Question

The minimum distance between source of sound and reflecting body to hear an echo is ____________.

Answer 1

Hint: The memory of a sound wave remains for $0.1$ s in the human brain. To distinguish between the original sound and its echo, there should be at least a gap of $0.1$ s before the reception of the echo.

Complete step-by-step answer:
Speed of sound in air is around
$v=344$ m/s at ${{25}^{\circ \,}}\,\text{C}$. The medium of sound propagation is considered to be air. If the minimum distance between the source and the reflector is ${{d}_{min}}$, its value should be such that the sound wave takes $t=0.1\,\text{s}$ to return. The sound wave traverses the distance between the source and the reflector twice. Therefore,
$2{{d}_{min}}=vt$
Speed of sound is assumed to be constant. Substituting $v=344\,\,\text{m/s}$ and $t=0.1\,\text{s}$,
$2{{d}_{min}}=(344\,\,\text{m/s)(0}\text{.1}\,\,\text{s)}$
${{\text{d}}_{min}}=17.2\,\,\text{m}$
Hence, the minimum distance between source of sound and reflecting body to hear an echo is $17.2\,\,\text{m}$

Note: To distinguish between the original sound pulse and the echo, there should be a time gap of m. If the distance between the source and the reflector is less than the minimum distance, the echo will appear as a reverberation.