Chapter 23, Problem 22SP

Three seconds after a gun is fired, the person who fired the gun hears an echo. How far away was the surface that reflected the sound of the shot? Use 340 m/s for the speed of sound.

To determine

The distance of the surface, which reflected the sound of the shot, from the observer when the observer hears the echo of the sound of gun fire after $3\text{ s}$.

Answer to Problem 22SP

Solution:

$510\text{ m}$

Explanation of Solution

Given Data:

Speed of the sound is $340\text{ m/s}$.

Time of receiving the echo is $3\text{ s}$.

Formula Used:

The formula for distance is

$d=vt$

Here, $d$ is the distance, $v$ is speed, and $t$ is the time.

Explanation:

Echo is defined as the reflection of sound thatreaches to the observer after reflection from any surface with some delay.

Thus, the distance travelled by the sound during the echo is twice the distance of the reflecting surface from the observer.

$d=2d^{\prime }$

Here, $d^{\prime }$ is the distance of the reflecting surface from the observer.

Recall the formula of the distance travelled:

$d=vt$

Substitute $2d^{\prime }$ for $d$

$\begin{array}{c}2d^{\prime }=vt\\ d^{\prime }=\frac{vt}{2}\end{array}$

Substitute $340\text{ m/s}$ for $v$ and $3\text{ m/s}$ for $t$

$\begin{array}{c}{d}^{\prime }=\frac{\left(340\text{ m/s}\right)\left(3\text{ s}\right)}{2}\\ =510\text{ m}\end{array}$

Conclusion:

The distance of the reflecting surface is $510\text{ m}$.