#### Question

A SONAR (sound navigation and ranging) uses ultrasonic waves to detect and locate objects under water. In a submarine equipped with a SONAR the time delay between generation of a probe wave and the reception of its echo after reflection from an enemy submarine is found to be 77.0 s. What is the distance of the enemy submarine? (Speed of sound in water = 1450 m s^{–1}).

#### Solution 1

Let the distance between the ship and the enemy submarine be ‘*S*’.

Speed of sound in water = 1450 m/s

Time lag between transmission and reception of Sonar waves = 77 s

In this time lag, sound waves travel a distance which is twice the distance between the ship and the submarine (2*S*).

Time taken for the sound to reach the submarine = `1/2 xx 77 = 38.5 s`

∴ Distance between the ship and the submarine (*S*) = 1450 × 38.5 = 55825 m = 55.8 km

#### Solution 2

Here speed of sound in water v = 1450 m s^{-1}and time of echo t = 77.0 s.

If distance of enemy submarine be d, then t = 2d/v

∴ d=vt/2 =1450 x 77.0/2 =55825 m=55.8 x 10^{3} m or 55.8 km