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

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

Feb 16, 2010
112
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
783
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.