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 = $1450$ $m{s}^{-1}$).

Answer 1

Let the distance between the ship and the enemy submarine be$S.$
Speed of sound in water $=1450m/s$
Time lag between transmission and reception of Sonar waves $=77s$
In this time lag, sound waves travel a distance which is twice the distance between the ship and the submarine $\left(2S\right).$

Time taken for the sound to reach the submarine $=\frac{1}{2}\times 77=38.5s$

Distance between the ship and the submarine, $S=1450\times 38.5=55825m=55.8km$