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Sound (harmonic) waves questions

  1. Nov 25, 2013 #1
    Hello,
    I have two question regrading sound waves.
    The first one:
    The pressure P(x;t) at a point x at time t in a medium through which a harmonic wave is
    travelling can be described by:
    P(x,t) = Asin(wt -kx)
    If the equation describes a pressure wave travelling in air, with amplitude 2 Pa and frequency 100 Hz,
    find the instantaneous pressure at a distance 10 cm from the source at time 5s.
    My solution(am I doing right?):
    w=2pi*f
    w=2pi*100Hz = 200pi rad/sec;

    k=2pi/λ; v=f*λ; λ=343m/s /100 Hz = 3.43m and k=2pi/3.43 =1.83 rad/m;

    Finally I have this:
    P(x=0.1 ,t=5) = 2sin(200pi*5 -1.18*0.1) = -0.34.

    The second question is here ORWfejn.png
    Hope you can help me to figure out the solutions.
    Thanks
     
  2. jcsd
  3. Nov 25, 2013 #2

    NascentOxygen

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    Staff: Mentor

    I can see how you approached this, but the assumption of v = 343 m/sec seems unreasonable in light of knowing nothing more than it is sound in "a medium". I think the best you can do is state " I can't see how this can be solved without knowing v or λ so to allow computations I am going to imagine the medium is air at 25C " or something like that.

    For your second problem, you'll need to use trig identities, cos (A) + cos (B)
     
  4. Nov 25, 2013 #3
    Thanks for you reply,
    In the end of question's paper it says 343m/sec, so I decided to use it. I'm just confused with the negative result.
     
  5. Nov 25, 2013 #4

    NascentOxygen

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    Staff: Mentor

    A sinusoid "with amplitude of 2 Pa" is a convention or standard expression implying pressure varies cyclically from 2 Pa below ambient (rarefaction) to 2 Pa above ambient (compression). If it were intended to be otherwise, the question would be worded to make that clear.
     
  6. Nov 25, 2013 #5
    So the negative result translates into;
    Atmospheric(Pa) + (-0.34 Pa) = Absolute (Pa) ?
     
  7. Nov 25, 2013 #6

    NascentOxygen

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    Staff: Mentor

    I assume that's how it is. There is an incremental change in pressure given by that sinusoid.
     
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