Physics of a Guitar String | Science Minisode

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  • เผยแพร่เมื่อ 2 ต.ค. 2024
  • The motion and sound of a guitar string can be explained with some basic wave physics. It won't take long, so let's see how much we can cram into one Science Minisode.
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ความคิดเห็น • 225

  • @ScienceofLoud
    @ScienceofLoud  5 ปีที่แล้ว +29

    The motion and sound of a guitar string can be explained with some basic wave physics. It won't take long, so let's see how much we can cram into one Science Minizode.
    Gain access to exclusive content at: www.patreon.com/csguitars
    Target Mids available now:
    csguitars.co.uk/target-mids
    Buy CSGuitars Merchandise:
    csguitars.bigcartel.com/

    • @nathangaspar4989
      @nathangaspar4989 5 ปีที่แล้ว

      CSGuitars you just described the overtone series, good job.

    • @jacktowers7533
      @jacktowers7533 5 ปีที่แล้ว +1

      CSGuitars Colin you need to get a lab coat that has your logo and "all the gain!" Embroidered on it

    • @joshuavovk3788
      @joshuavovk3788 5 ปีที่แล้ว

      Yay Math! Also, why do you say "maths"? It's harder to say than "math", or even "mathematics", due to the "ths" sound.

    • @jacktowers7533
      @jacktowers7533 5 ปีที่แล้ว

      Joshua Vovk if Colin doesn't answer allow me, people in the British isles and the commonwealth (like myself in Australia) are by and large raised saying maths instead of math, simple as that

    • @joshuavovk3788
      @joshuavovk3788 5 ปีที่แล้ว

      @@jacktowers7533 I know, but why is that when it's easier to not use the "ths" sound. I'm trying to get to the root of the "ths". Why would anyone think, "Hey, how do we shorten 'Mathematics' and still make it hard to say, and thus continue to make mathematics the most underappreciated subject in school?" Ye get my point?
      Still: yay math and hail to nerds!

  • @SgtAbramovich
    @SgtAbramovich 5 ปีที่แล้ว +98

    CSGuitars but it's actually a Numberphile video.

    • @asamcqueen3513
      @asamcqueen3513 5 ปีที่แล้ว +1

      Can you imagine Colin as a guest on a video with Brady?

    • @weswheel4834
      @weswheel4834 5 ปีที่แล้ว +1

      Got a picture in my head now of Colin performing a monster guitar solo and the drummer saying, "That's Numberwang!"

  • @adamtaylor2142
    @adamtaylor2142 5 ปีที่แล้ว +56

    As a guitar player and a math/engineering nerd, I request more videos like this. Thanks Colin!

  • @XxS4NN4SxX
    @XxS4NN4SxX 5 ปีที่แล้ว +23

    Oh please I need more of this.

  • @markhammer643
    @markhammer643 5 ปีที่แล้ว +18

    Thanks for this. Too many guitar players never stop to think much about the physics of the string, and how it can impact on their tone. Much comes from considering the physics of the string. For instance, one of the reasons why fanned-fretboards have become mainstream in recent years is because we understand more about how scale length impacts on string compliance, and how string compliance affects harmonic content. Going in the other direction, anyone who has ever used an analog octave-up or octave down unit will know that both behave much better above the 7th fret, or higher. Why? Because the shorter the string length, the stiffer the string, the less compliant, and the more the fundamental dominates over the harmonics, making it easier to identify the note pitch and reliably generate the derived octave up or down.
    The physics also pertains to the string as a body-set-in-motion. We too often think of it like it was a steady-state oscillator, but much like ourselves, it is dying from the moment it is plucked/picked. That includes not only overall decaying amplitude, but also the disappearance of various harmonics as the string comes to rest. The manner in which the various harmonics are damped over time, by the bridge (e.g., floating wooden vs Tele-style) or the very string material itself, plays a role in creating the tone of the guitar, and sometimes even the tone of effects. We overlook the fact that many hard-to-replicate "classic" fuzz tones were produced by studio players wielding big jazz boxes with floating bridges, that coaxed very different sounds out of a fuzz than an SG might, largely by the idiosyncratic manner in which the string decayed, and the signal hitting the fuzz quickly fell below clipping threshold.
    Finally, there is a reason why a great many guitar synths have/had their pickup snuggled against the bridge. Deriving a unique signal from each string with such a pickup requires that there be no bleedthrough or crosstalk from adjacent strings. And the only dependable way to do that is by sticking the pickup where the strings "wiggle" the least.

