Question

A SONAR device uses ultrasound to find out the average depth of the Caspian Sea. The sound of wavelength $10\text{mm}$ and frequency $150\text{kHz}$, reflects back to the device in about $1.4\text{s}$. What is the depth of the sea in $\text{km}$?

• A. 1.05

Answer 1

The correct option is A 1.05
Given:
The frequency of sound, $\text{f}=150\text{kHz}$
Wavelength of the sound, $\lambda =10\text{mm}$
$⟹$ Speed of the sound in the sea, $\text{v}=\lambda \text{f}=10\times {10}^{-3}\times 150\times {10}^3$
$=1500\text{m}{\text{s}}^{-1}$
Time taken by the sound to reflect back to the SONAR, $\text{t}=1.4\text{s}$
Let the depth of the sea be $d$.
Total distance travelled $=2d$
The depth of the Caspian Sea,
$\text{d}=\frac{\text{st}}{2}=\frac{1500\times 1.4}{2}=75\times 14$
$=1050\text{m}$
$1000\text{m}=1\text{km}$
$⟹1050\text{m}=\frac{1050}{1000}\text{km}=1.050\text{km}$