Question

How the process of sound navigation is used to measure the depth of ocean, give the mathematical expression also,
no copy or spam is allowed!!

Answer 1

Sound navigation and ranging (Sonar) is one of the criteria of echo which is used to determine the depth of water bodies. It is calculated by the speed of the sound and the time taken by the sound to bounce back again.

Consider a ship floating on the surface of sea. A transmitter T and receiver R are fitted at the bottom. Transmitter T is capable of emitting ultrasonic sound and receiver R receives them after reflection from P at the bottom of sea. The wave follows a path PTR.

Let, t be the time by the wave to go from P to R via T.

Let's come to the point of mathematical expression:

Time taken by the sound to travel the path PT = t/2

∴ PT = v× t/2

[∵ v= Velocity of the sound]

Let, x = separation between T and R.

In right angled triangle POT_

OP² = PT² - OT²

or, h² = (vt/2)² -(x/2)²

=(v²t²-x²)/4

Or, h ={√(v²t²-x²)/2}

If d = length of portion of ship in water, depth 'H' of sea is given by

H = h+d

or, H= {√(v²t²-x²)/2} +d

Answer 2

Answer:

Sound navigation and ranging (Sonar) is one of the criteria of echo which is used to determine the depth of water bodies. It is calculated by the speed of the sound and the time taken by the sound to bounce back again. Consider a ship floating on the surface of sea.