Serway & Jewett — Wave Motion: Problem 59

Equation 16.40 states that at distance \(r\) away from a point source with power \((Power)_{avg}\), the wave intensity is \[I = \frac{(Power)_{avg}}{4\pi r^2}\] Study Figure 16.25 and prove that at distance \(r\) straight in front of a point source with power \((Power)_{avg}\) moving with constant speed \(v_S\) the wave intensity is \[I = \frac{(Power)_{avg}}{4\pi r^2} \left( \frac{v - v_S}{v} \right)\]