Question

Dolphins emit clicks of sound for communication and echolocation. A marine biologist is monitoring a dolphin swimming in seawater where the speed of sound is 1522 m/s. When the dolphin is swimming directly away at 8.5 m/s, the marine biologist measures the number of clicks occuring per second to be at a frequency of 2770 Hz.
1. What is the difference (in Hz) between this frequency and the number of clicks per second actually emitted by the dolphin?

Answer 1

From Doppler effect we have that the frequency observed for the relation between the velocities is equivalent to the frequency observed. That is mathematically,

$F_r = \frac{v}{v+v_s}F_s$

Here,

Speed of sound in water $v = 1522m/s$

The Dolphin swims directly away from the observer with a velocity $v_s = 8.5m/s$

Observed frequency of the clicks produced by the dolphin $F_r = 2770Hz$

Replacing we have,

$F_r = \frac{v}{v+v_s}F_s$

$F_s = \frac{v+v_s}{v}$

$F_s = 2770 (\frac{1522}{1522+8.5})$

$F_s = 2754.61Hz$

Therefore the frequency emitted by the dolphin is 2754.61Hz