job, physisists. Keep politics away from the field.
This video is incredible. So many brilliant camera techniques used to explain such a broad variety of concepts. 15:38 is such an effective way of visualizing exponential decay; I've never seen something like that done before.
not the same problem exactly, the millennium bridge did not suffer from the wind, it suffered from the pedestrians walking in sync. the answer was simple add dampeners to absorb and dissipate that frequency and you are good to go. it was a different lesson that the millennium bridge taught us
@@nilsdock Fair point but in both cases, the cause was still resonance that the engineers hadn't planned for 🤷♂️. Also my comment was mostly a joke 😅.
I mean, this has been an issue with structural engineering for a long time. I forget which one it was, but I seem to recall there was a skyscraper where the engineers had tuned its twisting resonance to be outside the normal range that weather events could amplify. But when the synchronized steps of an aerobics class on the 13th floor happened to hit that exact frequency, it triggered an earthquake panic on the upper floors. Stuff like this can be VERY difficult to foresee, even WITH computer simulations.
This is really exceptionally well done! Bravo. The ARRL and anyone interested in antennas or traveling wave theory should watch and share this episode.
Now try your string wave in a vacuum to exclude the dampening of the wave due to wind resistance at the high velocity points...If you plot your amplitude vs. frequency and drive power experiment it should get more linear. Or repeat your experiments with "less stretchy" materials like steel cable or as we did in school a glass rod. Maybe you can even destroy a glass rod like in the resonance experiments we did with a speaker and wine glass.
To add a bit more rigor to the calculation of the limit on how much it can resonate: Let's say an individual wave has an initial amplitude of A, and each time a wave makes a round trip to end up back at the motor, it loses energy and has its amplitude reduced by a factor of B. With that, when the motor emits a wave, that will have an amplitude of A, while the previous wave that arrives at the same spot has an effective amplitude of AB, and the one before that is AB², continuing with AB³, AB^4, AB^5, etc. When you continue this infinitely, you get the sum over A×B^k, with k going from 0 to infinity. This sum is known as a geometric sum, and evaluates to A × 1/(1-B). This means that the overall amplitude will just be proportional to the strength of a single wave that is emitted by the motor, since B, i.e. the amount of a wave preserved by the bridge carrying it, is constant. By that logic, it makes perfect sense that a weak motor would have noticeable limitations, but it stays plausible that a stronger motor would have much stronger effects.
@@arthurmoore9488 The proof is actually pretty simple. First consider a finite sum, for example: x = 1 + B + B² then, multiply the equation by (1 - B) on both sides. As a result, you get: x (1 - B) = (1 + B + B²)(1 - B) = (1 + B + B²) * 1 - (1 + B + B²) * B = 1 + B + B² - B + B² - B³ = 1 - B³ Then, you can divide by (1 - B) on both sides, and get: x = (1 - B³)/(1 - B) You can do an analogous calculation for any arbitrary sum size. As a result, you get: 1 + B + B² + ... + B^n = (1 - B^(n+1)) / (1 - B) In this, the only part where n appears (which is what you want to be infinite) is in B^(n+1), but because the wave always loses a bit of energy instead of gaining or staying the same, you have 0
a single pendulum driven with a motor is a classic physics lab demonstration for a reason, it's so well behaved and lets you play with resonance and nonlinearity without needing special equipment and without having to go into waves immediately
Always love the questions you ask and consequent explanations. As a fun adjacent experiment to explain the boundary conditions, you could try and build an oscillator into a string loop launcher ^^
A description about Q factor would be good, how quickly the amplitude drops off as the freq +/-'s from the resonant freq. And when you described the energy been used up in heat, sound, etc and the rate the amplitude drops away, this is called 'damping'. The Thiele/Small Parameters for loud speakers are calculated by all the fundamental physics of resonance.
He mentioned avoiding getting deep into the math for the sake of the video. Counter-intuitively, if you introduce too much complexity, people learn less, not more. I think his broad explanation and demonstration that the amplitude depends on a very narrow range of frequencies is enough for most people to get the general idea without having to know the technical terms we use in industry.
Good demo. These effects happen in speaker cones too. I wonder if some of your fine-tuning problem is due to the delay of the actuator. The motor arm itself also has resonance. These things might be skewing results a bit at the really fine detail level.
At one point I had a really long motor arm - it let me put a really big initial wave in, but the reflections got wacky. I’d get a reflection off the interface between the plastic arm and the string, then another reflection from back near the stand. The final design was a compromise
I love the pace and depth of your videos! I feel like no other science youtuber gets it right. Any time a question builds up in my head while watching (string stretching) you address exactly that later, it's fantastic!
I was about to comment on how this is the first resonance video I watch in a long while that DOESN'T mentions the Takoma bridge, but he came in clutch at the last minute. It's a fascinating case and I love to hear about it every time.
Great demonstration of resonance. The main setup of the experiment is satisfyingly low tech but very effective with the high-speed camera and signal generator input.
It's crazy how quickly and clearly the fundamentals of calculus show up in this. I could very easily see the adding up of forces in a string canceling each other out in a textbook.
Oh this brings back memories of physics labs of days past, with one of those oscillation machines (probably made by Pasco or another "educational lab warehouses" that supplies stuff to schools at prices that seem way to expensive), and me and a couple guys stretched a string across the entire lab, and managed to get 13 or 14 nodes to a standing wave, and they were so tiny but we felt like we accomplished something. In reality, as a teacher of physics myself, I now realize internally the teacher was probably thinking "can you guys finish, I want to go home already". P.S. I love the "as an exercise for the viewer" bit, had me cracking up.
Yup, this was very cool. I had never really thought through why resonance doesn't build forever... this was a beautiful explanation... and, the idea of superposition of repeated waves instead of just amplitude building is the key to understanding this. Great job. I thought for sure that you'd show how you can add different frequencies (and phase offsets) to create a monster peak anywhere along the string (in the world of ocean navigation it's called the "rogue wave"). It requires using Fourier series with D/As instead of just simple frequency generators... but a great way to show how these waves add together in some pretty magical ways.
Great video, was just having a buddy create standing wave animations for our chemistry section of our physics site. That slow mow standing wave on the reflection was so pleasing to see!
Even when the answer to the thesis question seems intuitive to me, the journey from A to B always includes a wealth of detail I never considered. I love this channel more with every new video. And so help me if you ever say the words "this video is brought to you by raid shadow legends" I will explode into pink mist.
As an electrical engineer, I'm accustomed to thinking of resonant electrical circuits. I was happy to learn about these details that explain the deviation of physical string vibrations from the simple models, which I had never heard before. The other comments explaining how this affects musical instruments (especially guitars) are also delightfully informative. I was not expecting to have a phenomenon confirmed that I puzzled me since I was a child.
love your content. deep diving on often intimidating concepts in intuitive ways through curiosity. i'm convinced this is the best way to develop deep intuition instead of mindlessly applying complex math and theory to situations. you need the deep intuition to use math in appropriate ways. although sometimes mindless use of math to abstract and transform information leads to insight, which can then be used to lead the math in a new direction.
Just realizing this now, but I would _LOVE_ a collab between you and Grady from Practical Engineering! You guys are both great explainers with a knack for demonstration through experimental results. It would be a real power duo!
I really appreciate your focus on how the model we use of resonance and superposition is merely that: a model. It's based on assumptions that are close enough in many situations but don't hold in every case. Any time you push something to the extremes (very small, very large, very slow, very fast) you reach the edges of where the assumptions hold and the model becomes less and less accurate. This is a common misconception about science. People think science is "wrong" and can never make up its mind, but that's not true at all. Scientists realize that their models are only close approximations of the real world - we are aware of its limits. As we experience more of the world, we discover new things that don't fit our existing models and so we augment those models, adding more details to account for that previously unobserved behaviour. The old models don't cease to be useful approximations - the new models are just closer approximations. A quote by a famous statistician says, "All models are wrong. Some models are useful." By knowing the limitations of our models, we can make use of them within their limits to tell us a lot about the world that we wouldn't otherwise know. But we have to know those limits so that we don't exceed them, giving us wrong predictions. Over time we can make better models that allow us to predict even more, but we can still use those old models within their limits; the new models simply expand the limits of what we understand. We never know everything exactly, but we can continue to improve our knowledge over time. Anybody who claims they know something about the world with absolute certainty doesn't realize their own limits. You know that the sky is blue and the grass is green, but those are only approximations - every bit of sky is a different color of blue and every blade of grass is a different color of green. The more you know about the sky and the grass, the more accurately you can say just how blue and green they are, but there are always limits to just how accurately you can say what that color is - the more we learn, the more accurate we become.
