Question

You are given information on the intensity level (which is a measure of the sound intensity) at a point and its distance from the sound source. To make use of this information, you will need to determine the relation between sound intensity and distance from the source. Which of the following statements correctly expresses that relation?
a) The intensity at any distance r is directly proportional to r.
b) The intensity at any distance r is directly proportional to r^2.
c) The intensity at any distance r is inversely proportional to r.
d) The intensity at any distance r is inversely proportional to r^2.
e) The square of the intensity at any distance r is directly proportional to r.
f) The square of the intensity at any distance r is inversely proportional to r.

Answer 1

Answer:

d) The intensity at any distance r is inversely proportional to r².

Explanation:

The power per unit area is know as intensity of the sound.

$I=\dfrac{P}{A}$

The dimension of power is W so the dimension of the intensity will be W/m².

The sound intensity (I) at any distance r given related as

$I\alpha \dfrac{1}{r^2}$

Intensity I is inversely proportional to r²

$I\alpha p^2$

p=Pressure

So we can say that

$\dfrac{I_1}{I_2}=\dfrac{r_2^2}{r_1^2}$

So the option d is correct.