Question

Navy ships use sonar (sound navigation and ranging) to detect submarines. A sound pulse sent by the ship reflects off the submarines. If the submarine is $1.58km$ away from the ship, and the speed of sound in seawater is $1463\dfrac{m}{s}$ . How long will it take the sound pulse to travel out and back?

Answer 1

In order to find the solution for the above question, we will be using a simple formula of kinematics in one dimensional motion. We will be following the concept of displacement and velocity.
$\begin{aligned} & velocity=\dfrac{displacement}{time} \\\ & \Rightarrow v=\dfrac{d}{t} \\\ \end{aligned}$

Complete step by step answer:
In order to calculate the time taken by the sound pulse sent by the ship to travel out, get reflected back by the submarine and get back to the ship, we will use a simple formulae of kinematics.
$\begin{aligned} & velocity=\dfrac{displacement}{time} \\\ & \Rightarrow v=\dfrac{d}{t} \\\ & \Rightarrow t=\dfrac{d}{v} \\\ \end{aligned}$
Now, the total displacement travelled by the wave to travel out and back will be $1.58km+1.58km=3.16km$ . Therefore, it will be $3.16\times 1000=3160m$ and the velocity of the sound pulse is given as $1463\dfrac{m}{s}$ . Placing the values, we get
$\begin{aligned} & \Rightarrow t=\dfrac{3160}{1463} \\\ & \Rightarrow t=2.16\sec \\\ \end{aligned}$
The time taken by the sound pulse will be $2.16\sec$ .

Additional Information:
Submarines have a distinct advantage over other military vessels in that they can remain concealed under the water floor. Using passive or active acoustics to detect and locate submarines is one method.
Passive acoustics is used to detect sounds produced by a submarine, such as propeller, engine, and pump noise. Experienced sonar operators may recognize these sounds. Each type of submarine has a distinct sound signature that serves as the vessel's acoustic "signature."
The Navy may also use active acoustics to locate submarines, similar to how people use it to locate fish. The sonars will calculate the location of the echoes that return from objects struck by the sound by transmitting a sound pulse and receiving the echo on an array. They can also determine the distance to the source that caused the echo by measuring the time it takes for echoes to return. Submarine echoes can be distinguished from those of ocean bottom features, whales, schools of fish, and other objects by a professional sonar operator or a computer programme.

Note:
Here, it is very important to keep in mind that the ship and the submarine are assumed to be stationary. If they are not stationary, then we will have to calculate every quantity with a different reference frame. Or we will have to use the concept of relative velocity.