Great video! It's amazing to me how resonance appears in so many forms (mediums), from sound to electricity to light and mechanics or the body of stars.
Before watching this I thought I had a pretty good grasp on resonance but this video really makes the "why" much clearer, indeed almost obvious at points. I wasn't previously aware that the resonant frequency changes when waves are present but the diagram makes it pretty obvious and I thought "the string is longer" before you said it 😊. But I didnt spot that the effect of this was opposite and the whole tension making the wave travel faster thing.
Honestly, the minute I saw the simulated demo of a wave on a bent rope it started to make sense. You aren't adding more energy into a single wave, but rather layering waves on top of each other. And as you demonstrated, a wave will eventually decay. So you get to this point where even though you are adding more waves onto the layer, the first ones are dropping out in a sort of FIFO stack.
These videos are better than every EE class I've taken lol. A cool way to build up to Tesla coils (or just more nonlinear electrical fun) would be to look more at the coil used here and explain why a flyback diode or some snubber is needed to prevent kickback from the inductance (which could lead to a deeper look at inductance and capacitance as a continuation of transmission line concepts, or even RF, or just pure Tesla madness haha).
You could greatly improve your string driving mechanism by using a 10” or 12” woofer with a vertical rod attached to the cone and a 100-200 watt audio amp. That would also allow you to use more than one signal generator (summing to mono) to create multiple simultaneous waves on the string. Your visualizations of the physics are among the best I’ve EVER SEEN on TH-cam. Great Work! 👍🏼🤓👍🏼
Noise cancellation, surprised nobody has mentioned yet this is why it's so important your speakers are correctly wired. Between two with mono (same) sound on each, there is silence in the middle, it's amazing to experience. This is key to how active noise cancelling works, how audio sound extraction works, etc.
wahoo, another video from my favorite creator! This is also an example of why the coil frequency calculators and an approximation. You always have to add or remove loops of wire on the coil to come close to the predicted oscillation. There are so many factors like insulation thickness, wire thickness, air gaps between windings. Even if you created a perfect math calculation to predict it, you would still only get close because some adjacent turns may be stretched or closer together than others on the same coil. I always wanted a better calculation but I think there are just too many tiny unmeasurable things in real life that would determine the actual frequency. Great video as always by the way. You are one of the few creators that has a broad and deep stroke of education broken down into simple concepts. Thank you for all the videos you create! I wonder what the minimum power to break a wine glass from a speaker is. I have seen it done many times, but there has to be some minimum power to make it happen. Great demo and animations as always. I really appreciate your videos.
wow... i cant believe i found this interesting. I mean it isnt exciting by nature lol, but i couldnt help but keep watching. Somehow watching a string vibrate and all the stuff i cant understand that went into it was somehow mesmerizing. the subtle nuances of each factor going into it was somehow interesting.... Cool man, right on. Thanks
Yeah resonance has to be my favorite intersection of concepts in physics and engineering. I had learned of Tesla's little box that could shake buildings before the MB episode, and have always wanted to try to build one... I've built a few tesla coils and the concept of a resonant tank circuit is super cool. Your observation regarding the frequency increasing along with total energy is something that occurs in Tesla coils. In coils however, the frequency DROPS as you add energy. This has to do with the capacitance formed by the topload and how the length of conductive arc will increase this capacitance. Your graph of amplitude vs. frequency was very pointy, indicating a high "Q" factor. High Q systems can reach very high amplitudes, however the frequency range is very narrow, and thus very susceptible to detuning. Tesla coils are designed to track the resonant frequency and drive at that frequency, even as it changes. One way to do this is to use a PLL, or Phase-Locked Loop, which is one of my favorite concepts in electronics. You could sense the vibrations in the string, and use the output from a PLL to drive your solenoid, and it would track. I suspect Tesla had something like a mechanical PLL in his shaker box that would sense induced vibrations and adjust the driving frequency to match. I bet mythbusters could have made the bridge shake more if they had a frequency feedback loop instead of a fixed (manually adjusted) frequency going in. As a funny afterthought, both my brother and I will often seek out the resonant frequency of any room-type enclosure that has highly sound-reflective walls--like pedestrian tunnels, and tile bathrooms. If you hum starting at the low end and as you slowly increase the tone, you will hear notes that get louder. Hum that note, and you will hear a beat frequency as you drift off the peak. You can often get a room to "ring" quite loudly. As such, we've both been caught humming cryptically to ourselves while at the urinal in a sundry of public restrooms :)
Anyone else wish he would have tuned the length so it would resonate at a whole number frequency (4hz) so the trickiness of the 2 super imposed waves was easier to "see" in the non-integer multiple of the required frequency? Great video - love your stuff!
How did this pop up literally the day I watched the mythbusters bridge episode, I just found out that so many mythbusters episodes are on youtube from them so I've been watching through them recently as comfort watching as I do other things. It's bittersweet to see Grant always being the person that made people love and respect him and then realizing he isn't around in the world anymore, that's why it's called loss, and accepting that is just the way of the world.
I love that waves deflect upside down because, assuming my thought process is correct, it models one of Newton's laws perfectly. The wave hits the wall, pulling it in one direction, we'll say contacting it a little, and the wall expands back to its original size, but not perfectly, expanding just a little too much and exerting that extra force used to expand it as a wave with lower amplitude in the opposite direction to conserve momentum. Of course this deformation of the wall in incredibly tiny with rigid structures, but the heat lost in this compression/expansion is part of the reason the wave bounces back with a noticable amount less amplitude.
I loved this part of my calculus classes. It was amazing to model the harmonics and see how they would sync and amplify. More fascinating to me was offsetting them slightly and watching the patterns that emerged with the period slightly off the harmonics frequency. A tuning parameter which allowed slowly passing the wave through harmonics and anharmonics was cool to suddenly see the wave snap into harmony and then almost resist leaving that harmony back into disordered frequencies.
Nice! One point about the exponential decay you show: The first initial decay seem to have a much faster decay that the rest of the curve, I think that is an indication of a non-linear decay that you get when your string is already oscillating at amplitudes where the nonlinear terms in the wave-equation are no longer negligible. Also, nice to see a video of the Tacoma bridge, and the man walking off it was very very calm, much calmer than I'd be...
I'd love to see the resonance of brass instruments modeled and explained on this channel if you can ever get to it! The point about harmonics not being exactly integer multiples in the real world made me think about the way brass instruments work. On a brass instrument, you can get multiple notes on the same length of tubing by going through the harmonics (called "partials" in this context). However, they end up not all being in tune, meaning you sometimes need to pitch a particular partial up or down. This is usually done by adjusting the input frequency to get the partial back in tune, and experienced musicians have these tunings memorized so they can hit the right pitch immediately. It's also not as simple of a relationship as on the string model, because the tubes on brass instrument loop around and change diameter. Depending on where the nodes end up in the tube, you could get different interactions with the bends in the pipe (or even with any dents that might be there). Another interesting interaction on brass instruments is that the partials actually influence the player's input frequency, nudging it towards that partial's resonant frequency like a ball rolling into a valley. It's a neat effect that I don't think can be represented with your string model, but I'd love to understand it better.
I had an instructional guitar book called "How to Become Dangerous on Rock Guitar" when i was a kid. It was an awesome book and i did indeed become quite dangerous, not only on rock guitar but a number of different genres. Anyway, one of the things that made it such an awesome book was the amount of depth and detail it went into. It started with a thorough explanation of how a guitar string vibrates and how these vibrations result in the fundamental tone and subsequent harmonics (overtones) that make up each note. It was quite mind blowing to learn how a single string could vibrate simultaneously in halfs, thirds, fourths, etc. and that each of these different vibrations produced its own harmonic that was higher in pitch and lower in volume all making up what is heard as one note. In fact you can see this happening if you look at a plucked guitar string in a certain light along with the nodes at certain intervals. You can actually isolate different harmonics by touching the string lightly over a node.
