Question

Find out the minimum size of a room required to hear an echo of sound with a speed of 300m/s.

Answer 1

Hint
Echo is a repetition of sound produced by the reflection of sound waves from a wall, mountain, or other obstructing surface. We use wavelength formulas to solve the question.

Complete step by step solution
To hear a distinct echo the time interval between the original sound and the reflected one must be at least $0.15$. The max velocity of the sound is approx $343m/s$ at a temperature of $25^0C$.
As,per the wavelength formula,
$f = \dfrac{1}{T}$
Let the size of room is $= x$
Total distance covered by wave during travel $=2x$
$V = f\lambda = \dfrac{1}{T}2x$ … [we can say this from the formula]
$\therefore x = \dfrac{{V \times T}}{2} = \dfrac{{343 \times 0.1}}{2}$
Or, $x = 17.15m$.

Note
This is a fact that the reflecting object must be more than $17.2m$ from the sound source for echo to be perceived by a person located at the source. The wavelength is the distance between successive crests of a wave, especially points in a sound wave or electromagnetic wave.