Take a look at this video: https://www.youtube.com/watch?v=TKF6nFzpHBU
You would expect guitar strings to produce standing waves, and in fact, the upper, thickest string does often produce long, standing waves. Nevertheless it can be seen many times in the video that the waves are actually traveling in one direction. Is this an illusion related to the framerate of the camera, or is this effect real and caused by something?
Is this an illusion related to the framerate of the camera
Yes, as is explained in words and video here:
This story begins not with how guitar strings actually vibrate, but a curious phenomenon when combining the regular oscillation of the string with the rolling shutter of a CMOS digital camera — namely, the iPhone’s. To accurately capture motion, you need to record an image all at once (or at least come close). Rolling shutter or line scan as exhibited in a CMOS camera sensor like the iPhone is a side effect of the capture being scanned from top to bottom, so the bottom portion of the image is saved later than the top. That causes motion to skew across the image. (Long before digital, people played around with the same effect in analog video and even using film photography – all you need is something moving and a way of capturing the image that moves gradually in a different direction.)
When the regular oscillation of the scanning combines with the oscillation of what you’re filming – as with a vibrating guitar string, or the rotating propeller on an airplane — the two frequencies effectively phase, causing some curious distortion. In the case of the guitar, this means seeing the appearance of standing waves that, while they can occur in nature, don’t occur on any conventional guitar. (You can also think of the basic effect as aliasing, as seen optically when video shutters capture the frequency of rotation of a rotating car wheel in such a way that it appears to move backwards.)
See the last animation in http://www.acs.psu.edu/drussell/Demos/SWR/SWR.html
A standing wave can appear to move if the ends exhibit any damping properties. In this case the fingers touching the strings, or the wood in the guitar (via the frets) provide the damping. This is confirmed if you notice that there are no perfect nodes in the string (points with no motion). Just areas if high and low amplitude, the ratio of which is called Standing Wave Ratio (SWR).
If the strings were driven by a sine oscillator at the proper frequency, the standing wave nature would appear with fixed nodes. The frame rate wouldn't affect where the nodes are. You would need the antinodes flexing up and down, but the lateral positions wouldn't change.
However, in this video several things appear to be happening. First, the pluck generates several harmonics on the string. Few of the nodes of these coincide, and as the numerous standing waves damp out for one particular note, they disappear at different rates. Also, in real strings, the overtones are not perfect harmonics causing any alignment of nodes that might ideally be present to be a tiny bit off. The nodal mismatch and the different damping rates of the overtones change the wave form on the string dramatically as a function of time, and the "strongest" nodal positions change as a function of time. This, combined with the frame rate, gives the effect that you see.
A second-order, very small effect that might be visible (I'm not sure, but it would be a tiny effect) is that when a string is plucked, the tension is higher than normal. As the amplitude decreases, the tension decreases (remember, these are real string and have real stiffness), so the pitches change a miniscule amount. To see this, use a good tuner and pluck guitar strings hard vs. soft.
Another effect that's visible is when the player changes notes. This causes a dramatic waveform shift (especially for sliding or bending notes) which, again, is caught by the frame rate.