The one side fixed string is the best live demo of what superposition and linearity is. It visualises the math concepts very well. You can calculate lots of stuff and test it in real world.
You just made tesla coils cool. I never understood the appeal, "woo big sparks?". The fact that it is a resonating circuit that more or less sheds free electrons. Is awesome in the literal sense.
You are asking exactly the right questions ☺ I have another wave-related question: When it comes to electromagnetic waves, there are antenna arrays that can do a thing called "beam forming" by cancelling out parts of the beam. But: When 2 electromagnetic waves superimpose on a destructive way, where does the energy go? Or do the waves still co-exist and just cancel each other out along their travel path?
I LOVE videos that says exactly what I was about to comment before I hit the comment button. I noticed in the video at 22:00 the process was backwards from what I'm used to. (don't know if I'm being helpful or not but here it goes) You can mathematically add a second wave to a physical string starting from the highest frequency to the lowest. The higher the frequency has the smaller variation amplitude, so the smaller variation in "length" of the string. As you can see in a Fourier series, the base resonant frequency is the lowest frequency with the higher amplitude. knowing that, obviously the higher frequency has the least amount of amplitude, so less variation on the physical size of the string, up the limit of saying that a static string is equivalent to a string oscillating at an infinite frequency. With that you can estimate the height of the highest frequency as "thickness" of the string and by comparison with the static string deduce how much it "shortened", with these values as the "new" string you can calculate the new lower resonant frequency you want to add. The process of doing this backwards (from the lower frequency to the highest) mathematically is a nightmare, or I was not presented to a simpler method 🤣
Yeah it’s a mess lol! In order to get the visible 9-node signal on the 1-node wave I massively increased the higher frequency amplitude. The picture on the function generator looks nothing like the real string after high frequencies are attenuated!
The thing I love about discussing has tension is you can imagine yourself as a person in a string of people linked hand to hand. And as you imagine that you can actually feel the tension in your arms as the mote wave passes by.
I work with high end servo systems and this resonance is a common issue you run into once you start tuning linear systems tightly. The whole system starts creating resonances based on the minor mechanical flection in gantries, changes in bearing preload passing the CG, offset loads, etc. Once that resonance starts you either need to tune around that frequency on the PID loop, notch filter the frequency of resonance to dampen it.
I'm surprised you aren't talking about stringed musical instruments because that is where this is all studied most for hundreds of years, albeit often in more intuitive non-scientific ways (aka by ear) Ears are very accurate. When I was studying piano string tuning, we learned that all the resonant harmonics go higher up in pitch vs the fundamental. This is because string is not perfectly ideal and has a stiffness to it. That that looks like is the section at the node(s) that is flat and doesn't bend due to the material stiffness of the string. I had never heard about the idea that the string became longer when it has waves in it, though graphically that looks true. But the important point is that the harmonics all go to higher pitch because the more nodes you have in the string the shorter the string is, hence more tension/higher pitch. Interesting meandering video. Thank you.
The animation and explanation from 15:44 are very well done. Your videos are so incredibly good, you manage to formulate and answer the questions we used to ponder over while these things are explained to us. You make physics intuitive again. So, when can we expect you to do this for quantum mechanics and relativity? 😉
Harmonics are actually always integers above the base freq. But there is such thing as overtones which is any freq. above the base one. Also if you're trying to modulate one frequency with another (doesn't matter FM or AM) it gives you two side frequencies: Base+Mod and Base-Mod. It's often used in radio communication.
Personally, I'd be really interested in learning how resonance plays into tesla coils, especially if it's "causing electrons to literally fall out of the wire". It might also be informative for people who want to build their own tesla coils, so they can understand how they're supposed to tune the frequency. I built a spark-gap tesla coil using a neon sign transformer, a couple of carriage bolts for the spark gap (i used the heads of the bolts because i didn't want the spark to jump out of that gap, or at least that's the reasoning i used), a PVC pipe that i hand wound some regular wire that i had pulled out of a motor (yes, i hand unwound a motor... that wasn't fun), and some very floppy high gauge wire as the primary (later upgraded to a length of copper pipe that came pre-coiled), and was able to get some tiny sparks off the end of it. i never got a top load for it, but i did build a VERY crude capacitor bank for it out of some glass jars (saurkraut specifically), salt water, and vegetable oil. tbh, the whole thing terrified me, but i know the output of the tesla coil was safe thanks to my youngest brother. I had a screwdriver with a wooden handle that had cracked for some reason, and while i had it set up, he would use the screwdriver to 'grab' the arc from the output, which would zap his hand through the handle... he kept at it for well over a minute though, lol. the spark gap put out an INCREDIBLY bright and loud spark though (pretty sure i maxed out the gap at around 1.5 inches, and it seemed to be about 1/4th of an inch thick... that spark scares me.), and the ozone it made was incredible. easily enough to be smelled anywhere in the ~1,200sqft room i ran it in after approximately 20 seconds.
constructive interference is the best word for this 6:43 lol bless up. resonance is like a tuning fork at the same frequency that hasnt been hit starting to vibrate when it encounters a vibration from a similar/like tuning fork.
Vibrations are still the most interesting and dangerous things in structural design. As a Mechanical Engineer we were taught that if your structure gets vibrated at one of its resonant frequencies, it's game over. If, in a real world structure all the factors you mention lined up, possibly a bolt will fail, as it is designed to in such situations, if you keep on doing this more bolts will fail until they cannot support the loads acting on the structure and its weight. On structures that are not as meticulously designed as a bridge, or building, the risks are far greater. The reason is simply, imposed displacement. If you put a very tiny force on a piece of paper it will deflect by say 5mm. It's very hard to actually find the force that will make the deflection exactly 5mm so you just take your hand, or device and move it to be 5mm. In a similar sense, you can model the stress within an object subject to an imposed displacement, and if that displacement is big enough, it can exceed the material's yield strength. That object will break and the whole structure may not be as redundant as a bridge, causing it to fail entirely. That object can be a beam or a bracket of a frame, supporting something not so critical as cars or people, but maybe an electric motor, so we still design those frames with their resonant frequencies being well away from the rotational velocities of that motor.
The final observation about how the equations physicists like to use are all wrong was actually kinda crushing for me to learn (but it was a sow realization so I got to distribute the disappointment over time lol) after leaving school. When I learned this, and I still do wish, that my teachers had made it more clear that the things we learned were simplifications and idealized models that don't represent the real world. I'm not mad that I wasn't made to do *actual* optical calculations for physically accurate lenses in physics, but I *am* mad that I spent a significant amount of time thinking that paparabolic lenses were actually perfectly physically ideal in the real world. I felt lied to, or at the very least I felt like an assumption was made that I would not have been able to understand the reason that things were being simplified. Videos like this are awesome, and should be required viewing when learning a subject. It would have been intensely helpful in school to have something that explains "This is why everything you are about to learn is technically wrong, and *this* is why you should be happy not to have to do it the hard way, because shit is complicated" lol. I consider myself lucky that I did not end up going into any of the hard sciences, because If I had learned this stuff after making a more serious commitment I'm not sure what I would have done. It's like the education equivalent of scope creep. In other industries if you sign up for a job with a certain scope and then the scope gets increased out from under you we usually consider that to be bad and hopefully not allowed by the contract if you have one. It's weird to me that school effectively just does that repeatedly and seemingly no one cares.
2:08 "the real-world is not a frictionless vacuum" no shit! 4:35 it's beautiful seeing a real life, physical, tangible, solid, string move in this way. Not water or something. 8:13 "why does the string continue after the wave looks flat" yea it's a good question. 9:20 this is a beautiful animation. 17:50 "a climb and then a snap, a climb and then a snap" 😂😂😂 I love that idea. It's so whimsical. 20:34 that is a good question wtf does this have to do with model assumptions breaking. I just thought this was some cool shit. My favorite part of this video was when tensional imbalance was explained to drive the wave's movement.
A new ham radio operator was telling me that my end-fed half wave antenna would only resonate at one frequency. I assured him it would resonate at the 2nd, 3rd, 4th... harmonics as well. I'll have to show him your video!
