The Wave Equation for BEGINNERS | Physics Equations Made Easy
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- เผยแพร่เมื่อ 28 ก.ย. 2024
- Ever wondered what the Classical Wave Equation is all about? Well now you can find out!
Hey everyone, I'm back with another video. This time, I'm breaking down the Classical Wave Equation for you, because I really enjoy making these videos where I explain what a physics equation is trying to tell us.
The Classical Wave Equation describes the behaviour of waves (duh) as they move through space and time. In this video we discuss one particular solution of the wave equation in detail - sinusoidal waves. Remember though, that there are other solutions to the wave equation, such as spherical waves. However, sinusoidal waves make the wave equation the easiest to explain in my opinion.
We will first learn about differentiation, which is a very important sub-section of calculus. We will learn about this because the Wave Equation is known as a differential equation. Well technically, the equation being discussed in this video is a one-dimensional second-order linear partial differential equation. It might seem like I'm just throwing jargon at you, but in this video I will describe exactly what each bit of that description means. And the best part is, you don't need to be studying physics or mathematics at university to understand it! If I've made this video correctly, then you should be able to understand it if you've studied mathematics or physics up to high school level.
We will learn about differentiation in this video because differentiation is heavily featured in the wave equation. We take an equation that describes the wave we happen to be studying, and differentiate it with respect to both time and position. We do this until we can test if our wave obeys the rules set down by the wave equation (of sorts). If it does, then our wave is said to "obey" the wave equation.
The wave equation describes lots of classical waves, such as light waves, sound waves, mechanical waves, etc. However, there are many other kinds of wave equation - the Schrodinger Equation being a good example. The Classical Wave Equation discussed in this video only deals with the subset of waves known about long before the advent of Special Relativity or Quantum Mechanics.
With all of that being said, if you have any questions, please do let me know in the comments section down below. I will try to answer as many as possible.
If you enjoyed this video, please do leave a thumbs up and subscribe for more fun physics content. Hit that bell button if you want to be notified every time I upload. Follow me on Instagram @parthvlogs to see what I get up to on a more day-to-day basis.
Hi friends, thanks so much for watching! If you'd like to see more about the wave equation, including a discussion about the solutions of this equation, check out my video here: th-cam.com/video/x2bD2QhOxd0/w-d-xo.html
And as always, let me know what other topics to cover in future videos!
This video ended very quickly , would have been great if it were a bit longer. All I want to say is that , this was very good.. ❤❤
Nice video paji
Sir could you please teach me what is potential difference high potential low potential our books have only definition I literally understand something form that
Parth, for the sake of education, I hope you take teaching for a career, or the world will be losing an amazingly gifted educator.
Nah, we cannot really do this same kind of explanation to a group of individuals, where the interest level of individuals is a distributed function. I think youtube is a very good platform.
or not cuz he will be something much better for his own sake. Don't tell him what to do, let him lead his own life.
@@therandomvidguy5141 lol chill out, he wouldnt decide what he would do with his life through a youtube comment
The comment was meant to be a compliment
Yes, he is a gifted educator. But I ask that he organize the order of his play-lists.
@@sjlegends I completely disagree. Most of the students I'm in class with are extremely motivated, and instructors who can actually break material down are heavily sought after. One of the problems with universities is some of the most brilliant people can't always teach. It's a problem in many engineering classes, especially the more advanced ones.
8:22 "Let's differentiate YOU with respect"
Thanks for the respect, but I prefer to stay integrated :)
yeah same man
i'd actually like my laplace transform taken
You could make a video about Navier-Stokes equations.
You just remembered me that I just handed in a homework in which I had to prove that the Navier Stokes equation for linear elasticity in 3D follows a classical wave equation.
I'd post a video of it, but I'm too afraid that my head might explode. :)
I did a full derivation on the NSE if you would like to have a look.
Hello Ivan, I have a video about the Navier Stokes Equations and how I can simplify them and Solve them. But this video is in german.
Here is the link for my Video of N S Equations
th-cam.com/video/qCt-z4lJbME/w-d-xo.html
Please let me know if you liked this video :-)
We also use the same in fluid mechanics.
I am an electrical and electronics engineer myself and I have seen many professor's and highly talented engineers but hats off to you since your on my top list for the best instructor/professor ever seen..I really enjoy watching your videos..you are such A gifted talented technician ...and I by technician I mean the you have it in your DNA...so plz never stop what you're doing...
