Question

What is the effect on the 1) loudness of a sound when the amplitude of the vibrating body gets double? 2) pitch of a sound when the frequency of the vibrating body doubled?

Answer 1

1) When the amplitude gets doubled.....
Let Amp1 = x, hence Amp2 = 2x
and Loudness1 = y and Loudness2 = z
We know, Loudness is DIRECTLY PROPORTIONAL to square of amplitude.

Hence, y/z = k.x²/k.(2x)² [where k.x² means k (multiply) x²] and k is a constant

Hence, k and k gets cancelled. We get y:z ratio = x²/4x², where x² and x² gets cancelled.

Hence, y:z ratio is 1:4
Hence the loudness increases by 4 times.

2) Pitch is directly proportional to frequency, hence of frequency is doubled, pitch is also doubled



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