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Sound Waves

  1. Apr 24, 2012 #1
    A wave on a string is described by the equation y = 0.150 m sin(1.795 x + 2010.6 t).

    Two questions:

    1. How do I find wave speed?
    velocity = λ * f​
    My pathway λ → (2pi/λ) = 1.795 ... λ = 3.50m ​
    My pathway f → f = (ω/2pi) ... ω = 2010.6 ... f = 320 Hz ​
    velocity = λ * f ... velocity = (3.50m)*(320Hz) = -1120m/s (Motion→Left)​

    2. What are the first two times when the vertical position is y = 0.050 m?
    Not sure how to go about this...​
     
  2. jcsd
  3. Apr 25, 2012 #2

    haruspex

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    1. You have sin(1.795 x + 2010.6 t).
    If you evaluate for any pair (x, t), and also for pair (x-2010.6, t+1.795), you must get the same result. I.e. wave is moving in the -ve x direction at speed 2010.6/1.795.

    2. 0.05 = 0.150 sin(1.795 x + 2010.6 t)
    You don't say what x to use here, so I'll take it as zero.
    0.05 = 0.150 sin(2010.6 t)
    1/3 = sin(2010.6 t)
    arcsin(1/3) = 0.3398... I'll use 0.34
    2010.6 t = 0.34 + 2n.pi or pi - 0.34 + 2n.pi
    The two smallest non-negative solutions are both with n = 0:
    0.34, pi - 0.34
    So t = 0.34/2010.6, (pi - 0.34)/2010.6
     
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