Plz omit " the " after "gifted "
spitefully growing out your hair and beard to annoy youtube commenters is a MOOD
It’s so helpful having someone who actually explains it all without assuming you already understand A level and university level Maths and Physics.
Parth, as a non-physics student I have been trying to sit in on some open course ware physics classes. The prof obviously believes the students already understand what you just explained, because he doesn't explain it in his lectures. The students must get it from their books and homework which I do not have. I can't tell you how great it is to find this video. Now, I get what is going on in class. Thanks. Cal
At first I was intimidated by this complex equation; thanks to your explanations. I can't believe how simple this equation is.
I (and I'm sure a lot of others) would LOVE to watch a series on the Einstein Field Equations (EFE) explained by you. I have been following you for a long time and your explanations are phenomenal. Since you mentioned in a previous video that you are brushing up on General Relativity, an intro series (or whatsoever you believe is right) on EFEs would be LOVELY. Thank you Parth bhaiya! :) @ParthG
EFE would be phenomenal
Great video! Loved the explanation, it was very understandable even for a second year high school student. Keep it up, love your videos!
Thanks for watching, glad you could understand my ramblings :)
Solving the Wave Equation with Fourier Series and Vectorspaces is really a great time! One problem takes like 1hr to do 😃
_Parth, your cranial foliage is _*_glorious!!_*
_And so are your explanations!_
You are truly a great explainer. There are very few people who can make basic things understandable so easily.
First, your videos are awesome! Second, I have an engineering degree and I'm sure there are plenty of other users on here who would like to hear more about the deeper math. So I would like to put in a vote for videos which are "way too advanced" :D
This got recommended to me. Reading the comments is like whole other language lol.
Isn't it absurd to think someone could take a derivative of a function while holding certain other variables constant?IMPOSSIBLE! :-|
@@guitarttimman
You can think of it like this:
Imagine standing on a valley. Now you wonder about taking its derivative; but it's futile, for the valley is three dimensional, and we learnt derivatives only for two dimensions. No problem, brother! Bring it down to two dimensions! Take a knife and cut through a cross section of the valley. What do you see? You see the outline of the mountain and the valley in the section you just cut. That's a two dimensional function. Differentiate the heck out of it now. Did you see what we did here? We fixed one of our coordinates (by slicing a plane at a particular place) and then differentiate the other. There you go. Well, you can watch a lot of videos on TH-cam about this visualisation. Partial differential equations come in handy while doing waves, heat, oscillations and even quantum mechanics. Thanks,
A. Mukherjee
Kolkata, India
@@kakalimukherjee3297 I got you. I was utilizing sarcasm. I know about the del operators, gradients, and directional derivatives. I learned that a very long time ago my friend. Also, it's good to understand that the magnitude of a cross product is the same thing as finding the area of the parallelogram that is formed when opposite sides are completed. That's the idea of deriving the surface area formula in 3-space. The directional derivative dotted with the gradient points in the direction of steepest descend/ascent. I also understand what Gauss and Greene contributed to to the subject Sir. Have you seen my videos? I have a nice demonstration that proves Greene's Theorem that links the line integral to double integrals and later the "CURL" determinant operator. I also ACE'D Differential Equations brother. That was a long time ago. LOL
@@kakalimukherjee3297 LOL I can't believe you fell for it. Sorry.
@@kakalimukherjee3297 What's your opinion on time travel? Personally, I think it's possible. I have an idea for another approach too. Yeah, I know about Dr. Mallett's light bending machine which is not practical. You should see what I came up with in my early 20's. I've kept that to myself. It's dangerous. I did that way back when I was an erudite student of mathematics at Purdue University. It's scary stuff man!
bro I have my physics olympiads coming up and as a 9th grader, I found this video amazing as it was easy to understand
Pretty clear, thank you very much. With this kind of videos for those who interested we'll make the World a better place to live in.
This is the first video I've found that can explain things in a way that makes sense. I would pay you to do videos like this on discretization/finite differences with the linear advection equation, going into the modified wave number, truncation errors, etc. However, that might be a little specific to CFD, but maybe not after seeing this? Seriously though, I've been skimming through videos and content for weeks. This is the only video that made sense.
As a teacher i must say you are a fantastic teacher. Very clear explanation you should consider to write a book filled with your colored drawings by hand and explanations of every detail... I will buy it for sure
from one Parth to another, Thank you!
i think you just saved me with my exam
Great explanation. Actually I really like your screen explanation setup. Can you explain how you do this thing?
