Question

How does the intensity of a sound wave change if the distance from the

source is increased by a factor of 4?
A. The intensity decreases by a factor of 4.
B. The intensity increases to by a factor of 16.
c. The intensity decreases by a factor of 16.
D. The intensity increases by a factor of 4.

Answer 1

The new intensity decreases by a factor of 16.

Step-by-step explanation:

The intensity of sound wave is given by :

`I=(P)/(A)`

P is power

A is area

`I=(P)/(4\pi r^2)`

or

`I\propto (1)/(r^2)`, r is distance from the source

If the distance from the source is increased by a factor of 4, r' = 4r

So,

`I'=(1)/(r'^2)\\\\I'=(1)/((4r)^2)\\\\I'=(1)/(16)* (1)/(r^2)\\\\I'=(I)/(16)`

So, the new intensity decreases by a factor of 16.