    • @mboyer68
      @mboyer68 2 ปีที่แล้ว

      Dang I wish we were neighbors. I live outside of Rochester NY, how about you? I'm an engineer and guitar player. We could nerd out.

  • @Noel11897
    @Noel11897 5 ปีที่แล้ว +49

    Basically u twang string and noise comes out?

  • @NicuMihai
    @NicuMihai 5 ปีที่แล้ว +6

    vibrato of any KEIND! luv yur accent

  • @witeshade
    @witeshade 5 ปีที่แล้ว +4

    Nice succinct video, and good explanation. However I think you definitely need a follow-up explaining why string tension and gauge are important for hitting the right notes and not snapping necks.

  • @thecharlieramirez
    @thecharlieramirez 5 ปีที่แล้ว +2

    Mate, you're something of a guitar scientist. Love the content. Cheers!

  • @georgekasiouras
    @georgekasiouras 5 ปีที่แล้ว

    This is probably one of the very few channels on TH-cam that talks about things like this and that's why I love it. In fact, I'm sure that at least one video here can't be found anywhere else on TH-cam right now. Do you have anything on how guitar cabinets work/shape the sound of the amp? Most certainly sounds like an interesting topic.

    • @ScienceofLoud
      @ScienceofLoud  5 ปีที่แล้ว +1

      A video on speaker cabinets is on the list, slowly gathering together some research material to write the script.

  • @ThrashingBasskill
    @ThrashingBasskill 5 ปีที่แล้ว +6

    Damn, Adam Neely, you got long hair! Good for you! :D

  • @iirazor1086
    @iirazor1086 4 ปีที่แล้ว

    Man this is freaking awesome

  • @mk_rexx
    @mk_rexx 5 ปีที่แล้ว

    Many of my subscriptions are about science or music, and I'm happy that a good number of those channels do both before I knew it.

  • @NACHTEULE13X
    @NACHTEULE13X 5 ปีที่แล้ว

    Always getting mindblown from your videos, love your videos.

  • @MEGABL0CKS
    @MEGABL0CKS ปีที่แล้ว

    this is 1st guitar lesson i watched. ill have to write it down but im super curious! AWESOME VIDEO

    • @doris4469
      @doris4469 ปีที่แล้ว

      More like a physics lesson

  • @User-jk8wq
    @User-jk8wq 5 ปีที่แล้ว +7

    As an a level physics student, this was incredibly informative and helpful! This channel gets better with ever video!

    • @iscdrummer5003
      @iscdrummer5003 5 ปีที่แล้ว

      A.D Fairhurst same here! I do A level physics too!

    • @myevilfish
      @myevilfish 3 ปีที่แล้ว

      same here. im trying to figure out my Physics homework!

  • @jakethemisanthrope9442
    @jakethemisanthrope9442 5 ปีที่แล้ว +7

    hell yes that is the way to learn science do more of these videos with more complicated math

  • @ashtonbrown81
    @ashtonbrown81 5 ปีที่แล้ว

    What even is there anything you don't know about Colin! these vids are freakig brilliant!

  • @sirforcer
    @sirforcer 5 ปีที่แล้ว +1

    Thanks for helping me study for my physics exam!

  • @balshankar6140
    @balshankar6140 3 ปีที่แล้ว

    Can't thank you enough.. You helped big time

  • @famitory
    @famitory 5 ปีที่แล้ว +6

    the integer harmonic thing isn't as universal as mathematicians would have you believe. while it applies solidly to air chambers and strings, there are plenty of musical instruments that sound nice, but are not composed of mostly integer harmonics. marimbas, xylophones, and glockenspiels are all governed by the vibrating bar equation, where the stiffness and thickness of the material causes the overtone series to be "stretched" sharp, or "dampened" flat. this effect is known as Inharmonicity. you can actually hear this effect in strings too, if the gauges, tension, and scale length are of a strange combination.

    • @famitory
      @famitory 5 ปีที่แล้ว +1

      generally speaking, the thicker the string under the same tension and at the same length, the greater the inharmonicity (i'm not sure if it's flat inharm or sharp inharm, can't find anything on the internet) which is why bass guitars are longer than guitars. if you want to experiment with inharmonicity, put some real fat strings on a les paul and play up by the 14th fret.

