Question

4. Consider a sound wave in the air that has displacement amplitude 0.0200 mm. Calculate the pressure amplitude for frequencies of (a) 150 Hz; (b) 1500 Hz; (c) 15 000 Hz . In air at normal atmospheric pressure and density, the speed of sound is 344 m/s and the bulk modulus is 1.42×10^5 Pa.

Please show all work

Answer 1

pressure amplitude has a formula,

$P_{0}=\rho cA\omega$

Here,

$\rho$ - density of air

- speed of sound

- displacement amplitude

$\omega$    - angular frequency

putting corresponding values will get,

$P_{0}=1.2\times344\times0.02\times10^{-3}\times2\times3.14\times150$

Case a

$P_{0}=7.777pa$

Now just changing the values of frequency will get

Case b

$P_{0}=77.77pa$

Case c

$P_{0}=777.7pa$