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If a traveling wave has amplitude of d, it feels certain amount of force at that moment in time when it is displaced for equilibrium. Thus there is also strain on the string corresponding to that amount.

However, I'm curious of what happens to the strain on the string at the moment when two waves destructively interfere to create the same wave of same amplitude of d. Would it be the same as the previous case? Or would it be larger because it is the outcome of two waves pulling towards different direction?

So in essence, I want to know if concept of superposition is a priori to related phenomena or if it is a simple description to the outcome of related phenomena.

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  • $\begingroup$ Can you state what specifically you mean when you say "strain" here? Is it simply the vertical displacement of the string, or do you mean something more akin to mechanical stress? $\endgroup$
    – probably_someone
    Nov 8, 2019 at 7:44
  • $\begingroup$ yes, so I was wondering if the molecular separation along the direction of displacement of those constituting the string would be greater or same for destructive interference. $\endgroup$
    – VVC
    Nov 8, 2019 at 7:55

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I am not sure I understand your question, but superposition is simply the cumulative outcome of coinciding effects. Physicists use the idea of superposition to break down complicated movements or functions into a sum of simpler components.

When two travelling waves meet on a string their superposition simply means the net effect of their individual movements. The tension in the string at any instance can be modelled as the sum of the tension due to the waves individually.

If the waves cancel exactly, at the instant in which there is no amplitude of vibration whatsoever, the tension in the string will be instantaneously the same as it would be if there were no waves. It is the same as a string vibrating in its fundamental mode with a single stationary wave- the wave oscillates from side to side, and as it moves further from the central position the tension increases to the point at which it prevents any further displacement, following which the string accelerates back to its undisplayed position and repeats the cycle in the other direction. The tension due to the wave is maximum at the extreme limits of displacement and zero when the string passes through its central (undisplaced) position.

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  • $\begingroup$ so if at the moment of destructive interference when no net wave is present, would there be equal and opposite forces on the string, or would the string be same as undisturbed one where no force at all is present? A box can be motionless because there is no net force on it. But also since equal and opposite forces act on it. But in the latter case, the box will feel stress. So I suppose from your answer that there will be strain on the string? $\endgroup$
    – VVC
    Nov 9, 2019 at 7:52
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    $\begingroup$ Hi Patrick, I've extended my answer to cover the point your raise. $\endgroup$
    – Marco Ocram
    Nov 9, 2019 at 9:02

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