    • @incyder
      @incyder ปีที่แล้ว

      @@famitory Strictly speaking, a thicker string would require more tension to achieve the same harmonic at the same fret if length is constant. Bass instruments are longer because they produce lower octives than guitars. The longer wavelengths require more neck to produce the same frequency of the harmonics..

  • @t3mpestw879
    @t3mpestw879 2 ปีที่แล้ว

    I love you bro, You saved my physics 11 CPT. God bless you

  • @IceGene
    @IceGene 5 ปีที่แล้ว +4

    I love these nerdy videos. i hurt my brain but it's the good kind of hurt hahaha

  • @gurjeetsing4160
    @gurjeetsing4160 ปีที่แล้ว +1

    My thinking also goes in logical way, I am getting more interest in Music while reading and practising the Science of Music in my daily life❤❤❤

  • @silverdragon0000120
    @silverdragon0000120 5 ปีที่แล้ว

    Wow I’m learning so much 😊

  • @jonathanfarmer5458
    @jonathanfarmer5458 5 ปีที่แล้ว

    Colin! Use the metal zone in the efx loop of amps with no tubes like your Marshall mg and your orang micro dark!!

  • @SynMusique
    @SynMusique 5 ปีที่แล้ว

    I can't but says that's a lot of hairs(hertz). 🤣 Great video as always.

  • @peteredie9108
    @peteredie9108 5 ปีที่แล้ว

    Oh I really hope this turns into a series, nice work!
    Just thought i should point out the clip at 0:48 of the string vibrating is a little misleading as thats just a camera artifact and not at all how a string really moves in slow motion, the string will move in a more"jump rope" fashion than a "snake", with the exeption of harmonics as you pointed out which will be shaped like a snake but for example the 12th harmonic would be a snake with two humps.

    • @ScienceofLoud
      @ScienceofLoud  5 ปีที่แล้ว

      Looks cool though, but yes it's an illusion resulting from messing around with the shutter speed.

  • @toastyyy2458
    @toastyyy2458 5 ปีที่แล้ว

    Physics class: i don't get anything
    Colin: i understand everything

  • @rottalmusik6563
    @rottalmusik6563 5 ปีที่แล้ว

    Love this stuff😍

  • @hazrod13
    @hazrod13 5 ปีที่แล้ว +7

    Yes to all science videos ! don't be afraid to make longer videos if the subject needs it.
    This is becomming my favourite youtube channel for all the reasons.

    • @ScienceofLoud
      @ScienceofLoud  5 ปีที่แล้ว +1

      Don't worry, there will still be long science videos.
      There are some topics though that I can rattle out in 3:30 minutes (play time, this still took my days to put together...) and it's a good challenge to keep things condensed.
      I could do this exact same video in a very hand holding, step by step way that would take about 15 minutes, but I think this quick way is a lot more fun.

    • @hazrod13
      @hazrod13 5 ปีที่แล้ว

      @@ScienceofLoud you're right, and short videos are good to help people be more interested in all of this.

  • @angelocatapang6054
    @angelocatapang6054 5 ปีที่แล้ว +2

    what a smart scottish chap,lad.

  • @noi5emaker
    @noi5emaker 5 ปีที่แล้ว +2

    So... in summary... when you hit a string it makes a sound, right?

  • @Mr.Goldbar
    @Mr.Goldbar 5 ปีที่แล้ว +4

    I'll drop out of high school just to learn more useful maths from you

  • @RobertBakerGuitar
    @RobertBakerGuitar 5 ปีที่แล้ว +3

    Love it!

  • @Bugkiller666
    @Bugkiller666 5 ปีที่แล้ว +3

    Pretty cool!! thanks for explain it in simple words Colin!!

  • @Steph-de6ne
    @Steph-de6ne 5 ปีที่แล้ว +2

    Is this the nerd way to say that the Colins Sexy Guitars Tshirts are happening, Colin?
    Ps. Wery informative and well thought thru video as always.

  • @UncleRJ
    @UncleRJ 5 ปีที่แล้ว +1

    Is it possible to make another scientific view on strings? I was invested in this video quite more than the others.

    • @ScienceofLoud
      @ScienceofLoud  5 ปีที่แล้ว +3

      Lots more to come. This was the introduction to get the simple ground work laid down.

