Could transverse wave on a string could be used to produce sound?

[Jackson Lee]

At the moment before you pluck and release the string, there are no frequencies in the string at all. All you do is impose a shape on the string. If you analyze the shape using Fourier series, then all your terms have to look like $\sin (n\pi x/L)$ because the sum of the waves must have a node at each end. Those are exactly your standing modes, which oscillate at harmonic frequencies.

If you could excite a traveling wave on the string by some other method besides plucking, then you could create non-harmonic frequencies. These frequencies would be hard to continue forcing for very long, since your reflected wave would be out of phase when it returned to the forcing point, but sure, you could in principle generate a pulse or a wave packet that propagates up and down the string.

I have just remembered a theory: when the non-periodic function was analyzed via Fourier transformation, the frequency will range from zero to infinite. If I just plucked once, this situation will occur. Thus, I suppose there very possible be a principle that could diminish unsuitable frequency.

 

[olivermsun]

The plucked string is not non-periodic.

If you sent an impulse or a square wave down a real string, various losses would quickly attenuate the shortest wavelengths, similarly to the way higher modes are quickly damped in a plucked string.

 

[rcgldr]

Not sure if these were posted before, a couple of videos of transverse waves. Should be more like these.

guitarvideo.htm

https://www.youtube.com/watch?v=tLL0Rb3pOT4

 

[Jackson Lee]

The plucked string is not non-periodic.

If you sent an impulse or a square wave down a real string, various losses would quickly attenuate the shortest wavelengths, similarly to the way higher modes are quickly damped in a plucked string.

Maybe I should post a summary. Because the string is fixed at two ends, all waves of various frequencies will be limited at this area. Then according to Fourier series, all possible frequencies will be harmonics, no matter what the initial waves are like.

 

[sophiecentaur]

update (I thought the op was thinking of the sound produced from the longitudunal component of transverse (traveling) waves.) - The sounds from a stringed instrument do not require standing waves, and "traveling" waves can also generate sound. The sound board on a stringed instrument could also have standing waves at specific frequencies, but generally it will have waves traveling across and around a 2d plane.

For a guitar, standing wave overtone notes can be forced by placing a finger at what will be a node of a standing wave, for 2x, 3x, ... , frequency.

You have no idea just how pleased I am to find people, at last, using the term 'overtone' where it is appropriate. At one time I thought I was the only PF contributor to distinguish between overtones and harmonics.

I recently read something (can't quote it) which pointed out that tuning using the 'harmonic' (aka overtone) method for (guitar) tuning would introduce audible tuning errors. I guess it would depend on whether or not one has golden ears and on the playing style.