Question

Fill in the blank.
Loudness of a sound is proportional to ------- of the amplitude of the vibration producing the sound.
(A) Square
(B) half
(C) cube
(D) quarter

Answer 1

Loudness of the sound is the ability of the sound that makes the hearer able to hear it. It depends upon the amplitude of the sound wave. It is directly proportional to sound amplitude. If the amplitude of the sound is greater, then the sound is said to be loud to hear.
Useful formula:
The relation between the loudness and the amplitude is given by
$l = {A^2}$
Where $l$ is the loudness and $A$ is the amplitude of the sound wave.

Complete step by step solution:
Amplitude is the maximum height at which the wave propagates from the coordinate axis. Loudness of the sound deals with the hearing nature of the sound. The loudness is directly proportional to the square of the amplitude. That means when the amplitude of the sound becomes the power of two, then the loudness of the sound becomes the power of four.
$l = {A^2}$
The unit of the amplitude is metres. The unit of the loudness is decibel. If the loudness of the sound is greater than $80$ decibel, then the sound is assumed to be noise to the human ears and unpleasant in nature. Let us consider that the amplitude of the sound is $5\,m$ , then the loudness of the sound is ${5^2} = 25\,db$ .

Thus the option (A) is correct.

Note: Let us consider the examples and the values for the loudness of the sound.
1. Amplitude of normal breathing is $10\,dB$
2. Amplitude of the normal conversation is $30\,dB$
3. Amplitude of the traffic is $60\,dB$
4. Amplitude of the factory with many sounds is $80\,dB$