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Wave Intensity

  1. Sep 15, 2011 #1
    1. The problem statement, all variables and given/known data

    For two equal-amplitude waves of nearly equal frequencies w+d/2 and w-d/2 (at a fixed position x), you have shown that the intensity exhibits \beats"
    which for d = 2pi Hz can be perceived directly by the ear, even though the
    main frequency is perceived only through the signal processing of the auditory
    nerve. How does the maximum intensity compare to the sum of the maximum
    intensities of either wave separately?

    2. Relevant equations

    3. The attempt at a solution

    So, I wrote both waves as: y1 = ACos[xk+t(w+d/2)], y2 = ACos[xk'+t(w-d/2)]. Adding them together yields: Y = y1 + y2 = 2Acos[{x(k-k')+d}t/2]cos[{x(k+k')+2tw}t/2]. So I am not really sure what it means to find the maximum intensity? Do I have to find the maximum intensity for y1 and y2 separately, and then find the mx intensity for Y? Can someone give me a hint on how to solve this problems. Thanks.
  2. jcsd
  3. Sep 15, 2011 #2


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    Homework Helper

    Yeah, pretty much. You find the intensities of y1, y2, and Y, and then compare them, i.e. is the intensity of Y larger, smaller, the same...?
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