Answered

Which statement is true about the loudness of sound?



AIt is directly proportional to the distance of the listener from the source.



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



CIt is directly proportional to the square of the distance between the listener from the source.



DIt is inversely proportional to the distance between the listener from the source.

Verified Answer :

AL2006

Just like the gravitational force, the electrostatic force, the perceived
brightness of a light, and the strength of a radio station . . .

The loudness of a sound is inversely proportional to the square of
the distance between the observer and the source.

Answer : The correct option is, (B)

Explanation :

There is a direct relation between the loudness of sound and the intensity of sound.

\(L=10\log \frac{I}{I_o}\)         ..........(1)

where,

L = loudness of sound

I = intensity of sound

\(I_o\) = intensity of reference

From this we conclude that the loudness is directly proportional to the intensity of the sound.

There is an indirect relation between the intensity of sound and the distance of the listener from the source.

\(\frac{I_1}{I_2}=(\frac{d_2}{d_1})^2\)          ...................(2)

From this we conclude that the intensity of sound is inversely proportional to the square of the distance of the listener from the source.

From equation (1) and (2) we conclude that the loudness of sound is inversely proportional to the square of the distance of the listener from the source.

Hence, the correct option is, (B)

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