Question

Submarine A travels horizontally at 11.0m/s through ocean water. It emits a sonar signal of frequency f = 5.27 x 10^3 Hz in the forward direction. Submarine B is in front of submarine A and travelling at 3.00m/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. Determine what is heard by the crewman in submarine B. The speed of sound in water is 1533m/s

Answer 1

We can find the frequency of the sonar signal heard by the crewman in submarine B from the Doppler Shift formula:

$$f_o=f_s(\dfrac{v-v_o}{v-v_s}),$$ $$f_o=5.27\cdot10^3\ Hz\cdot(\dfrac{1533\ \dfrac{m}{s}-3\ \dfrac{m}{s}}{1533\ \dfrac{m}{s}-11\ \dfrac{m}{s}})=5.3\cdot10^3\ Hz.$$