Chapter 13, Problem 9A

How does the intensity of light, radiation, and sound change when a point source is twice as far away?

To determine

To explain: Effect on intensity of light, radiation and sound due to given condition.

Answer to Problem 9A

The intensity of light, radiation and sound becomes one-fourth of the original value.

Explanation of Solution

Given:

Point source is twice as far away that is $d\text{'}=2d$

Formula Used:

The inverse square law is given as,

  $\text{Intensity }\propto \frac{1}{\text{Distance}}$

Calculation:

In a three-dimensional space, light, sound and radiation are evenly radiated outward from a point source. So, intensity of light, radiation and sound will follow inverse square law.

Since, distance is doubled that is $d\text{'}=2d$

So, the effect on intensity will be

  $I\text{'}=\frac{1}{{\left(2d\right)}^2}=\frac{1}{4}I$

Conclusion:

Therefore, the intensity of light, radiation and sound becomes one-fourth of the original value.