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 = (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 = (v)/(v+v_s)F_s`

`F_s = (v+v_s)/(v)`

`F_s = 2770 ((1522)/(1522+8.5))`

`F_s = 2754.61Hz`

Therefore the frequency emitted by the dolphin is 2754.61Hz