Question

To increase loudness of the sound by four times, by how much
should the amplitude of vibration be changed?

Answer 1

Loudness is directly proportional to the square of amplitude. So to increase the loudness by 4 times:- Loudness should be directly proportional to twice the square of amplitude.

Answer 2

Answer:

• To increase the 'loudness of the sound' by four times, the amplitude should be increased to the 'square of amplitude'.
• A sound is produced by vibrating a body. The 'loudness of the sound' produced depends upon the 'amplitude of the vibrations' made by the vibrating body.
• With an increase in vibrations, the amplitude will increase and the loudness also increases. When amplitude is more, the sound is more and when amplitude is less, sound is less or feeble.  
• Loudness is proportional to the 'square of the amplitude'. So when the amplitude is 'doubled', then the "loudness of the sound" produced will be increased to four times.