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Check out Acoustics Today at https://acousticstoday.org, the ASA’s magazine featuring accessible articles about the latest discoveries and ideas in acoustics.
This video takes a close look at the true motion of string instruments, such as the guitar, which has really bizarre movement compared to how you might imagine!
Many thanks to Destin from Smarter Every Day for lending me his high speed camera! https://youtube.com/@smartereveryday
References:
- Making Music with Math: https://aatishb.com/stringmath/
- Solving the Sound of a Guitar String: http://large.stanford.edu/courses/2007/ph210/pelc2/
- Rolling Shutter Explained: https://youtu.be/dNVtMmLlnoE?si=6QiIjKM5HgmgYRKN
Link to Patreon Supporters: http://www.minutephysics.com/supporters/
And Facebook: http://facebook.com/minutephysics
Minute Physics provides an energetic and entertaining view of old and new problems in physics -- all in a minute!
Created by Henry Reich
Produced by Joshua Chawner
Check out Acoustics Today at https://acousticstoday.org, the ASA’s magazine featuring accessible articles about the latest discoveries and ideas in acoustics.
It makes sense that plucking one point on the string doesn't cause the whole string to immediately become a jump rope-ish shape, now that I think about it.
This blew my mind particularly because this was something my undergrad classical mechanics class ran into. We had to code a simulation of a plucked and struck string, and doing all the math right we got these weird triangular waves we see in the video. Everyone was mystified because we "knew" what it was "supposed to" look like. But sometimes in physics you need to be prepared to trust the math over your intuition.
What an absolutely brilliant video
The bass being plucked in the background really adds to this one in a unique way, when normally it goes unnoticed. I noticed what you did at 4:11. Nice use of instrument.
Hi hi! Former physics student here, I actually did my thesis on this exact topic and specifically focused on ways to visualize this unintuitive string motion with the naked eye! I actually had a talk I gave many a moon ago where I got to show some of this behavior to an audience in real time and it was so much fun to do! I went into more depth in that talk, but if anyone is curious to try it out and see this behavior for themselves: you can pretty cheaply build a stroboscope (basically just a light that flashes really fast at a specified frequency) and use it on the guitar in a dark room. If you set the light to flash at the fundamental frequency of the string, you visually cancel out that wave's motion and can isolate the overtone vibrations of the string, BUT if you then raise or lower the frequency ever so slightly so it's just a bit out of phase with the fundamental frequency, it'll act to visually slow down the motion of the string. From there you can pluck it at different points along the string's length and see how differently the string vibrates as a result in real time, like how it emphasizes different overtones to make the sound twang-ier close to the bridge or more pure-toned closer to the middle. Doing harmonics is also VERY cool to see with this setup as well! Edit: I confused stroboscope and oscilloscope because it's been a minute
3:23 It doesn't even matter that I understand how Fourier expansions and 2nd-order wave equations work. I had no idea that the vertex of that triangle wave sweeps out an ellipse during each oscillation. That is just mind-bogglingly beautiful. I think you might've outdone yourself with this video.
Even for minutephysics standards, this one is an absolute gem. I feels like I need to pay for this haha
never before has the subdued bass playing through the whole video stood out so much
I will never look at a stringed instrument the same way again...
3:30 In fact, the shape traced by the corner of an ideal string ends up being another conic section, a parabola!
I feel so vindicated, i remember solving the PDE for a plucked string and thinking "Huh, that's really weird, that's obviously not what real plucked strings look like so I wonder where the model breaks down." Tried adding air resistance to the model and it didn't even help. Now this video comes out and it turns out that's actually just how they vibrate. Incredible, and also weird.
0:56 it's like a stretched slinky being being dropped (the bottom point doesn't move until the rest of the slinky gets to it)
I wish you would have shown harmonics in slow motion, to see what holding your finger at the node does to the vibration.
1:29 curiously, as the strinf swings for longer, it begins to smoothen and resemble the round bow a bit more.
Playing guitar and bass for almost 40years. Learned something new today.
This has to be a glitch they didn't patch because they never thought we would notice
This is something that's always kinda bothered me about wave education. Everyone always jumps straight to sine waves, so we've kinda lost how revolutionary that idea even was. As it turns out, waves are exactly what your intuition says, they form any random shape and just move through a medium. It's actually a mathematical miracle that you can decompose _any_ of those shapes _into_ a sum of sine waves, and it all works out. A lot of brilliant minds went into figuring that out, and it has be revolutionary for modern society.
Thank you guys! As a physicist, I've always felt that something is odd here, because so many harmonics cannot be glued into one of them.
So, the vibrating string creates odd harmonics because it is a literal triangle wave. Bless high speed cameras.