Which statement is true about the loudness of a 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.

Answer : The correct option is, (B)

Explanation :

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

 ..........(1)

where,

L = loudness of sound

I = intensity of sound

= 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.

  ...................(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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