### Theory:

SONAR:
The SONAR is the acronym for Sound Navigation And Ranging. Sonar is a device that uses ultrasonic waves to measure the distance, direction and speed of underwater objects.

• The transmitter produces and transmits ultrasonic waves into seawater, and these waves after striking the object on the sea surface, get reflected, and the detector senses them..
• The function of the detector is to convert the ultrasonic waves into electrical signals.
• The distance of the object that reflects the sound wave can be calculated by knowing the speed of sound in water and the time interval between transmission and reception of the ultrasound.
Let us take

$$v$$ - speed of sound through seawater.
$$t$$ - the time interval between transmission and reception of the ultrasound.
$$2d$$ - total distance travelled by the ultrasound.

Then, by using the formula,

$\mathit{Speed}=\frac{\mathit{Distance}}{\mathit{Time}}$

$\mathit{Distance}=\mathit{Speed}×\mathit{time}$

Apply all the terms, we will get the formula to find the total distance travelled by ultrasound

$2d=v×t$

The sonar technique is used to determine the depth of the sea and to locate underwater hills,  icebergs, valleys, submarines, sunken ships etc. This method is also called echo-ranging.

Example:

1. A Sonar emits a pulse on the surface of the water, which are detected after reflection from the bottom. If the time interval between the emission and detection of the pulse is $$6$$ $$s$$, find water depth. Take velocity of sound in water as $$1500$$ $$m/s$$.

Solution:

$$t$$ $$=$$ $$6$$ $$s$$
$$v$$ $$=$$ $$1500$$ $$m/s$$

To find: distance(d)

Applying all the values in the formula, we get

$\begin{array}{l}2d=v×t\\ d=\frac{v×t}{2}\\ d=\frac{1500×6}{2}\\ d=4500\phantom{\rule{0.147em}{0ex}}m\end{array}$

So, the depth of the water is $$4500$$ $$m$$.