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Homework Help: Archived Standing Waves Proof for Open-Open Tubes

  1. Sep 17, 2014 #1
    My teacher assigned me to prove open-closed and closed-closed standing waves patterns using math.
    With closed-closed, it was fairly easy:

    Isolate $$L$$ to find that $$\lambda=2L/m$$.
    Similarly for closed-open.
    D(x=L,t)&=\pm 1=2A\sin(kx)\\
    I wanted to prove open-open too. But I am stuck.
    I know that:
    D(x=0,t)&=2A\cos(\omega t) \\
    D(x=L,t)&=2A\cos(\omega t).

    Where do I go next?
  2. jcsd
  3. Feb 5, 2016 #2


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    I'm not quite sure what the D() function represents. Judging from the factor 2 on the right hand side it represents the range of 'y', e.g. range of movement of air. That being so, eqn 4 should read ##A-(-A)=2A\sin(kL)## (where, presumably, k and λ are the same thing).
    Equations 6 and 7 seem to have gone off in a different direction, using the travelling wave equations at x=0. Applying equation 4 at x=0 and x=L would be the logical continuation.
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