  • @jimstiles5278
    @jimstiles5278 ปีที่แล้ว

    Your discussion of the simple math of string frequencies was good. However you left out the discussion of string stiffness. Apparently stiffness is a major contributor to the need for intonation - if my understanding is correct (?) perfectly flexible strings would not require any intonation (still working on undertstanding this). Bottom line - I'm looking for more flexible electric guitar strings to play around with. Any suggestions? I'm thinking about multi-strand cores with thin wrapping as one approach. Or maybe loose, low-carbon iron bits and aramid fibers embedded in nylon. Have you ever heard of such things?

  • @Chiiiivo
    @Chiiiivo 5 ปีที่แล้ว +2

    I just finished a music project for one of my math courses discussing this as one of the topics. If only this vid came out sooner it would have saved me a couple of hours of research! 😁

  • @scotttaylor5928
    @scotttaylor5928 4 ปีที่แล้ว

    Great video, I have to make my own physics lab for school and I’m trying to think of what I can do

  • @mboyer68
    @mboyer68 2 ปีที่แล้ว

    Hairdrdrtz. Hertz. Thank you for the physics lesson Shrek! Shrek only in accent:)

  • @jonathanwapner6262
    @jonathanwapner6262 5 ปีที่แล้ว +1

    In Scotland, Hz is the abbreviation for hairtz.

  • @jesusmtz29
    @jesusmtz29 7 หลายเดือนก่อน +1

    what did he say? just kidding 😂

  • @Gabriele..
    @Gabriele.. 5 ปีที่แล้ว +2

    it's a mini episode but with great value, good work Colin!

  • @OmManiPeme
    @OmManiPeme 4 ปีที่แล้ว +1

    always after me lucky charms

  • @antmax
    @antmax 5 ปีที่แล้ว

    Looks like your trying to dethrone Johnny Ball in the science education stakes lol. If you don't know who I mean check out the 70's early 80's kids science show "Think of a Number" used to love that when I was a kid. Might be just before your time, plenty of episodes on TH-cam and still interesting and fun today.

  • @omegaflameZ
    @omegaflameZ 5 ปีที่แล้ว +1

    Brilliant explanation, only wish you could have dug into the frequency spectrum for a wee bit more depth, admittedly with bringing up the idea of a Fourier transform you might need another Minizode...

  • @radiojet1429
    @radiojet1429 5 ปีที่แล้ว +1

    Thanks, Colin. I'm continually impressed with your explanations and presentations. Concise, accurate, useful. Science is real - for all of you out there who doubt that :-)

  • @Pauly421
    @Pauly421 5 ปีที่แล้ว

    I can't believe I've played for 15 years and never knew this shit lol. Nice video bro, need more of this pls. Sub'd

  • @Leggendar
    @Leggendar 5 ปีที่แล้ว +1

    Nice video Colin! Such informations should be known by every guitar (or every other instrument too) player, along with basic maintenance of instruments.
    Keep going this way!
    Cheers from Italy

  • @DarkSideofSynth
    @DarkSideofSynth 5 ปีที่แล้ว

    Next up - how you can surf and ride the waves generated by your guitar. Grab your pedal boards, I mean surfboards! ;)

  • @oatmeal710
    @oatmeal710 5 ปีที่แล้ว

    i learned more from this video than my high school physics class

  • @bpabustan
    @bpabustan 5 ปีที่แล้ว +1

    If there is something that is mind boggling yet very very clear - this is it!

  • @bohonye
    @bohonye 3 ปีที่แล้ว

    pls make a subtitle, cause you use very much music-sleng words (whammy-bar; etc...) and these words are not in the auto-subtitle. GREAT video! I am a physics teacher and rock-guitarist, too, from Hungary.

  • @CostasCTS
    @CostasCTS 5 ปีที่แล้ว +1

    Words cannot describe how much I loved this video, as a fan of both music and physics! Thanks Colin :)

  • @brotendo
    @brotendo 5 ปีที่แล้ว

    Shout out to all my math and science major pals out there. I miss university when life was easy and I didn’t have so many damn bills to pay. But at least I’ve got money now for... strings. I don’t have to wait every semester to change strings anymore! Haha.

