# The displacement amplitude

1. May 29, 2010

### roam

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 $$\Delta P = \rho v \omega s_{max}$$ to find the displacement amplitude when I don't know what the pressure amplitude $$\Delta P$$ 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

$$I=\frac{(\Delta P_{max})^2}{2\rho v}$$

But I ended up with $$8.67 \times 10 ^{-6}$$ 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