Serway & Jewett — Wave Motion: Problem 51

A pulse traveling along a string of linear mass density \(\mu\) is described by the wave function \[y = [A_0 e^{-bx}] \sin (kx - \omega t)\] where the factor in brackets is said to be the amplitude. (a) What is the power \(P(x)\) carried by this wave at a point \(x\)? (b) What is the power \(P(0)\) carried by this wave at the origin? (c) Compute the ratio \(P(x)/P(0)\).