Question

A sonar device on a submarine sends out a signal and receives an echo $5\,s$ later. Calculate the speed of sound in water if the distance of the object from the submarine is $3625\,m$.

Answer 1

In order to solve this problem we will first see the definition of sonar device and echo; and then we will solve the given problem by using a simple formula relating velocity to distance.

Formula Used:
$v=\dfrac{d}{t}$
Where $v$ is the velocity of an object, $d$ is the distance travelled by the object and $t$ is the time taken by the object to travel the distance.

Complete step by step answer:
Sonar is a method that uses sound propagation to navigate, communicate with, and locate objects on or under the surface of the water, objects such as other vessels (usually underwater, as in submarine navigation). A sound that has been reflected over a surface, such as a wall, an object or a cliff, is called an echo.

In this case,time taken to hear the echo, $t=5\,s$.
The object's distance from the submarine, $d=3625\,m$.
The total distance travelled by sonar waves in water during transmission and reception$=2d$.
The velocity of sound in water will be $v=\dfrac{d}{t}$, but here as we know sound will have to be transmitted and reflected back so the distance travelled will be twice of the distance of the object from the submarine so,
$v=\dfrac{2d}{t}$
$\Rightarrow v=\dfrac{2\times 3625}{5}$
$\therefore v=1450\,m{{s}^{-1}}$

Note: It's important to remember that the distance covered will be twice the distance between the object and the submarine since sound must be transmitted and reflected back from the object to the submarine; if this is overlooked, the answer will be incorrect.