# Adding waves to a standing wave

Discussion in 'Math' started by boks, Nov 16, 2008.

1. ### boks Thread Starter Active Member

Oct 10, 2008
218
0
How can I show that
$Aexpi(\omega t - kx + \phi_{1}) + Aexpi(\omega t + kx + \phi_{2}) = 2Aexpi(\omega t + \frac{\phi_{1} + \phi_{2}}{2})cos(kx - \frac{\phi_{1} - \phi_{2}}{2})$?

2. ### steveb Senior Member

Jul 3, 2008
2,433
469
One way is to factor out $2Aexpi(\omega t + \frac{\phi_{1} + \phi_{2}}{2})$ from the left hand side.

You will then be left with a much easier problem, which is to show that

${{expi( - kx + \phi_{1}-\frac{\phi_{1} + \phi_{2}}{2}) + expi( kx + \phi_{2}-\frac{\phi_{1} + \phi_{2}}{2})}\over{2}} = cos(kx - \frac{\phi_{1} - \phi_{2}}{2})$