A SONAR (sound navigation and ranging) uses ultrasonic
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 $77.0 \mathrm{~s}$. What is the distance of the enemy submarine? (Speed of sound in water $=1450 \mathrm{~m} \mathrm{~s}^{-1}$ ).

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 $=\frac{1}{2} \times 77=38.5 \mathrm{~s}$

$\therefore$ Distance between the ship and the submarine $(S)=1450 \times 38.5=55825 \mathrm{~m}=55.8 \mathrm{~km}$
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