Halliday, Resnick & Walker — Waves–II: Problem 37

A sound source sends a sinusoidal sound wave of angular frequency \(3000 \text{ rad/s}\) and amplitude \(12.0 \text{ nm}\) through a tube of air. The internal radius of the tube is \(2.00 \text{ cm}\). (a) What is the average rate at which energy (the sum of the kinetic and potential energies) is transported to the opposite end of the tube? (b) If, simultaneously, an identical wave travels along an adjacent, identical tube, what is the total average rate at which energy is transported to the opposite ends of the two tubes by the waves? If, instead, those two waves are sent along the same tube simultaneously, what is the total average rate at which they transport energy when their phase difference is (c) 0, (d) \(0.40\pi \text{ rad}\), and (e) \(\pi \text{ rad}\)?