Question

A ship on the surface of water sends a signal and receives it back from a submarine inside water after 4 s. Calculate the distance of the submarine from the ship :

(The speed of sound in water is 1450 $m{s}^{-1}$)

• A. 2.9 km
• B. 2.5 km
• C. 1.8 km
• D. 3.2 km
  

Answer 1

The correct option is A 2.9 km

The sensation of any sound persists in our ear for about 0.1 seconds. This is known as the persistence of hearing. If the echo is heard within this time interval, the original sound and its echo cannot be distinguished. So the most important condition for hearing an echo is that the reflected sound should reach the ear only after a lapse of at least 0.1 second after the original sound dies off.
As the speed of sound in water is $1450m/s$ in the question, the distance traveled by sound in $4$ seconds is calculated from the formula
Distance traveled $=velocityofsound\times timetaken$. That is, $1450\times 4$ = 5800 m. This is twice the minimum distance between a source of sound (ship) and the reflector (submarine) as it is reflected sound.
So, the submarine is at a distance of 2900 m or 2.9 km at least from the ship, for the reflected sound or the signal to be heard distinctly.