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

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Discussion Overview

The discussion explores the formation of standing waves when sound waves travel along a string, specifically comparing the behavior of sinusoidal and square waveforms. It addresses theoretical aspects of wave reflection, harmonic content, and boundary conditions in the context of string vibrations.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions why sound waves reflect and form standing waves with sinusoidal waveforms but not with square waveforms.
  • Another participant speculates on the expected standing wave pattern if a string is excited with a square wave, suggesting that the string length must accommodate all harmonics in the correct phases for a square wave to form.
  • A different viewpoint argues that a square wave can be seen as a superposition of sinusoidal waves, implying that a perfect square wave cannot travel along a string due to discontinuities, and that a finite number of harmonics would be necessary for standing waves.
  • One participant raises the question of whether an approximation of a square wave using a few odd harmonics would still meet the requirements for forming standing waves, expressing uncertainty about boundary conditions.
  • Another participant asserts that a square wave cannot mechanically travel in a string, suggesting that striking a string with a square pulse would lead to vibrations settling at the fundamental frequency over time due to dissipation and wavelength-dependent speed.

Areas of Agreement / Disagreement

Participants express differing views on the feasibility of square waves forming standing waves in strings, with no consensus reached on the underlying mechanics or boundary conditions involved.

Contextual Notes

Participants note limitations related to boundary conditions, the nature of harmonics, and the effects of dissipation on wave propagation, which remain unresolved in the discussion.

hobmarcus
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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 ?
 
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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.
 
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.
 
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.)
 
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?
 

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