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Velocity of a Wave

  1. Feb 18, 2015 #1
    1. The problem statement, all variables and given/known data
    For a wave described by y = 0.02 sin[ pi(30x - 400t)] (SI units), the velocity of the wave (in m/s) is

    a) 3/40 b) 40/3 c) (60pi)/400 d)400/(60pi) e) 400


    2. Relevant equations


    3. The attempt at a solution
    I found the derivative of the function as v= -25.132 cos[pi(30x-400t)] so I assumed the velocity is 25.132 m/s which is none of the options and the correct answer is 40/3.
     
  2. jcsd
  3. Feb 18, 2015 #2

    lightgrav

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    Homework Helper

    they wanted the velocity of the disturbance along the string, not the maximum velocity for one point on the string.
    the velocity is hiding in the trig function's argument (kx-ωt) ≈ k(x-vt)
     
  4. Feb 18, 2015 #3
    That makes sense! So right now the kx-ωt is (30pi)x-(400pi)t, where k= 30pi. So factoring out 30pi we get v=(400pi)/(30pi) which is 40/3. Thank you!
     
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