Question

A man standing between two cliffs produces a sound and hears two successive echoes at intervals of $3\mathrm{s}$ and $4\mathrm{s}$ respectively.

Why will an echo not be heard, when the distance between the source of sound and the reflecting surface is $10\mathrm{m}$ ?

Answer 1

Step 1: Given data:

Distance between the source of sound and the reflecting surface $=10m$
Time $t=0.1sec.$ [persistence of hearing]

Step 2: Calculating the minimum distance between the object and the source of sound for hearing distinct echoes:

The time delay between the original sound and the reflected sound must be at least $0.1s$ to hear a definite echo.

Assume that the speed of sound is $344m/s$.

The sound must travel to the obstacle and then reflect back to the listener's ear after $0.1s$ at a particular temperature, such as $22°C$ in air.

Since, $dis\tan ce=spee{d}_{sound}\times time$

Thus, the total distance traveled by sound from its source to the reflecting surface and back should be at least $=344\times 0.1=34.4m$.

Hence, the minimum distance between the object and the source of sound for hearing distinct echoes must be half of this distance, or $17.2m$
Since the given distance between the source of sound and the reflecting surface which is $10m$, is less than $17.2m$.

Therefore, as the distance is only 10m, therefore, no echo is produced.