Question

A SONAR device uses ultrasound to find the depth of a lake to be $20\text{m}$. If the sound is reflected back to the device in about $\frac{1}{29}\text{th}$ of a second, what is the speed of the sound in the lake?

• A. 1160

Answer 1

The correct option is A 1160
Given:
The depth of the lake, $\text{d}=20\text{m}$
The sound sent into the lake is reflected back to the SONAR device in time, $\text{t}=\frac{1}{29}\text{s}$
Here, $\text{t}$ is the total time taken for the sound to hit the bottom of the lake, and then come back to the device, i.e. the distance covered by the sound in time $\text{t}$ is equal to twice the depth of the lake.
$⟹2\text{d}={\text{s}}_{\text{L}}\times \text{t}$, where ${\text{s}}_{\text{L}}$ is the speed of the sound in the lake.
$⟹{\text{s}}_{\text{L}}=\frac{2\text{d}}{\text{t}}=\frac{2\times 20}{\left(\frac{1}{29}\right)}=2\times 20\times 29$

$⟹{\text{s}}_{\text{L}}=1160\text{m}{\text{s}}^{-1}$
So, sound travels at a speed of $1160\text{m}{\text{s}}^{-1}$ in the lake.