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Finding the time between beats

  1. Jan 30, 2013 #1
    1. The problem statement, all variables and given/known data
    The displacement of a mass as a function is given by the equation

    x = 3cos((10pi )t) + 3cos((11\pi)\t)

    What is the time between beats, i.e the time between occurrence of the maximum displacement?

    2. Relevant equations

    At a maximum v = 0

    3. The attempt at a solution

    I took the derivative of the function and set it equal to zero
    10sin((10pi)t) + 11sin((11pi)t) = 0

    I can't find an analytical way of solving this problem. I have tried various trig identities , expanding the functions which took an hour but go no where. Is my strategy of finding the zeros this way the right one or should I come up with a different strategy. And if the latter than where should I start from?
     
  2. jcsd
  3. Jan 30, 2013 #2

    Simon Bridge

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    You want the period of the envelope function.
    http://en.wikipedia.org/wiki/Beat_(acoustics [Broken])

    The time between beats would be one over the beat frequency.
     
    Last edited by a moderator: May 6, 2017
  4. Jan 30, 2013 #3
    Thank you very much for your help.
     
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