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Finding displacement amplitude given frequency and pressure

  1. Oct 19, 2011 #1
    1. The problem statement, all variables and given/known data

    What is the displacement amplitude of a sound wave of frequency 160.0 Hz in air at 20 °C at the pain-threshold pressure amplitude of 29.0 Pa?

    f = 160 Hz
    Vs = 343 m/s
    ΔP = 29 Pa

    2. Relevant equations

    ΔP(x,t) = (ΔP)cos(kx - wt) = β*s*k*cos(kx - wt)
    k = f/Vs

    3. The attempt at a solution

    ΔP = βsk

    Therefore, s = ΔP/(β*k) = (ΔP*Vs)/(f*β)

    β = 1.4 * 10^5 Pa

    So the answer I got was 4.44*10^-4 m which is wrong. Am I missing something here?
  2. jcsd
  3. Oct 20, 2011 #2
    k=f/Vs is not accurate, since k is 2π/λ

    λf = Vs

    ω/k = Vs
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