23:20 Fun fact: When you use a slinky, Mersennes's laws (the proportionality laws that describe the increased frequencies with greater tension, shorter length and smaller linear density) perfectly cancel out such that the frequency stays the same, even if the swinging slinky is longer! (A slinky under tension is an approximately linear spring with negligible resting length and a diameter much smaller than the length under tension)
Before watching the PS section, I wasn’t planning to destroy a bridge using resonance. Now, I’m going to do it because a guy on TH-cam assured me the bridge would be fine. Wish me luck!
for the section at 20:30, i wrote my first physics lab paper on this phenomenon, i had a very similar setup to you, only with guitar strings and i just plucked it with my finger. one improvement you could make is maybe have a ferromagnetic cable, and pul on the cable directly with the electromagnet so that you can make the other end of the cable hold tight also, this way it loses energy way slower
That was some really nice footage of the waves on a string. I know this wasn't the point of the video but I would be very interested to see a similar setup with a steel string under tension and preferably fixed on both ends. The source to make the string resonate could be electromagnetic (like an e-bow?) and can be placed anywhere along the string. I imagine different positions/ intervals would encourage certain overtones to form more pronounced. The harmonic series is a fascinating phenomenon that naturally occurs with resonating body's. I would even dare to say that the significance of the harmonic series is immensely overlooked and probably not even fully understood yet.
FAQ and corrections in this comment! (video Q&A will be on the second channel!)
1) This is the first time I'm using the A/B split thumbnail tool. because I was kinda lost - I just think waves on strings are really cool. If anybody has good title/thumbnail ideas, I'm all ears lol.
2) Real Q&A coming soon - after there are Qs to A...
Could you get the string to glow/radiate if you placed the whole apparatus inside a vacuum?
@@GabeSullice It already does if you count IR. If you mean visible light - No, it would melt way before that. And probably lose resonance way before melting because of softening.
@@AlphaPhoenixChannel Thumbnail idea: INFINITE WAVES??? In red with you (just your head) doing a click bait face on the bottom right confused looking up trying to find the top and a wave dwarfing you in the background.
There is a red arrow pointing off screen to the top of the wave.
Directs the viewers eyes to the wave, and makes them wonder what's so special at the top.
Correction: At the end you accidentally left out the "dis" part of "disheartening."
Next up Fourier transformation for dummies
25:40 Did he say "I hope you enjoyed this Fourier into resonance today?" :)
No but now I wish I had
I said it in my head.
@@UncleKennysPlace
I’m only saying it now, don’t give me away 🤭
THANK YOU for finally saying that "superposition" = "adding things together". Its probably the most overused term for something very lame lol
I wouldn't necessarily say it's "overused." In fact, I think the opposite is true. People think superposition is magic because it's only really used in the context of quantum weirdness, but many different things in physics obey the superposition principle. Waves, forces, fields.
Superposition itself is just a boring, but useful tool. The WHY (why can you just add two waves?) is way more interesting because it leads you to the simplifying assumptions discussed in this video.
For my entire life this was known as "linearity". A more precise: passing something through linear function does not change how things are added. In Math language f(A + B) = f(A) + f(B). I do not understand why we need another term (and I know this property holds for some definitely not linear functions, so I guess "linear" might be misleading), but what is crazy, is how simple this property is and how often explanation of superposition is made so complicated, that you have no idea what people are talking about.
@IlluminatiBG linearity and superposition are not quite the same thing. As you said, linearity can be described as f(a) + f(b) = f(a+b). That's not what superposition is. If you wanted to put it into mathematical notation that way, superposition would be much more akin to h(a) = f(a) + g(a). The superposition principle says that for certain quantities if there are two (or more) sources of that quantity at the same position the value you get when you measure that quantity at that location is the sum of the values for all sources.
The big difference between the two is that the measured function (h in my example) *need not be the same* as either of the original source functions (f and g). This is why two traveling waves can add together to form a superposition which is a standing wave.
There are a lot of terms that people don't understand and use all the time.
I like how this video seems to answer the questions that pop into my head almost right after they appear, extremely intuitive structure
😁
exactly! I was literally reading about standing waves before I clicked on the video!
smart people tend to think in similar ways.
In my case, he is about 37 years late.
I literally Just posed the same question in my head and found this video 2 mins after a little scrolling lol
As an instrument maker this is super cool. One thing I would add is there are two types of nodes. Really, a node just means a spot where a certain property is zero or minimal, so there are many depending on what property you are interested in but two are usually important. The node you mention at 4:18 is a velocity node where the movement or velocity is zero. However this spot also represents a stress/pressure anti-node, where the internal tension in the string is maximal. This is similar to pressure anti-nodes in a woodwind instrument where the air isn't moving because it is being squished from both sides evenly, but the pressure changes are highest.
in transmission lines, an electrical node is a currents antinode...
with a standing wave induced, the electric node can reach potentials so high the insulation breaks down.
and 1/4 wave from there, the current so high the conductor fuses and melts...
That part near the end where you mentioned "Knowing when your model is about to break" is a whole entire video (or series) in itself. I'd love to deep dive that point applied to models of the universe or climate or even traffic or holiday shopping.
A lot of people distrust scientific models because they have a limit where the model breaks down, but the accuracy of a model up to that limit isn't linear, and it's that accuracy and knowing those limits that allows us to do things like predict the future (e.g. meteorology) with astounding precision.
Yes! This is why statistics is so important. The models predict things with infinite precision, so you need statistical analysis of real-world data to assess how valid the model is under given parameters.
Please don't say infinite until weve seen infinity
Statistics is and will always be a "stereotype" - it's a way to draw pictures of shapes - minimal insight will be gained from this approach
I LOVE this approach for now
BOTH are true - Life is Quantum
There's No Ledge in Knowledge - keep jumping
@@BracaPhoto They are using the word infinite correctly here. You can't "see" infinity - it's a mathematical concept that means that, for any number, there is always a number bigger than it. In the case of a mathematical model, you can always keep calculating more digits of precision. As an example, say you calculate the model out to 10 digits. That's just when you choose to stop. You can continue to 11 digits, 12, 13, and so on. There is never a number of digits N for which there isn't another number N+1 that you could continue to. That's the definition of infinite.
Keep in mind that they are also using the word "precision" for it's mathematical meaning. Precision simply means the number of digits we have in the number - how little we leave out. That doesn't mean the model is perfectly "accurate" - the value calculated need not match the value you would observe in the real world. People often use these words interchangeably without realizing they mean two distinctly different things.
Like it or not, statistics is how we summarize our knowledge of the world. We can't see everything happening for all of eternity. We can't measure it to infinite precision. We only have moments in time measured to some fixed precision. These are representations of the real world (think Plato's shadows on the cave wall), but they nonetheless are a result of the things that happen in the real world. Without a way to know exactly how the real things come to be, we can only create models - ideas - of what's happening based on our observations. This is statistics - combining all of the discrete observations we have to form an idea that could explain what we have observed. The insight that is gained is that we move from individual observations to an overall understanding of the whole by combining those observations and finding the set of possible relationships that would agree with those observations. The more observations we have, the fewer models we are left with that agree, bringing us ever closer to the true behaviour. It has nothing to do with pictures or shapes.
Please understand that without a thorough understanding of what statistics is and how it's used, you can't make a fair judgment of it. Just like you said, you are making a stereotype out of statistics - you think of it based on your own observations while not seeing the whole picture. Those who work with statistics every day have many more observations and as a result have a much better picture of what it is. Keep an open mind and keep learning - don't assume that you know all there is to know about a subject, whether that's about life or just about statistics. Otherwise, you make the same error that you are telling others to avoid.
@reverse_engineered ok i do think i might have a new understanding ... so we can keep adding imaginary concepts together...
I LOVE MATH for that very reason - it allows is to "Picture" infinity
Sorry for joking about statistics "painting pictures" - I just LOVE a good Graph and a Laugh 😃
Math is sooooo precise but is it precision if the timing is off?
Time is the joke - I'll wait for it
Plancks "h" is the real 🔑 I suppose - Good luck picturing it
@reverse_engineered you spent a whole page to explain what I already said 🙄
I LOVE MATH 2
It let's us paint "pictures" just like you said - Infinity symbols - don't be embarrassed- it's just a mistake
Peace
How glad are you that Mythbusters is finally available on TH-cam?
Personally, I would even pay money to buy a complete series on dvd's. I'm just glad it's finally available!
I remember it so fondly, but I find it so unbearably unwatchable now with the way tv used to be at the time with all the recaps and breaks.
