# Sonar Numericals (sound physics)

In this post, we will solve Sonar Numericals (from the sound chapter of Physics).

Formula Used

The average speed of sound = distance moved/time taken
=> v=s/t
=>distance moved s =vt

Numericals on Sonar

A fishing boat uses sonar (sound navigation and ranging) to detect shoals of fish under the water. A pulse of sound is sent from the surface and is reflected back after it hits the shoal of fish. Sound travels at 1500 m/ s in water and the time between the ping and its echo is 0.40 s.
(i) State the equation linking the speed of sound to the distance moved and time taken.
(ii) Calculate the depth of the water where the shoal is located.

Solution:

(i) The average speed of sound = distance moved/time taken
=> v =s/t
=>s =vt

ii) The data given are:
v = 1500 m/s
The time between the ping and its echo is 0.40 s.
This means the time taken by the sound to travel and hit the shoal, and then come back is 0.40 s.
=> So the time of one-way travel to go and hit the shoal is t = 0.40 / 2 = 0.20 s

So, the depth of the water where the shoal is located is s=vt = 1500 x 0.2 = 300 m