Question

A sound signal is simultaneously sent in air and water from a boat on a river. The echo of sound returned by the river bed is heard is $4\text{s}$, while the echo returned by the aeroplane is heard in $8\text{s}$. Find the distance between the aeroplane and the river bed.

[velocity of sound in air = $350\text{m/s}$, velocity of sound in water = $1500\text{m/s}$]

• A. $4.4\text{km}$
• B. $6.4\text{km}$
• C. $8.8\text{km}$
• D. $13.4\text{km}$

Answer 1

The correct option is A $4.4\text{km}$

If the distance of reflector from the source is $d$, then
Total distance travelled by the sound before reaching the detector $2d=vt\Rightarrow d=\frac{vt}{2}$
where $t$ is the time taken to receive the reflected sound.

From the data given in the question,

Distance travelled by the sound in air from source to the reflector,
$d_1=\frac{350\times 8}{2}=1400\text{m}......\left(1\right)$

Distance travelled by the sound in water from source to reflector,
$d_2=\frac{1500\times 4}{2}=3000\text{m}........\left(2\right)$

Seperation between the aeroplane and the river bed is given by $d^{\prime }=d_1+d_2$

From $\left(1\right)$ and $\left(2\right)$ we get,
$d^{\prime }=3000+1400=4400\text{m}\text{or}4.4\text{km}$

Thus, option (a) is the correct answer.