@@BeefIngotneed mythbusters abridged
@@runforitman I've seen a few episodes of "mythbusters abridged" on youtube. (although they might have been taken down by now) and after taking out the fluff, those episodes are like 5 minutes, lol. I don't blame @BeefIngot for not being able to watch em anymore.
@@BeefIngot Get yourself SponsorBlock, it has options to skip those sections.
You have Allan Pan to thank for it.
Excellent video! Another fun example: the change in resonant frequency as tension increases is easily observed with a guitar string which is strummed too aggressively, especially the lower-pitched strings. Playing a string too hard results in its pitch going sharp and then returning to its proper pitch as the amplitude decays.
That’s fascinating! Makes sense!
The whole metal music style was born above this phenomena. Called "Jent".
@@Ma_X64Djent?
Was just about to say the same! Well known effect
@@AlphaPhoenixChannelanother music related phenomenon - the harmonics of a plucked string are not quite integer multiples. The higher harmonics are sharp because of the stiffness of the string. This is especially noticeable in the thick bass strings of a piano. This also affects that way that pianos are tuned, which is as much an art as a science.
It hasn't happened too often and only in buildings with the right construction, usually older wooden dance halls, but during some gigs where my bass is locked in with the drums and put through a decent PA system, I've sometimes felt the stage resonate beneath my feet. And the stage is attached is attached to the floor and of course the walls so you can actually get the whole building throbbing. It's an extremely visceral feeling with the shifting volume of air but also little puffs of dust coming of the tops of rafters provide visual evidence. Also I'm totally putting a slo-mo camera on my bottom B string now. Great video, cheers.
This made me realise that's probably the awe-inspiring effect they go for with those building-spanning pipe organs, having that happen back before electricity was widespread and buildings just didn't move without wind or calamity would have been quite something.
Now I wanna try amped up drone music in a cathedral...
the story regarding tesla and resonance did involve a building, and not a bridge.
I was playing drums, near the bass rig, last week. The bassist was using a 1000w amp, with the preamp turned down, and 2 15" + 2 12" cabinets (yeah...overkill). He began to play and I felt a literal "gut wrenching", sickening, pressure through my whole body. I asked him to stop and change something (anything) on his settings because I assumed I was in exactly the wrong spot in a "standing wave". He did and the effect disappeared. Now I wonder where I was in that wave...a node, crest, mid-rise/fall....??? It felt as if my body was resonating with the wave and soaking up too much energy from the amp.
I think Mr Phoenix should get a Moog Minitaur and start cracking bricks 😂
@@oleran4569 Cool
I love it when youtubers just happen to post stuff related to what I'm currently learning about 😂. Makes things so much easier 😁.
I don't think I would have graduated if it wasn't for mathematicians on TH-cam. Thanks old Indian guys!
It makes things more interesting for me
I never had this happen, it's always struggling to understand something, I manage to grasp it and then someone posts a video clearly explaining the basics of it that weren't explained at all that I had to spend hours looking for
@@AmorDeae Same 😅. This video was actually not perfectly timed for me either. I actually learned about resonance in strings 2 months ago, but since my final exam in roughly 45 days will most likely include resonance, I think it still counts 🤓. The video did add something new that our teacher didn't mention though, the struggles of trying to match the theory with reality 👀. And I have to agree, I've found so many videos after learning about a subject in school (college), barely passing the subject and perfectly understanding the subject with a 20-40 minutes video by a "random" guy on youtube 😅.
Yah, just a coincidence...not that all your apps have permission to listen to you
For my applied physics bachelor, we did string resonance experiments as well. We would put alternating current on a tensioned copper wire and make it vibrate by placing a magnet next to the wire
I was actually surprised regarding the derivation of Einstein field equtions. Lots of dancing around with the geometry on a sphere. Nothing complicated, easy to mess up due to a blunder in basic geometry.
What I love about physics: no politics envolved (unlike hystory or gender studies). Physisists find a way to say "we can bring politics in the field, but then your nuke fails to launch your tank wouldn't start moving".
Good job, physisists. Keep politics away from the field.
What I love about your videos - except of course from the great content, demos and animations - is the enthusiasm you radiate when explaining stuff.
I love the way these second-order effects make so much sense with just a little thought
No frickin way, I was just googling this exact question last night!
Perfect timing man :D
This video is incredible. So many brilliant camera techniques used to explain such a broad variety of concepts.
15:38 is such an effective way of visualizing exponential decay; I've never seen something like that done before.
27:20 Engineers learned from this event, so they repeated the same mistake with the Millenium bridge 😂.
not the same problem exactly, the millennium bridge did not suffer from the wind, it suffered from the pedestrians walking in sync. the answer was simple add dampeners to absorb and dissipate that frequency and you are good to go. it was a different lesson that the millennium bridge taught us
@@nilsdock This is why we now prefer Engineers learn their lessons in simulations before we use these items as human test dummys
@@BeefIngot I'm pretty sure accurate enough simulations didn't exist back when that bridge was built 🤔…
@@nilsdock Fair point but in both cases, the cause was still resonance that the engineers hadn't planned for 🤷♂️. Also my comment was mostly a joke 😅.
I mean, this has been an issue with structural engineering for a long time. I forget which one it was, but I seem to recall there was a skyscraper where the engineers had tuned its twisting resonance to be outside the normal range that weather events could amplify. But when the synchronized steps of an aerobics class on the 13th floor happened to hit that exact frequency, it triggered an earthquake panic on the upper floors. Stuff like this can be VERY difficult to foresee, even WITH computer simulations.
This is really exceptionally well done! Bravo. The ARRL and anyone interested in antennas or traveling wave theory should watch and share this episode.
Now try your string wave in a vacuum to exclude the dampening of the wave due to wind resistance at the high velocity points...If you plot your amplitude vs. frequency and drive power experiment it should get more linear.
Or repeat your experiments with "less stretchy" materials like steel cable or as we did in school a glass rod. Maybe you can even destroy a glass rod like in the resonance experiments we did with a speaker and wine glass.
To add a bit more rigor to the calculation of the limit on how much it can resonate:
Let's say an individual wave has an initial amplitude of A, and each time a wave makes a round trip to end up back at the motor, it loses energy and has its amplitude reduced by a factor of B.
With that, when the motor emits a wave, that will have an amplitude of A, while the previous wave that arrives at the same spot has an effective amplitude of AB, and the one before that is AB², continuing with AB³, AB^4, AB^5, etc.
When you continue this infinitely, you get the sum over A×B^k, with k going from 0 to infinity. This sum is known as a geometric sum, and evaluates to A × 1/(1-B).
This means that the overall amplitude will just be proportional to the strength of a single wave that is emitted by the motor, since B, i.e. the amount of a wave preserved by the bridge carrying it, is constant.
By that logic, it makes perfect sense that a weak motor would have noticeable limitations, but it stays plausible that a stronger motor would have much stronger effects.
To infinity you say? Sounds like calculus magic to me. :D Especially when I dont remember the identity and transformation equations.
@@arthurmoore9488 The proof is actually pretty simple. First consider a finite sum, for example:
x = 1 + B + B²
then, multiply the equation by (1 - B) on both sides. As a result, you get:
x (1 - B) = (1 + B + B²)(1 - B)
= (1 + B + B²) * 1 - (1 + B + B²) * B
= 1 + B + B² - B + B² - B³
= 1 - B³
Then, you can divide by (1 - B) on both sides, and get:
x = (1 - B³)/(1 - B)
You can do an analogous calculation for any arbitrary sum size. As a result, you get:
1 + B + B² + ... + B^n
= (1 - B^(n+1)) / (1 - B)
In this, the only part where n appears (which is what you want to be infinite) is in B^(n+1), but because the wave always loses a bit of energy instead of gaining or staying the same, you have 0
a single pendulum driven with a motor is a classic physics lab demonstration for a reason, it's so well behaved and lets you play with resonance and nonlinearity without needing special equipment and without having to go into waves immediately
Always love the questions you ask and consequent explanations. As a fun adjacent experiment to explain the boundary conditions, you could try and build an oscillator into a string loop launcher ^^
There cannot be an educational lesson about resonance without that bridge.
A nod to the footfalls of marching legions of Roman soldiers would have been kinda cool, too... Jus' sayin'...
