Question

A boy stands between the two walls as shown below and he claps his hands.


If ‘x’ is less than $60m$ and the time between the first and the second echo is $0.25s$, then calculate the distance ‘x’.
Velocity of sound in air is $344m{s}^{-1}$.

• A. $36m$
• B. $17m$
• C. $40m$
• D. $34m$

Answer 1

The correct option is B $17m$

Given:
Speed of sound, $v=344m{s}^{-1}$
Time difference between the first and the second echo, $\Delta t=0.25s$.

Total distance travelled by sound in $0.25s$ is
$\Delta s=v\Delta t$
$\Delta s=344\times 0.25=86m$

The distance of boy from the right wall is $60m$, the total distance travelled by the sound in the second echo is:
$s_2=120m$

The distance of the boy from the left wall is $x$.
The total distance travelled by the first echo is: $s_1=2xm$.

Total distance travelled by sound in $0.25s$ is equal to the difference in the distance covered by the second echo and the first echo.
$\Delta s=s_2-s_1$
$86m=120m-2x$
$x=17m$