A truly excellent video. One suggestion I have is to copy-paste (or re-do) the section on differentiation into its own video. Subsequent videos involving calculus can reference this, removing the need for repetition.
I've been stuck with understanding the concept behind the equations, but it's quite intuitive when you think about it. Great video.
Possible correction: being a bit pedantic here, but the equation being linear not just entails having the variable u appearing linearly but also the derivatives appearing in their linear powers, i.e. *no* allowed {(∂^2)u/(∂x)^2}^n terms, where n>1.
Magnificent explanation in the video though! Loved it :D
laplace and poisson equation
it will absolutely help me, brother. i am struggling to undestand
This was the best explanation of the wave equation that I could find. And you explained differentiation so clearly. Thank you so much for this.
Do you have an explanation for the Schrodinger equation as well?
Best explanation I have seen in a while. I am teaching seismic wave theory, in Portuguese though, but I am going to point your work for others. Thanks.
Thanks to this I have gone down the rabbit hole of PDE study. cool thang!
🌅🌅usefull for those who learns more about physics!!✨✨ thank youuu.
This channel coud be an educational dream🌾
Nice brief explanation of Derivatives but if someone finds it confusing you can watch khan Academy's video of Derivatives. By watching First two videos of derivatives anyone can get derivatives intuitively. Good luck 👍🏻
You could not explain this more easily...no one can...kudos.
Thanks, and it's so easy & simple!
bro... You did great work... Appreciate your efforts..!!
You are a genius at simplifying physics!!! Thanks a lot for all your great video uploads.
I have been searching for these kind of videos for a long time. I think I found the right one. Kep going
This is more informative than anything I ever studied in a math textbook. Math textbooks are written by left-brained people and only left-brained can really absorb the information that way. I need visuals and examples and less technical language and that's where videos like this come in
The best video ever! You are my life savior. Thanks
Can you explain the theory of conservation of both linear and angular momentum 🥰
More than wave equation explanation i like the differentiation explanation.
please make a video on basis set used in computational chemistry !
I love the way you explain ❤
Sylvanius Thompsons book "calculus made easy" is the best source for understanding differentiation. Its available in PDF form, on line courtesy of Gutenburg project. If you don't understand differention, you can't figure things out beyond a certain point. He is on Par with Parth, no pun intended
So nice and educative
Differentiation: nicely explained, at least to someone who learned it years ago but doesn’t use it regularly
Bro can you one video on Copenhagen interpretation and a dirac EQNs series?
Copenhagen interpretation definitely! I'll need to study the Dirac Eqn in much more detail if I want to make a video on it though :) I'll add it to my list
@@ParthGChannel can you please make a video about Quantum Gravity and String theory pleaseeeee! I am 13 years old and learning advanced quantum mechanics and i nn
@@theoreticalphysicistzeinaq2753 bruhh first get done with mechanics
@@theoreticalphysicistzeinaq2753 Dude, first finish classical mechanics and then you can try to do quantum mechanics. String theory and loop quantum gravity are even one more step ahead of that, so you might wanna wait with that.
@@rudrapatel2777 finished from mechanics
Please make a video on wave vector and wave number !
I find your work easily understood
it would be great if you would add some examples of real calculations using the equations
great video - i still don't understand why large wavelength waves (like sound) go round corners so easily but short wavelength waves (like light) don't. PS i know it's because of their wavelength but what would Huygens say?
Great explanation, but dk if you can explain why c^2 is the transformation?
Iam OTAI DAVID from Uganda . Iam pursuing bachelor of education physics and math.thank you very much for your explanation
U can a video about Schrödinger's equation
Please make a video on special functions and how these are useful in quantum mechanics
Beautiful explanation, mate
need more videos on maxwell equation as like 1st one;
thank u for your clear explanation
Hello sir, very nice explanation. Please lemme know which app you use to make videos. I mean the animations were fascinating. Please reply. Namaste 🙏
Excellent.... simply marvelous
I'm currently studying PDE's and I've just noticed something. Why is that sometimes the answer to the wave equation is simply a y(x, t)=sin(kx - wt) type of function and other times the solution is given by a Fourier series, let's say the vibration of a rope. I mean, in which cases the answer is just a sine function, and in which cases it's a Fourier series instead? Am I confusing concepts, physical situations or what?
