Question

A sound produced on the surface of a lake takes 4.5 s to reach a boatman. How much time will it take to reach a driver inside water at the same distance if speed of sound in water is 4.5 times the speed of sound in air?

• A. 1 s
  
• B. 2 s
  
• C. 3 s
  
• D. 4 s

Answer 1

The correct option is A

1 s

Let, $t_{air}$ be the time taken by the sound in air

$t_{water}$ be the time taken by the sound in water

$V_{air}$ be the velocity of sound in air

$V_{water}$ be the velocity of sound in water

Given,
$\frac{V_{water}}{V_{air}}=4.5$
$t_{air}=4.5s$
$t_{water}=?$
Now, $V_{air}=\frac{d}{t_{air}}$ and $V_{water}=\frac{d}{t_{water}}$
$\therefore \frac{V_{water}}{V_{air}}=\frac{\frac{d}{t_{water}}}{\frac{d}{t_{air}}}=\frac{t_{air}}{t_{water}}$
$\frac{V_{water}}{V_{air}}=\frac{4.5}{t_{water}}$
$t_{water}=4.5\times \frac{V_{air}}{V_{water}}$
$t_{water}=4.5\times \frac{1}{4.5}=1s$