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Homework Help: The displacement amplitude

  1. May 29, 2010 #1
    1. The problem statement, all variables and given/known data

    A bat can detect ultrasonic sound waves with an intensity as low as 1 × 10–13 Wm–2. An ultrasonic source emits sounds waves with a frequency of 54.0 kHz and a power of 1 × 10–7 W. Take the speed of (ultra)sound in air as 340 ms–1 and the density of air to be 1.2 kg/m3.

    At a distance of 10.0 m from this source, calculate

    (i) the displacement amplitude

    (ii) the pressure amplitude of the ultrasonic wave

    3. The attempt at a solution

    For part (i) how can I use the equation [tex]\Delta P = \rho v \omega s_{max}[/tex] to find the displacement amplitude when I don't know what the pressure amplitude [tex]\Delta P[/tex] is? I can't find the pressure amplitude when I don't know the displacement amplitude.

    Then I tried using the following formula to find the pressure amplitude

    [tex]I=\frac{(\Delta P_{max})^2}{2\rho v}[/tex]

    But I ended up with [tex]8.67 \times 10 ^{-6}[/tex] which is wrong. The answer has to be 1.84 x 10–12m and for part (ii) it is 0.255 mPa.

    (P.S. I also know that the furthest distance at which a bat can detect this source is 282m. And the sound level in decibels is 19 dB.)
    Last edited: May 29, 2010
  2. jcsd
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