Exercise 10.12
An experiment is being set up that requires echoes to arrive at least s after the emission of sound. What minimum distance should a reflecting surface be placed at? Assume the speed of sound to be m . Modern auditoriums and large concert halls are architecturally
NCERT’s answer
34.$\displaystyle 3$ m
The reflecting surface must be at least $\displaystyle 34.3$ m away.
The sound must travel to the surface and back, so in \(\displaystyle 0.2\ \text{s} \) it covers twice the distance \(\displaystyle d \).
\(\displaystyle 2d = v \times t = 343\ \text{m s}^{-1} \times 0.2\ \text{s} = 68.6\ \text{m} \).
\(\displaystyle d = \dfrac{68.6\ \text{m}}{2} = 34.3\ \text{m} \).
Any nearer and the echo returns sooner than \(\displaystyle 0.2\ \text{s} \), which the experiment does not allow.