Serway & Jewett — Wave Motion: Problem 38

Submarine A travels horizontally at 11.0 m/s through ocean water. It emits a sonar signal of frequency \( f = 5.27 \times 10^3 \text{ Hz} \) in the forward direction. Submarine B is in front of submarine A and traveling at 3.00 m/s relative to the water in the same direction as submarine A. A crewman in submarine B uses his equipment to detect the sound waves (“pings”) from submarine A. We wish to determine what is heard by the crewman in submarine B. (a) An observer on which submarine detects a frequency \( f' \) as described by Equation 16.46? (b) In Equation 16.46, should the sign of \( v_S \) be positive or negative? (c) In Equation 16.46, should the sign of \( v_O \) be positive or negative? (d) In Equation 16.46, what speed of sound should be used? (e) Find the frequency of the sound detected by the crewman on submarine B.