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})
     
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