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Instantaneous Displacement of a Sound Wave

  1. Jan 26, 2015 #1
    1. The problem statement, all variables and given/known data
    A sinusoidal sound wave moves through a medium and is described by the displacement wave function s(x,t) = 2.00cos(15.7x - 858t) where s is in micrometers, x is in meters, and t is in seconds. Find a) the amplitude, b) the wavelength, and c) the speed of this wave. D) Determine the instantaneous displacement from equilibrium of the elements of the medium at the position x=0.050 m and t=3.00 ms. E) Determine the maximum speed of the element's oscillatory motion.

    2. Relevant equations

    3. The attempt at a solution
    I have already figured out A, B, and C but cannot figure out D or E. I believe D is just to find the derivative and plug in the given X and T, but I do not know how to find the derivative of a three variable function. Also, I believe E just requires setting the derivative equal to 0 and finding when it is a maximum.
  2. jcsd
  3. Jan 26, 2015 #2


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    Homework Helper

    No need; it asks for the instantaneous displacement. The given function s(x,t) gives you the displacement at every position and every time.

    That would give you the maximum displacement, (not the maximum speed,) but you don't even need to differentiate to find that; it's simply the amplitude.
  4. Jan 26, 2015 #3
    Clearly I overthought this problem way too much. I got it now.

    Thank you very much.
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