Question

A sound made on the surface of a lake takes $3s$ to reach a boatman. How much time will it take to reach a diver inside the water at the same depth?

Velocity of sound in air $=330m{s}^{-1}$

Velocity of sound in water $=1450$

Answer 1

Step 1. Given:

$Time\left(t\right)=3s$

Velocity of sound in air $\left(v_a\right)=330m{s}^{-1}$

Velocity of sound in water $\left(v_w\right)=1450\raisebox{1ex}{$m$}\!\left/ \!\raisebox{-1ex}{$s$}\right.$

Step 2. Finding the time of travel in water

Let the distance travelled by the sound in air is (D_a)

$D_a=v_a\times Time$

First, find the distance travelled in the air

$D_a=330\times 3$

$D_a=990m$

Let distance travel in water in is (D_w)

It is given that D_a=D_w

Time taken by the sound to reach up to the diver.

$\therefore$ $Time=\frac{D_w}{Velocityofsoundinwater}$

$Time=\frac{D_a}{V_w}$

Now put the given value in the above formula

$=\frac{990}{1450}$

$=0.68sec$

Hence, the time taken by the sound to reach to the diver is $0.68sec$