A stationary ship generates a sound signal at the bow and has a receiver system at the stern of the ship 100 m away.The difference in time between the signal arriving at the stern traveling directly through the air and the signal reflected from the sea bottom is 0.5 second.If the velocity of sound in air is 331 m/s and in water is 1435 m/s,calculate the depth of water below the ship.
A)1150 m
B)574 m
C)359 m
D)396 m
E)450 m

Question

Quizplus · Accepted Answer

Let the depth of water be 'd'.
The time taken by the sound signal to travel directly from bow to stern through air = distance/velocity = 100/331 seconds
The time taken by the sound signal to travel from bow to seabed to stern through water = distance/velocity = (100 + 2d)/1435 seconds
The time difference between the two signals = 0.5 seconds
Therefore, (100 + 2d)/1435 - 100/331 = 0.5
This gives d = 574 meters. Therefore, option B is the correct answer.

A Stationary Ship Generates a Sound Signal at the Bow