  • @shihabrehan7054
    @shihabrehan7054 ปีที่แล้ว

    i still don't understand why at some point at a certain frequency does the string stop vibrating
    like if we say at 11 Hz the string shows only one N but why at 22 Hz does the string show 2 N? why does it stop vibrating at half L

  • @barbasbandas6665
    @barbasbandas6665 5 ปีที่แล้ว

    Awesome! Now calculate the integral of the function F(x,y)=2log(arctg(1-x)/x^2)/e^sen(2*pi*fc*t) dt
    LOVE U Colin

  • @fractalnomics
    @fractalnomics ปีที่แล้ว

    3:00 Does this (not vibrating at one frequency) demonstrate equipartition (shared vibration over all modes)?

  • @yin9413
    @yin9413 5 ปีที่แล้ว

    That's why Asians always good at playing musical instrument, because of maths

  • @michaelangeloh.5383
    @michaelangeloh.5383 5 ปีที่แล้ว

    I seriously zoned out halfway through... Don't make me feel like I'm back in school. That's very unMetal.

  • @Andresdha
    @Andresdha ปีที่แล้ว +2

    As a physicist I love how clear and straightforward this was presented without skipping the maths. Awesome video

    • @xflofyx
      @xflofyx 11 หลายเดือนก่อน +1

      calin is also a physicist so he knows this topic

    • @Andresdha
      @Andresdha 11 หลายเดือนก่อน

      @@xflofyx oh that makes sense! Cool thanks for sharing the info

  • @koffieverslaafde627
    @koffieverslaafde627 5 ปีที่แล้ว

    Hey colin @CSGuitars I have a question. I was playing guitar today, stopped for a while and turned my amp off etc, started again, and suddenly im not getting any distorion or almost none. It was a metal distorion (with a lot of mids of course, i listen to my favourite guitar youtuber) and now its a clean not even ac/dc distortion and i didnt change anything. Could it be the tubes? Or speaker? Im using an engl thunder 50 combo, a line 6 floor pod plus, and a jackson js22 dinky with iron gear pups. I have no clue what’s wrong and I’m kinda freaking out, what should I do

  • @reddwarf1999
    @reddwarf1999 5 ปีที่แล้ว +1

    I absolutely love learning through your videos Colin

  • @b.scottfarthingsworth
    @b.scottfarthingsworth 5 ปีที่แล้ว

    Colin love all your vids, absolutely. This was an excellent explanation of how math makes the guitar and strings work harmoniously. But what brought me here was the word: Minizode. With all due respect I musta missed the explanation, WTF is a minizode

  • @justinniederhauser1543
    @justinniederhauser1543 3 ปีที่แล้ว

    I got into tuning pianos and one problem I encountered was that I can’t tune the strings perfectly in tune, because when harmonies Are played, new frequencies propagate which sound off-key. Why is guitar different? On piano, I have to actually detune certain intervals or “stretch tune” to allow sound waves room to harmonize when played. I know it sounds confusing, but do guitars have to be intonated this way? Also why do so many guitar players never notice they have a string or two out of tune LOL. I don’t even use tuners anymore, because they make everything sound flat. Why are there not tuners with different intonation preferences?

  • @zackfraser6704
    @zackfraser6704 5 ปีที่แล้ว

    Christ! I wanna learn guitar cause I thought there was no math, but nooooo, you gotta go and add math into it.
    I kid though, great video man!

  • @2n3chordjams70
    @2n3chordjams70 5 ปีที่แล้ว

    My head just exploded but KOOL that you know and understand all that!

  • @luvlog5480
    @luvlog5480 7 หลายเดือนก่อน

    Can we have any vibration mode on a guitar string? And what about the modes that we've learnt in our last experiment? Can we have a resonance related to any wavelength value for a fixed L (height of the tube)?

  • @coopers1716
    @coopers1716 ปีที่แล้ว

    Alright now we're talking like it's actual math thank you goodbye😁😁

  • @AMB666
    @AMB666 5 ปีที่แล้ว +1

    Do you have a degree in physics or something😀?!

    • @ScienceofLoud
      @ScienceofLoud  5 ปีที่แล้ว +3

      Masters in Physics with Visual Simulation.

    • @AMB666
      @AMB666 5 ปีที่แล้ว

      @@ScienceofLoud That's awesome! Me too, I'm finishing mine but in theoretical physics.

