1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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:

    $$\begin{align}
    D(x=0,t)&=0\\
    D(x=L,t)&=0=2A\sin(kx)
    \end{align}$$
    Isolate $$L$$ to find that $$\lambda=2L/m$$.
    Similarly for closed-open.
    $$\begin{align}
    D(x=0,t)&=0\\
    D(x=L,t)&=\pm 1=2A\sin(kx)\\
    \lambda&=4L/m.
    \end{align}$$
    I wanted to prove open-open too. But I am stuck.
    I know that:
    $$\begin{align}
    D(x=0,t)&=2A\cos(\omega t) \\
    D(x=L,t)&=2A\cos(\omega t).
    \end{align}$$

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

    haruspex

    User Avatar
    Science Advisor
    Homework Helper
    Gold Member
    2016 Award

    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.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted