(adsbygoogle = window.adsbygoogle || []).push({}); 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/m^{3}.

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^{–12}m 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.)

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# Homework Help: The displacement amplitude

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