A SONAR (sound navigation and ranging) uses ultrasonic waves to d… - Vidyadip

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 $77.0s$. What is the distance of the enemy submarine? (Speed of sound in water = $1450m s^{–1}$).

✓

Answer

Let the distance between the ship and the enemy submarine be ' S '. Speed of sound in water $=1450 \mathrm{~m} / \mathrm{s}$ Time lag between transmission and reception of Sonar waves $=77 \mathrm{~s}$ 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 = $1 / 2$ $\times 77=38.5 \mathrm{~s}$
$\therefore$ Distance between the ship and the submarine $(S)=1450 \times 38.5=55825 \mathrm{~m}=55.8 \mathrm{~km}$

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