Chapter 12, Problem 10P

To determine

Difference between the sound level of the explosion

Answer to Problem 10P

Solution:

The sound level explosion is 5 time greater for a person who is standing at a point directly below the explosion than for a person a horizontal distance of 200 m away

Explanation of Solution

Given:

Fireworks explodes, at 100 m above the earth surface

One person standing right below the explosion

Other person is standing at a horizontal distance of 200 m

Formula used:

The loudness or intensity of the sound is inversely proportional to the square of the distance

     $I\propto \frac{1}{r^2}$

Here,

     $r$ is the distance from the sound source

Calculation:

Calculate the distance of 200 m person from the sound source by using Pythagoras theorem

     $\begin{array}{c}{r}_2 =\sqrt{{100}^2+{200}^2}\\ =223.6\text{m}\end{array}$

Now the intensity of sound at the person standing right below the explosion is calculated as

     $I_1=\frac{1}{{100}^2}$…… (1)

Now the intensity of sound at the person standing 223.6 m away from the explosion is calculated as

     $I_2=\frac{1}{{223.6}^2}$…… (2)

Divide the Eq. (1)by Eq. (2)

     $\begin{array}{c}\frac{I_1}{I_2} =\frac{{223.6}^2}{{100}^2}\\ I_1=5I_2\end{array}$

Hence, the sound intensity is 5 times greater.: