Separation of a Standing Wave into Time Dependent and Time Independent Functions

Discussion in 'Homework Help' started by Robert.Adams, Jun 7, 2011.

  1. Robert.Adams

    Thread Starter Active Member

    Feb 16, 2010
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    5
    For my modern physics class we looked at a standing wave and described a wave with n modes as
    phi(x,t) = [2*ym*sin(kn*x)]cos(wn*t);

    Where ym is the maximum amplitude of the vibration, kn is the wave number (defined as 2pi/(lambdan), with lambdan being the wavelength associated with that standing wave), and wn is the angular frequency for a certain mode.

    I have to break this down into a time independent and a time dependent equation so I can compare to my quantum mechanics stuff but I'm having trouble. I was thinking of using Euler's relation to rewrite the equation but that didn't seem to work.

    Can anyone help?
     
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
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    One approach is to arbitrarily fix (as a constant) either x or t. Not sure if that is of any use.

    One can resolve the function into it's "forward" and "reverse" traveling wave components, but they are also a function of both time & position - as you would expect.
     
  3. Robert.Adams

    Thread Starter Active Member

    Feb 16, 2010
    112
    5
    I determined it from a text book I found online. The time independent is the one we used for probability density functions and I determined it to be:

    A*sin(n*pi*x/L) where L is the length of the wire, A is the amplitude, and n is the mode number.
     
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