Question: A sound wave with a frequency of 400 Hz travels through air with a speed of 343 m/s. If the amplitude of the wave is 0.02 m, calculate the maximum and minimum pressure exerted by the sound wave on the air.

Answer: To calculate the maximum and minimum pressure exerted by the sound wave, we can use the equation for the pressure amplitude of a sound wave:

where $P_{\text{max}}$ = maximum pressure $P_{\text{min}}$ = minimum pressure $P_0$ = atmospheric pressure $\rho$ = density of air (approximately 1.2 kg/m^3 at room temperature) $v$ = speed of sound in air (343 m/s) $\omega$ = angular frequency ( $2\cdot\pi\cdot f$, where $f$ is the frequency of the sound wave) $A$ = amplitude of the sound wave (0.02 m)

We can use the given frequency to calculate the angular frequency: [ \omega = 2\cdot\pi\cdot400, \text{Hz} = 800\cdot\pi, \text{rad/s} ]

Now, we can calculate the maximum and minimum pressures: [ P_{\text{max}} = 101325 + 1.2 \cdot 343 \cdot 800\pi \cdot 0.02 ] [ P_{\text{min}} = 101325 - 1.2 \cdot 343 \cdot 800\pi \cdot 0.02 ]

Using a calculator to evaluate these expressions: [ P_{\text{max}} \approx 110594 , \text{Pa} ] [ P_{\text{min}} \approx 92056 , \text{Pa} ]

So, the maximum pressure exerted by the sound wave on the air is 110594 Pa, and the minimum pressure is 92056 Pa.