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
    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
    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
    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.