  • @mrkosmos9421
    @mrkosmos9421 5 ปีที่แล้ว

    Awesome!
    But... What kind of harmonics appear on a guitar?

  • @bradfuerst
    @bradfuerst 5 ปีที่แล้ว

    Wait. What's a "hairts?" Is that some Scottish lingo we Americans don't know?

  • @kirkbolas4985
    @kirkbolas4985 3 ปีที่แล้ว

    The guitar as solely a noise generator...my dear deceased father would have completely agreed with that notion. lol

  • @xflofyx
    @xflofyx 11 หลายเดือนก่อน

    we NEED a CS science chancel for fucks sake, i need to see caling teaching quantum mechanics

  • @luizalves8071
    @luizalves8071 5 ปีที่แล้ว

    I dig mathematical+musical videos even though I watch the whole thing and don´t understand jack shit

  • @AbsoluteAbsurd
    @AbsoluteAbsurd 4 ปีที่แล้ว

    Goddamnit i dont understand the maths bit

  • @DTPoe
    @DTPoe 5 ปีที่แล้ว

    Now I need a bucket for all the brain matter oozing from my ear. Thanks.

  • @JuveriSetila
    @JuveriSetila 5 ปีที่แล้ว +1

    PATREON NOTIFICATION SQUAD

  • @zeoalexo
    @zeoalexo 5 ปีที่แล้ว

    Hey, I was wondering if you could a video on the history of Superstrats

  • @ZakuBlk
    @ZakuBlk 5 ปีที่แล้ว

    This was a super cool lesson. But is there a way to apply this to improve my playing? Seriously

  • @stevemaass3074
    @stevemaass3074 5 ปีที่แล้ว

    I’m smart. And I kept up with about L/5 of that. But it was still cool.

  • @jonathancohen4427
    @jonathancohen4427 5 ปีที่แล้ว

    That feel when you see a piezo bridge and you're like- damn, im poor.

  • @mrdeeman5912
    @mrdeeman5912 3 ปีที่แล้ว

    How does Guage play apart in frequency?

  • @captainbeard3323
    @captainbeard3323 5 ปีที่แล้ว

    colin help me, what does 4 conductors mean on humbuckers?

  • @hawk6111
    @hawk6111 5 ปีที่แล้ว

    And hence you disprove tone wood and bring about tone bridges and tone nuts

  • @FlorianGuitar85
    @FlorianGuitar85 5 ปีที่แล้ว

    I failed all my math exams during school because I'd rather play guitar, because guitar is magic.
    You just turned the magic into maths.
    You killed the magic.
    Unsubbed.
    Damn you, Scotsman!

    • @ScienceofLoud
      @ScienceofLoud  5 ปีที่แล้ว

      Everything is maths, that's the real magic.

  • @GuitarQuackery
    @GuitarQuackery 2 ปีที่แล้ว

    I really enjoyed this one.

  • @TheNostalgicGoggle
    @TheNostalgicGoggle 5 ปีที่แล้ว

    This is the only video of yours I have watched and left confused.

  • @shatti886
    @shatti886 5 ปีที่แล้ว

    Hey hey hey. I just wanna play chill bro xd

  • @ryanm8879
    @ryanm8879 2 ปีที่แล้ว

    I want to learn math & physics just for music 🥲

  • @diegohernan82
    @diegohernan82 5 ปีที่แล้ว

    Be careful, you're about to step into the esoteric zone of tonewood people.

  • @parthjain5758
    @parthjain5758 5 ปีที่แล้ว +1

    I hate physics i even failed in it

  • @christopherwillcock-irving8538
    @christopherwillcock-irving8538 5 ปีที่แล้ว

    You tricked me into doing maths by disguising it as guitar!

  • @markfuller6464
    @markfuller6464 5 ปีที่แล้ว

    Jeez. My brain just melted!!

  • @muggens1520
    @muggens1520 5 ปีที่แล้ว

    I have no fucking clue what he is talking about

  • @JojoTheDivine1
    @JojoTheDivine1 9 หลายเดือนก่อน

    6 years of guitar and i just chose to search this up

  • @Yinte_Klop_Blunt666
    @Yinte_Klop_Blunt666 5 ปีที่แล้ว

    This arouses mr. Kevin very much

  • @DaveDoingDaveThings
    @DaveDoingDaveThings 5 ปีที่แล้ว

    Obvious when you think about it 😮