A description about Q factor would be good, how quickly the amplitude drops off as the freq +/-'s from the resonant freq. And when you described the energy been used up in heat, sound, etc and the rate the amplitude drops away, this is called 'damping'. The Thiele/Small Parameters for loud speakers are calculated by all the fundamental physics of resonance.
He mentioned avoiding getting deep into the math for the sake of the video. Counter-intuitively, if you introduce too much complexity, people learn less, not more. I think his broad explanation and demonstration that the amplitude depends on a very narrow range of frequencies is enough for most people to get the general idea without having to know the technical terms we use in industry.
Good demo. These effects happen in speaker cones too. I wonder if some of your fine-tuning problem is due to the delay of the actuator. The motor arm itself also has resonance. These things might be skewing results a bit at the really fine detail level.
At one point I had a really long motor arm - it let me put a really big initial wave in, but the reflections got wacky. I’d get a reflection off the interface between the plastic arm and the string, then another reflection from back near the stand. The final design was a compromise
I appreciate how this video's incredibly intuitive structure seems to address my questions almost immediately after they arise.
I love the pace and depth of your videos! I feel like no other science youtuber gets it right. Any time a question builds up in my head while watching (string stretching) you address exactly that later, it's fantastic!
I was about to comment on how this is the first resonance video I watch in a long while that DOESN'T mentions the Takoma bridge, but he came in clutch at the last minute. It's a fascinating case and I love to hear about it every time.
24:07 that extended tongue showcase was absolutely necessary for understanding.
Good video mate, very fascinating!
Great demonstration of resonance. The main setup of the experiment is satisfyingly low tech but very effective with the high-speed camera and signal generator input.
It's crazy how quickly and clearly the fundamentals of calculus show up in this. I could very easily see the adding up of forces in a string canceling each other out in a textbook.
It's also crazy that the word fundament once referred to ones butthole. Sorry my wife says I am an encyclopedia of useless knowledge.
Wonderful job. Excellent illustrations.
The number of ‘oh but of course’ moments in this video is 🎉 it’s fun when it all comes together so beautifully!
I do not really often comment, but I just wanted to say that I really appreciate your content! Have been for 3+ years now!
Oh this brings back memories of physics labs of days past, with one of those oscillation machines (probably made by Pasco or another "educational lab warehouses" that supplies stuff to schools at prices that seem way to expensive), and me and a couple guys stretched a string across the entire lab, and managed to get 13 or 14 nodes to a standing wave, and they were so tiny but we felt like we accomplished something. In reality, as a teacher of physics myself, I now realize internally the teacher was probably thinking "can you guys finish, I want to go home already".
P.S. I love the "as an exercise for the viewer" bit, had me cracking up.
Yup, this was very cool. I had never really thought through why resonance doesn't build forever... this was a beautiful explanation... and, the idea of superposition of repeated waves instead of just amplitude building is the key to understanding this. Great job. I thought for sure that you'd show how you can add different frequencies (and phase offsets) to create a monster peak anywhere along the string (in the world of ocean navigation it's called the "rogue wave"). It requires using Fourier series with D/As instead of just simple frequency generators... but a great way to show how these waves add together in some pretty magical ways.
Your mix of explanation and demonstration is the best!
Great video, was just having a buddy create standing wave animations for our chemistry section of our physics site. That slow mow standing wave on the reflection was so pleasing to see!
Even when the answer to the thesis question seems intuitive to me, the journey from A to B always includes a wealth of detail I never considered. I love this channel more with every new video.
And so help me if you ever say the words "this video is brought to you by raid shadow legends" I will explode into pink mist.
As an electrical engineer, I'm accustomed to thinking of resonant electrical circuits. I was happy to learn about these details that explain the deviation of physical string vibrations from the simple models, which I had never heard before. The other comments explaining how this affects musical instruments (especially guitars) are also delightfully informative. I was not expecting to have a phenomenon confirmed that I puzzled me since I was a child.
This is could be a fantastic way to demonstrate the intuition behind multiple calculus principles
You said it has nothing to do with quantum mechanics, but it absolutely does. A superposition is exactly when the wavefunctions sum like that.
QM doesn’t own the word
Onl yone minute passed, and you already explained resonance better than any other teacher in my life.
Thank you for helping to further our knowledge with such a nice physical example too. Neat stuff
It's amazing how good these videos are! Thank you, thank you, thank you!
love your content. deep diving on often intimidating concepts in intuitive ways through curiosity. i'm convinced this is the best way to develop deep intuition instead of mindlessly applying complex math and theory to situations. you need the deep intuition to use math in appropriate ways. although sometimes mindless use of math to abstract and transform information leads to insight, which can then be used to lead the math in a new direction.
Just realizing this now, but I would _LOVE_ a collab between you and Grady from Practical Engineering! You guys are both great explainers with a knack for demonstration through experimental results. It would be a real power duo!
I really appreciate your focus on how the model we use of resonance and superposition is merely that: a model. It's based on assumptions that are close enough in many situations but don't hold in every case. Any time you push something to the extremes (very small, very large, very slow, very fast) you reach the edges of where the assumptions hold and the model becomes less and less accurate.
This is a common misconception about science. People think science is "wrong" and can never make up its mind, but that's not true at all. Scientists realize that their models are only close approximations of the real world - we are aware of its limits. As we experience more of the world, we discover new things that don't fit our existing models and so we augment those models, adding more details to account for that previously unobserved behaviour. The old models don't cease to be useful approximations - the new models are just closer approximations.
A quote by a famous statistician says, "All models are wrong. Some models are useful." By knowing the limitations of our models, we can make use of them within their limits to tell us a lot about the world that we wouldn't otherwise know. But we have to know those limits so that we don't exceed them, giving us wrong predictions. Over time we can make better models that allow us to predict even more, but we can still use those old models within their limits; the new models simply expand the limits of what we understand. We never know everything exactly, but we can continue to improve our knowledge over time.
Anybody who claims they know something about the world with absolute certainty doesn't realize their own limits. You know that the sky is blue and the grass is green, but those are only approximations - every bit of sky is a different color of blue and every blade of grass is a different color of green. The more you know about the sky and the grass, the more accurately you can say just how blue and green they are, but there are always limits to just how accurately you can say what that color is - the more we learn, the more accurate we become.
Great video! It's amazing to me how resonance appears in so many forms (mediums), from sound to electricity to light and mechanics or the body of stars.
Before watching this I thought I had a pretty good grasp on resonance but this video really makes the "why" much clearer, indeed almost obvious at points.
I wasn't previously aware that the resonant frequency changes when waves are present but the diagram makes it pretty obvious and I thought "the string is longer" before you said it 😊. But I didnt spot that the effect of this was opposite and the whole tension making the wave travel faster thing.
Honestly, the minute I saw the simulated demo of a wave on a bent rope it started to make sense. You aren't adding more energy into a single wave, but rather layering waves on top of each other. And as you demonstrated, a wave will eventually decay. So you get to this point where even though you are adding more waves onto the layer, the first ones are dropping out in a sort of FIFO stack.
These videos are better than every EE class I've taken lol. A cool way to build up to Tesla coils (or just more nonlinear electrical fun) would be to look more at the coil used here and explain why a flyback diode or some snubber is needed to prevent kickback from the inductance (which could lead to a deeper look at inductance and capacitance as a continuation of transmission line concepts, or even RF, or just pure Tesla madness haha).
You could greatly improve your string driving mechanism by using a 10” or 12” woofer with a vertical rod attached to the cone and a 100-200 watt audio amp. That would also allow you to use more than one signal generator (summing to mono) to create multiple simultaneous waves on the string. Your visualizations of the physics are among the best I’ve EVER SEEN on TH-cam. Great Work! 👍🏼🤓👍🏼
Noise cancellation, surprised nobody has mentioned yet this is why it's so important your speakers are correctly wired. Between two with mono (same) sound on each, there is silence in the middle, it's amazing to experience. This is key to how active noise cancelling works, how audio sound extraction works, etc.
wahoo, another video from my favorite creator! This is also an example of why the coil frequency calculators and an approximation. You always have to add or remove loops of wire on the coil to come close to the predicted oscillation. There are so many factors like insulation thickness, wire thickness, air gaps between windings. Even if you created a perfect math calculation to predict it, you would still only get close because some adjacent turns may be stretched or closer together than others on the same coil. I always wanted a better calculation but I think there are just too many tiny unmeasurable things in real life that would determine the actual frequency. Great video as always by the way. You are one of the few creators that has a broad and deep stroke of education broken down into simple concepts. Thank you for all the videos you create! I wonder what the minimum power to break a wine glass from a speaker is. I have seen it done many times, but there has to be some minimum power to make it happen. Great demo and animations as always. I really appreciate your videos.
wow... i cant believe i found this interesting. I mean it isnt exciting by nature lol, but i couldnt help but keep watching. Somehow watching a string vibrate and all the stuff i cant understand that went into it was somehow mesmerizing. the subtle nuances of each factor going into it was somehow interesting.... Cool man, right on. Thanks
Great video! Excellent visualization of resonance and wave travel. Thanks!