Awesome. Well done. I especially liked your use of "uppy downiness" and "wobbliness". LMAO
You'd be a great Physics teacher. You have a new subscriber sir.
So beautifully explained. Keep this going, amazing talent and wonderful educator. 👍 🤝
Amazing! Clear, focused and simplified.............Thank you! Just one follow up question, is it ok to have the "d/dt" in the Schrodinger stationary wave equation instead of the curly "d" that is used for partial derivatives? Thank you again.
Could you make a video on how to solve the wave equation ?
Aren't there 3 distinct solutions to wave equation?
One is a photon. A spherical shell of sorts which expands in radius at c and the membrane thickness being the EM wave. When we interrupt the membrane we collapse wave function and all energy goes to that spot. You don't halls burst a balloon nor half burst a balloon.
The second world be another election/positron pair just like previous case but this time the wave is a standing wave over a single Planck. This standing wave form gives mass to proton and neutron. They are only standard particles with neutralized charge pair in core.
The third form is the standing wave which because of the fact that on surface of event horizon G = c and so there is a Planck frequency standing wave on surface of black hole which increases one Planck for each nucleon of infall.
Could you explain the Ramanujam’s equation about the addition of numbers from 1 to infinity . Please do it in simple terms so that all can learn
super thorough explanations! thanks!
but what I start to wonder is why do physicists have to write d like that? why can't they just use "d" all along?
This happens if you don't watch the whole video.
Now I know.
Make a video on NAVIER-STOKES EQUATION
AND REYNOLD'S TRANSPORT THEOREM ...PLEASE
Hey parth kindly post a series of videos on chaos, fractals,etc.
Please could you cover Euler Beam Theory and Longdituinal wave theory on rods for the split Hopkinson bar? That would be really helpful!
Hey Parth can u do an explanation of Legendre , Hermite , Bessel and Laguerre equation
your video make me easy to understand, thanks! i hope u can make a video about antenna, elctromagnetic field and microwave technology, etc.
I was just researching this and didn't come further, thanks!
at 13:45 you have that both d²u÷dt² and d²u÷dx² are negative while the constants inside the argument of sine in u are opposite signs and even du÷dt and du÷dx are opposite signs, how does that happen?
Make a video explaining schrödinger equation please.
Great explanation! 👏👏👏👏👏
Hi Parth G! Since you like simplifying complicated topics, how about trying to explain the bessel function in the field of acoustics and deriving it from the real world.
I think the speed plot should be exponential too as the displacement plot not linear.
Simply Excellent Superb
Thanks for all these,Can you explain what the phase and group velocities are?
Thank you very much for this video.
About 12:11, the drawing is less than perfect because the waves representing elongation and acceleration respectively don't match in wave length which they should.
They are "waves" who's phases at any time are opposite.
@parth why did they narrow it down to just the second order differential?? What's so special about the second order differential?
I like it made it mathicical. Thanks. Like you are a teacher.
Hey. I saw a professor at MIT use this equation E(x,0) = acos[2πx/λ] To describe how an electromagnetic field behaves. Does that have anything to do with the wave equation?
hi Parth,
I know you are probably not going to see this comment because you uploaded this video ages ago, but could you make a video on differentiation or leave some resources about it.
thanks
Brilliant. Well done.
Simply excellent!
That was really helpful. Thank you so much!
I am a PhD student. I want to study wave propagation in elastic solids. I need sample questions with solutions. Do you have Graff’s book manual solution? Can you help me, please?
Sir can you plz explain what is imaginary part of the wave and is imaginary in it????
when is part 4 coming up, i have assignment for monday
Well Schrodinger equation is not a wave equation at all, as Science Asylum said in a recent video. It's equivalent of the heat flow equation, indicating the flow of probability current density of the system.
Please explain Ampere's circuital law sir please 🙏🙏🙏🙏🙏🙏
Love from india 🇮🇳
I lost track midway. Don't blame Partha for that. Perhaps I need to go over this a couple of times.
Navier Stokes equation
And Laplace Equations
this time. 🙏🏼
Could you explain the einstein field equation next please
can you explain about the curvature of spacetime
Hi Parth, i wanna know which software you use to make video like this one. Plz help me
How about making next videos on heat, laplace and poisson equations hence completing the elementary 4 PDEs.
Btw amazing video.
You ARE a really smart thinker.