Question

A sonar device on a submarine sends out a signal and receives an echo $5\sec $ later. Calculate the speed of sound in water if the distance of the object from the submarine is $3625m$:
$\begin{align}
  & \text{A}\text{. }1450m{{s}^{-1}} \\
 & \text{B}\text{. }1650m{{s}^{-1}} \\
 & \text{C}\text{. }1350m{{s}^{-1}} \\
 & \text{D}\text{. }967m{{s}^{-1}} \\
\end{align}$

Answer 1

Hint: SONAR, sound navigation and ranging, is a technological device based on the principle of reflection of sound. An ultrasonic wave is transmitted from Sonar towards the bottom of sea or ocean resulting in waves coming back after reflection from the object or a submarine. We will calculate the total distance travelled by the sonar waves and distance, speed, time relation will give the velocity of the sonar wave.

Complete step by step answer:
Sonar is a device used for finding objects underwater using sound waves. Sonars transmit ultrasonic waves into the water below the ship and receive the returning echoes from the seabed. Any object that gets hit by these ultrasonic waves will emit a returning echo that will show up on the sonar display. The device which emits the ultrasonic waves is known as a transducer.
Sonar, sound navigation and ranging, is a technique for the purpose of detecting and determining the distance and the direction of underwater objects by acoustic means. Sound waves emitted by or reflected from the object underwater are detected by sonar apparatus and analyzed for the information they contain.
Sonar works on the principle of reflection of sound. An ultrasonic wave is transmitted from Sonar towards the bottom of sea or ocean resulting in waves coming back after reflection from the object or a submarine. We then record the total time taken by the ultrasonic wave to reach the sonar and by using speed of wave and time we can detect the location of underwater objects or submarines.

We are given that a sonar device on a submarine sends out a signal and receives an echo $5\sec $later. The distance of the object from the submarine is $3625m$ and we have to calculate the speed of sound in water.
Distance of the object from the submarine $d=3625m$
Time taken to hear the echo $t=5\sec $
Total distance travelled by the sonar waves during the transmission and reception of the signal,
$\begin{align}
  & D=2d=2\times 3625m \\
 & D=7250m \\
\end{align}$
Speed of the sound in water,
$v=\dfrac{D}{t}$
Put,
$\begin{align}
  & D=7250m \\
 & t=5\sec \\
\end{align}$
$v=\dfrac{7250}{5}=1450m{{s}^{-1}}$
The speed of sound in water is $1450m{{s}^{-1}}$

Hence, the correct option is A.

Note:
The basic principle of Sonar is reflection and receiving the echoes from the target. While calculating the distance travelled by the sound wave, we have to double the distance between the object and the submarine since echo’s transmission and reception involves the reflection of sound wave from the target.