What really fascinates me about these experiments is that they must absolutely apply 100% but in 3D waves to all quantum mechanics. Great demo!
Yeah resonance has to be my favorite intersection of concepts in physics and engineering. I had learned of Tesla's little box that could shake buildings before the MB episode, and have always wanted to try to build one... I've built a few tesla coils and the concept of a resonant tank circuit is super cool. Your observation regarding the frequency increasing along with total energy is something that occurs in Tesla coils. In coils however, the frequency DROPS as you add energy. This has to do with the capacitance formed by the topload and how the length of conductive arc will increase this capacitance.
Your graph of amplitude vs. frequency was very pointy, indicating a high "Q" factor. High Q systems can reach very high amplitudes, however the frequency range is very narrow, and thus very susceptible to detuning. Tesla coils are designed to track the resonant frequency and drive at that frequency, even as it changes. One way to do this is to use a PLL, or Phase-Locked Loop, which is one of my favorite concepts in electronics. You could sense the vibrations in the string, and use the output from a PLL to drive your solenoid, and it would track. I suspect Tesla had something like a mechanical PLL in his shaker box that would sense induced vibrations and adjust the driving frequency to match. I bet mythbusters could have made the bridge shake more if they had a frequency feedback loop instead of a fixed (manually adjusted) frequency going in.
As a funny afterthought, both my brother and I will often seek out the resonant frequency of any room-type enclosure that has highly sound-reflective walls--like pedestrian tunnels, and tile bathrooms. If you hum starting at the low end and as you slowly increase the tone, you will hear notes that get louder. Hum that note, and you will hear a beat frequency as you drift off the peak. You can often get a room to "ring" quite loudly. As such, we've both been caught humming cryptically to ourselves while at the urinal in a sundry of public restrooms :)
Anyone else wish he would have tuned the length so it would resonate at a whole number frequency (4hz) so the trickiness of the 2 super imposed waves was easier to "see" in the non-integer multiple of the required frequency? Great video - love your stuff!
Amazing video. You always help me relate to what I'm learning in theory. Thanks!
Love it. This is my research but in supersonic and hypersonic wind tunnels and plates not strings. Looking forward to the plates!
How did this pop up literally the day I watched the mythbusters bridge episode, I just found out that so many mythbusters episodes are on youtube from them so I've been watching through them recently as comfort watching as I do other things. It's bittersweet to see Grant always being the person that made people love and respect him and then realizing he isn't around in the world anymore, that's why it's called loss, and accepting that is just the way of the world.
MythBusters is now available on TH-cam, so finally when someone's referencing it I can just go and watch the thing.
I love that waves deflect upside down because, assuming my thought process is correct, it models one of Newton's laws perfectly. The wave hits the wall, pulling it in one direction, we'll say contacting it a little, and the wall expands back to its original size, but not perfectly, expanding just a little too much and exerting that extra force used to expand it as a wave with lower amplitude in the opposite direction to conserve momentum. Of course this deformation of the wall in incredibly tiny with rigid structures, but the heat lost in this compression/expansion is part of the reason the wave bounces back with a noticable amount less amplitude.
Super cool example and explanation, that was awesome!
I loved this part of my calculus classes. It was amazing to model the harmonics and see how they would sync and amplify. More fascinating to me was offsetting them slightly and watching the patterns that emerged with the period slightly off the harmonics frequency. A tuning parameter which allowed slowly passing the wave through harmonics and anharmonics was cool to suddenly see the wave snap into harmony and then almost resist leaving that harmony back into disordered frequencies.
Nice! One point about the exponential decay you show: The first initial decay seem to have a much faster decay that the rest of the curve, I think that is an indication of a non-linear decay that you get when your string is already oscillating at amplitudes where the nonlinear terms in the wave-equation are no longer negligible.
Also, nice to see a video of the Tacoma bridge, and the man walking off it was very very calm, much calmer than I'd be...
I'd love to see the resonance of brass instruments modeled and explained on this channel if you can ever get to it!
The point about harmonics not being exactly integer multiples in the real world made me think about the way brass instruments work. On a brass instrument, you can get multiple notes on the same length of tubing by going through the harmonics (called "partials" in this context). However, they end up not all being in tune, meaning you sometimes need to pitch a particular partial up or down. This is usually done by adjusting the input frequency to get the partial back in tune, and experienced musicians have these tunings memorized so they can hit the right pitch immediately. It's also not as simple of a relationship as on the string model, because the tubes on brass instrument loop around and change diameter. Depending on where the nodes end up in the tube, you could get different interactions with the bends in the pipe (or even with any dents that might be there).
Another interesting interaction on brass instruments is that the partials actually influence the player's input frequency, nudging it towards that partial's resonant frequency like a ball rolling into a valley. It's a neat effect that I don't think can be represented with your string model, but I'd love to understand it better.
I had an instructional guitar book called "How to Become Dangerous on Rock Guitar" when i was a kid. It was an awesome book and i did indeed become quite dangerous, not only on rock guitar but a number of different genres. Anyway, one of the things that made it such an awesome book was the amount of depth and detail it went into. It started with a thorough explanation of how a guitar string vibrates and how these vibrations result in the fundamental tone and subsequent harmonics (overtones) that make up each note. It was quite mind blowing to learn how a single string could vibrate simultaneously in halfs, thirds, fourths, etc. and that each of these different vibrations produced its own harmonic that was higher in pitch and lower in volume all making up what is heard as one note. In fact you can see this happening if you look at a plucked guitar string in a certain light along with the nodes at certain intervals. You can actually isolate different harmonics by touching the string lightly over a node.
The one side fixed string is the best live demo of what superposition and linearity is. It visualises the math concepts very well. You can calculate lots of stuff and test it in real world.
Incredible video, your passion really comes across ❤❤
The sensitivity of resonance is what makes interferometry such a powerful technique for measure minute changes.
You just made tesla coils cool. I never understood the appeal, "woo big sparks?". The fact that it is a resonating circuit that more or less sheds free electrons. Is awesome in the literal sense.
You are asking exactly the right questions ☺
I have another wave-related question: When it comes to electromagnetic waves, there are antenna arrays that can do a thing called "beam forming" by cancelling out parts of the beam.
But: When 2 electromagnetic waves superimpose on a destructive way, where does the energy go? Or do the waves still co-exist and just cancel each other out along their travel path?
OMG you make me so excited about this stuff.
I LOVE videos that says exactly what I was about to comment before I hit the comment button.
I noticed in the video at 22:00 the process was backwards from what I'm used to. (don't know if I'm being helpful or not but here it goes)
You can mathematically add a second wave to a physical string starting from the highest frequency to the lowest. The higher the frequency has the smaller variation amplitude, so the smaller variation in "length" of the string. As you can see in a Fourier series, the base resonant frequency is the lowest frequency with the higher amplitude. knowing that, obviously the higher frequency has the least amount of amplitude, so less variation on the physical size of the string, up the limit of saying that a static string is equivalent to a string oscillating at an infinite frequency.
With that you can estimate the height of the highest frequency as "thickness" of the string and by comparison with the static string deduce how much it "shortened", with these values as the "new" string you can calculate the new lower resonant frequency you want to add. The process of doing this backwards (from the lower frequency to the highest) mathematically is a nightmare, or I was not presented to a simpler method 🤣
Yeah it’s a mess lol! In order to get the visible 9-node signal on the 1-node wave I massively increased the higher frequency amplitude. The picture on the function generator looks nothing like the real string after high frequencies are attenuated!
@@AlphaPhoenixChannel on the good side, you technically can make a square wave on a string now!
