Question

Rafeeq goes to trekking, and finds a cave. He shouts into it, and hears his echo after $4.5\text{s}$. How long is the cave in $\text{km}$? Take the speed of sound in the air to be $340\text{m}{\text{s}}^{-1}$.

• A. 0.765

Answer 1

The correct option is A 0.765
Given:
The speed of sound in the air in the cave, $\text{s}=340\text{m}{\text{s}}^{-1}$
Rafeeq heard his echo after the time, $\text{t}=4.5\text{s}$
$\text{t}$ is the total time taken for the sound to hit the end of the cave, and return to Rafeeq. If $\text{l}$ is the length of the cave:
$2\text{l}=\text{s}\times \text{t}$
$⟹2\text{l}=340\times 4.5$
$⟹\text{l}=\frac{340\times 4.5}{2}=765\text{m}$
$1000\text{m}=1\text{km}$
$⟹765\text{m}=\frac{765}{1000}\text{km}=0.765\text{km}$
$\therefore$ the cave is $0.765\text{km}$ long.