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

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Solution

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 (2S).
Time taken for the sound to reach the submarine
∴ Distance between the ship and the submarine (S) = 1450 × 38.5 = 55825 m = 55.8 km

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