By how much will the loudness of a sound change when the amplitude of vibration is: A) doubled, B) tripled.

LOUDNESS = (amplitude)2
Amplitude is doubled then, the loudness of the sound becomes 4 times increased.
and If the amplitude is tripled, then the loudness is 9 times increased.
 
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Dear student

The loudness of a sound is the square of its amplitude. When amplitude is doubled, the loudness increases 4 times whereas when the amplitude is triped, the loudness is increased 9 times.

Regards
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The loudness of a sound is the square of its amplitude. When amplitude is doubled, the loudness increases 4 times whereas when the amplitude is triped, the loudness is increased 9 times.

 
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