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If you're like me, I bet you picture a vibrating instrument string as something like a swinging jump rope, with one bump, or two, or more… And sure enough when you film a plucked string on your phone, it does look wavy. But. the phone video is wrong, and the picture in my head (and maybe yours) is also wrong. Plucked guitar strings don't look like jump ropes. They look like triangles! The real shape and movement of a strummed or plucked string comes down to the physics of tension, and how the string is strummed. It's not shaken like a jump rope, instead, it's plucked into a triangular shape and released. Which maybe isn't that surprising,
but what happens after it's released is weird. Depending on where you pluck the string, it's a triangle that flattens out, or a triangular wave that slides diagonally back and forth, but the surprising thing is that the string is mostly moving as a series of straight lines and sharp angles, AND those straight lines go back and forth and back and forth. The reason most parts of a string stay straight when plucked is apparent if we zoom in on a single point: at the moment it's released the tension within the string pulls equally on both ends,
cancelling out so there are no forces on that part of the string, and it won't accelerate. But right on the pluck point, the string is bent, so the tension from both ends now combines to pull that point downwards. So the pluck point flattens and splits into two separate corners - one on the left and one on the right. In between, the string is again straight, so there are no forces and therefore no acceleration, but it keeps moving down with the speed it gained from being pulled straight in the first place. The two corners travel downwards and outwards,
reflecting off the string ends, and leaving us with a triangular wave that bounces up and down. THIS is what a guitar string looks like when it is plucked from the middle. If you pluck closer to one end, then the angles are slightly different, but you get a similar (and possibly more surprising) triangular, zigzag-y wave bouncing back and forth. So why does phone camera video of strings look so wavy? And aren't guitar strings supposed to vibrate according to the fundamental sine wave-shaped harmonics of a string? There are actually two different things going on. With the camera, the waves we see are actually an artifact of the camera's rolling shutter: the fact
that the camera doesn't take a single frame in a single moment, but "scans" down across the frame taking time to capture the image, and during that time the string will move back and forth, so the waves in the image are from different points in time. Even a straight bar that moves up and down periodically during the scan will appear wavy. You can tell that the waviness is just an artifact of the camera sensor by turning the camera 90 degrees and the waves go away. As for the sine-wave harmonics that we imagine are the way guitar strings vibrate - it's true
that a guitar string will vibrate like a sine wave if it's passively excited by sympathetic resonance from another instrument nearby (or from speakers). The reason a plucked guitar string isn't wavy is because it's composed of a superposition of harmonics that add up and cancel out to create the weird triangle shape. If you pluck the string closer to the middle, you get more of the fundamental lowest harmonic and so the string is closer in shape and sound to that fundemental, which is why the guitar plucked in
the middle sounds more "pure". If you pluck closer to the ends, the triangle you create needs more higher harmonics in the superposition, so the sound is more complex and also tinnier. But plucking a string is just one way to play a string instrument. You can also strike a string with a hammer, like in a piano. This gives the struck point of the string an initial upwards velocity, and the struck point moves upwards until the tension from the rest of the string slows it to a standstill - at which point the neighboring points will have been pulled upwards,
etc: the impact spreads as a pair of pulses which travel out along the string, reflecting at the ends. If instead you strike more off-center, one reflection happens first, making it look like a single up-and-down pulse that travels back and forth along the string. Or you can bow a string, like on a violin. Instead of releasing from a static triangle, or imbuing a momentary impulse to the string, a bow imparts a continuous steady pull on the string, so the string has to oscillate in a way that moves in tandem with the constant speed of the bow, then suddenly slips back, then sticks to the bow again,
etc. It turns out the shape that the string takes to achieve this repetition of sticking and slipping is like a slightly rounded triangle whose corner sweeps out something like an ellipse (although the geometry of real violin strings makes the ellipse-like shape very narrow). In summary: instrument strings don't actually look like jump ropes. Except… they kind of do: first, in real life the strings are moving so fast that the movement blurs into something that DOES kind of look like a sine-wave, second, the string isn't just vibrating in one plane - it can rotate around in 3D which makes things more spread-out, and third,
a plucked or struck string will transfer energy into the body of the instrument and back into the string so that it eventually "settles out" into a jump-rope-like sine wave-y oscillation. So perhaps we can all be forgiven for thinking that a string vibrates like a jump-rope; because that's what it looks like to our slow human eyes. But don't forget that hidden inside the blur is some profoundly weird physics… and some triangles. The weird and wonderful world of acoustics can be explored much further in "Acoustics Today", the official magazine from the Acoustical Society of America, who are the sponsors of this video.
Acoustics Today is full of fascinating articles on vibration, sound, music, and more, going in-depth while maintaining accessible coverage of acoustics topics, including the very latest scientific discoveries, such a recent article on "How We Hear Age in the Human Voice". If you want to explore more fascinating stories about the physics of sound and acoustics, check out Acoustics Today FOR FREE at acousticstoday.org. Many thanks to the Acoustical Society of America for supporting this MinutePhysics video.
