### Question 2.30

NCERT Class XI Physics

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).

### Physical Concept

we can apply the speed distance formula if we assume that the speed of sound is uniform throughout the river.

Significant digits in the given data are 3 each in 77.0 and 1450, so the answer obtained by multiplication/division will also be precise to 3 significant digits.

### Solution

$ \begin{aligned} &\text{let distance be } d \text{ meters}\\\\ &\text{time to return given } t = 77.0 \text{ s [SF = 3]}\\ &\text{speed given } v = 1450 \text{ m/s [SF = 3]}\\ &\text{to-and-fro distance covered } 2d \text{ meters}\\\\ &\text{by speed formula } 2d = v \times t\\\\ &\therefore d = \frac 12 \times v \times t\\\\ &\therefore d = \frac 12 \times 1450 \times 77.0\\\\ &\therefore d =55825 \text{ m}\\ &\text{rounding to 3 SF} \\ &\text{d = 55800 \text{ m}}\\\\ &= 55.8 \text{ km}\:\underline{Ans} \end{aligned} $

### Video Explanation

Please watch this youtube video for a quick explanation of the solution:

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