Square wave and sine wave -- How standing waves are formed?

[hobmarcus]

Why do the sound waves reflect and form standing wave when they travel along a string with sinusoidal waveform?
But they do not reflect back when they are in square waveform ?

 

[sophiecentaur]

What sort of standing wave pattern would expect if you excite the end of a string with a square wave?

Suppose you wanted the standing wave to be a square wave. The string would need to have a length so that all the harmonics (overtones) would form standing waves in their own and in the right phases. That would require the length to be an integral number of half wavelengths at the fundamental, third, fifth, seventh etc harmonics. Is there a solution to that requirement? I can't get my head around it at this time of night (wine / food etc). I'm sure it wouldn't work with a real string for which the end effects would be different for each overtone.- and probably the wave speed, too.

 

[synMehdi]

I don't think that's true. You should think of a square wave as a superposition of sinusoidal waves. A perfect square wave cannot travel along a string because it would cause a discontinuity in the string so we must assume that we have a finite number of harmonics. I think that if the length of the string is a integral of the fundamental, it will be integral of all of the next harmonics, so that a standing wave would be possible.

 

[sophiecentaur]

Of course, a real wave would be an approximation (low pass filtered) to a perfect square wave. But even allowing for an approximation to a square wave, using only a few odd harmonics, would they still satisfy the requirement?
I can't think that I have ever come across a square standing wave so my initial reaction was that there must be some problem with the boundary conditions. But n half waves would also be 3n half waves of a third harmonic - so why don't we see this all the time? (Perhaps we could.)

 

[synMehdi]

I don't think a square wave could mechanically travel in a string, for example, if we strike a string giving it a square pulse, it will end by vibrating at it fundamental after some time. Dissipation? speed depending on wavelength?