Halliday, Resnick & Walker — Waves–II: Problem 106

The loudest. One way to measure “loudness” is with the sound pressure level SPL (units dB SPL), which is defined as \[SPL = 20 \log \left( \frac{\Delta p_m}{p_0} \right),\] where \(\Delta p_m\) is the measured pressure amplitude of the sound wave and \(p_0\) is the reference pressure of \(20 \mu\text{Pa}\) (\(= 20 \mu\text{N/m}^2\)). For a sustained sinusoidal sound wave, the upper limit for the pressure amplitude is \(\Delta p_m = 1 \text{ atm}\). In that case, what are (a) the maximum pressure and (b) the minimum pressure in the wave? (c) What is the SPL? (This is the “loudest” that a sustained sound wave can be in Earth’s atmosphere.)