Question

Which statement is true about the loudness of sound?

A.
It is directly proportional to the distance of the listener from the source.
B.
It is inversely proportional to the square of the distance of the listener from the source.
C.
It is directly proportional to the square of the distance between the listener from the source.
D.
It is inversely proportional to the distance between the listener from the source.
Reset Next

Answer 1

B. It is inversely proportional to the square of the distance of the listener from the source.

Step-by-step explanation:

The loudness of a sound is directly related to the sound intensity, which is inversely proportional to the square of the distance between the source and the listener:

`I \propto (1)/(r^2)`

where r is the distance between the source and the listener.

From the formula, we observe for instance that

- if we double the distance between the source and the listener, the loudness is decreased by a factor 4

- If we halve the distance between the source and the listener, the loudness quadruples