The thing I love about discussing has tension is you can imagine yourself as a person in a string of people linked hand to hand. And as you imagine that you can actually feel the tension in your arms as the mote wave passes by.
I work with high end servo systems and this resonance is a common issue you run into once you start tuning linear systems tightly. The whole system starts creating resonances based on the minor mechanical flection in gantries, changes in bearing preload passing the CG, offset loads, etc. Once that resonance starts you either need to tune around that frequency on the PID loop, notch filter the frequency of resonance to dampen it.
23:52 NGL, that's a great sample right there. I would love to use that in a track. Something so satisfying about the bass and crispy audio 😌👌
Love this, also explains radio resonant antennas.
I'm surprised you aren't talking about stringed musical instruments because that is where this is all studied most for hundreds of years, albeit often in more intuitive non-scientific ways (aka by ear)
Ears are very accurate.
When I was studying piano string tuning, we learned that all the resonant harmonics go higher up in pitch vs the fundamental. This is because string is not perfectly ideal and has a stiffness to it. That that looks like is the section at the node(s) that is flat and doesn't bend due to the material stiffness of the string. I had never heard about the idea that the string became longer when it has waves in it, though graphically that looks true. But the important point is that the harmonics all go to higher pitch because the more nodes you have in the string the shorter the string is, hence more tension/higher pitch.
Interesting meandering video. Thank you.
You just snuck up and ambushed us with the knowledge of exactly how tesla coils work.
your videos set the bar for educational youtube. hell yeah
I absolutely love this channel
The animation and explanation from 15:44 are very well done. Your videos are so incredibly good, you manage to formulate and answer the questions we used to ponder over while these things are explained to us. You make physics intuitive again. So, when can we expect you to do this for quantum mechanics and relativity? 😉
Harmonics are actually always integers above the base freq. But there is such thing as overtones which is any freq. above the base one.
Also if you're trying to modulate one frequency with another (doesn't matter FM or AM) it gives you two side frequencies: Base+Mod and Base-Mod. It's often used in radio communication.
Personally, I'd be really interested in learning how resonance plays into tesla coils, especially if it's "causing electrons to literally fall out of the wire". It might also be informative for people who want to build their own tesla coils, so they can understand how they're supposed to tune the frequency.
I built a spark-gap tesla coil using a neon sign transformer, a couple of carriage bolts for the spark gap (i used the heads of the bolts because i didn't want the spark to jump out of that gap, or at least that's the reasoning i used), a PVC pipe that i hand wound some regular wire that i had pulled out of a motor (yes, i hand unwound a motor... that wasn't fun), and some very floppy high gauge wire as the primary (later upgraded to a length of copper pipe that came pre-coiled), and was able to get some tiny sparks off the end of it. i never got a top load for it, but i did build a VERY crude capacitor bank for it out of some glass jars (saurkraut specifically), salt water, and vegetable oil. tbh, the whole thing terrified me, but i know the output of the tesla coil was safe thanks to my youngest brother. I had a screwdriver with a wooden handle that had cracked for some reason, and while i had it set up, he would use the screwdriver to 'grab' the arc from the output, which would zap his hand through the handle... he kept at it for well over a minute though, lol.
the spark gap put out an INCREDIBLY bright and loud spark though (pretty sure i maxed out the gap at around 1.5 inches, and it seemed to be about 1/4th of an inch thick... that spark scares me.), and the ozone it made was incredible. easily enough to be smelled anywhere in the ~1,200sqft room i ran it in after approximately 20 seconds.
constructive interference is the best word for this 6:43 lol
bless up. resonance is like a tuning fork at the same frequency that hasnt been hit starting to vibrate when it encounters a vibration from a similar/like tuning fork.
very cool to get an actual analog / physical representation of digital signal
Vibrations are still the most interesting and dangerous things in structural design. As a Mechanical Engineer we were taught that if your structure gets vibrated at one of its resonant frequencies, it's game over. If, in a real world structure all the factors you mention lined up, possibly a bolt will fail, as it is designed to in such situations, if you keep on doing this more bolts will fail until they cannot support the loads acting on the structure and its weight. On structures that are not as meticulously designed as a bridge, or building, the risks are far greater. The reason is simply, imposed displacement. If you put a very tiny force on a piece of paper it will deflect by say 5mm. It's very hard to actually find the force that will make the deflection exactly 5mm so you just take your hand, or device and move it to be 5mm. In a similar sense, you can model the stress within an object subject to an imposed displacement, and if that displacement is big enough, it can exceed the material's yield strength. That object will break and the whole structure may not be as redundant as a bridge, causing it to fail entirely. That object can be a beam or a bracket of a frame, supporting something not so critical as cars or people, but maybe an electric motor, so we still design those frames with their resonant frequencies being well away from the rotational velocities of that motor.
The final observation about how the equations physicists like to use are all wrong was actually kinda crushing for me to learn (but it was a sow realization so I got to distribute the disappointment over time lol) after leaving school. When I learned this, and I still do wish, that my teachers had made it more clear that the things we learned were simplifications and idealized models that don't represent the real world. I'm not mad that I wasn't made to do *actual* optical calculations for physically accurate lenses in physics, but I *am* mad that I spent a significant amount of time thinking that paparabolic lenses were actually perfectly physically ideal in the real world. I felt lied to, or at the very least I felt like an assumption was made that I would not have been able to understand the reason that things were being simplified.
Videos like this are awesome, and should be required viewing when learning a subject. It would have been intensely helpful in school to have something that explains "This is why everything you are about to learn is technically wrong, and *this* is why you should be happy not to have to do it the hard way, because shit is complicated" lol.
I consider myself lucky that I did not end up going into any of the hard sciences, because If I had learned this stuff after making a more serious commitment I'm not sure what I would have done. It's like the education equivalent of scope creep. In other industries if you sign up for a job with a certain scope and then the scope gets increased out from under you we usually consider that to be bad and hopefully not allowed by the contract if you have one. It's weird to me that school effectively just does that repeatedly and seemingly no one cares.
2:08 "the real-world is not a frictionless vacuum" no shit!
4:35 it's beautiful seeing a real life, physical, tangible, solid, string move in this way. Not water or something.
8:13 "why does the string continue after the wave looks flat" yea it's a good question.
9:20 this is a beautiful animation.
17:50 "a climb and then a snap, a climb and then a snap" 😂😂😂 I love that idea. It's so whimsical.
20:34 that is a good question wtf does this have to do with model assumptions breaking. I just thought this was some cool shit.
My favorite part of this video was when tensional imbalance was explained to drive the wave's movement.
Almost first! But was privileged to have a Patreon preview. Awesome as always Alpha Phoenix!
A new ham radio operator was telling me that my end-fed half wave antenna would only resonate at one frequency. I assured him it would resonate at the 2nd, 3rd, 4th... harmonics as well.
I'll have to show him your video!
23:20 Fun fact: When you use a slinky, Mersennes's laws (the proportionality laws that describe the increased frequencies with greater tension, shorter length and smaller linear density) perfectly cancel out such that the frequency stays the same, even if the swinging slinky is longer!
(A slinky under tension is an approximately linear spring with negligible resting length and a diameter much smaller than the length under tension)
Before watching the PS section, I wasn’t planning to destroy a bridge using resonance. Now, I’m going to do it because a guy on TH-cam assured me the bridge would be fine.
Wish me luck!
This is so similar to the flow of water. The entire video was very intuitive.
Thanks so much! Super nice video! Extremely interesting🤩 More videos on wave theory would be so perfect!
for the section at 20:30, i wrote my first physics lab paper on this phenomenon, i had a very similar setup to you, only with guitar strings and i just plucked it with my finger.
one improvement you could make is maybe have a ferromagnetic cable, and pul on the cable directly with the electromagnet so that you can make the other end of the cable hold tight also, this way it loses energy way slower
That was some really nice footage of the waves on a string. I know this wasn't the point of the video but I would be very interested to see a similar setup with a steel string under tension and preferably fixed on both ends. The source to make the string resonate could be electromagnetic (like an e-bow?) and can be placed anywhere along the string. I imagine different positions/ intervals would encourage certain overtones to form more pronounced. The harmonic series is a fascinating phenomenon that naturally occurs with resonating body's. I would even dare to say that the significance of the harmonic series is immensely overlooked and probably not even fully understood yet.