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Question
Let the source propagate a sound wave whose intensity at a point (initially) be I. Suppose we consider a case when the amplitude of the sound wave is doubled and the frequency is reduced to one-fourth. Calculate now the new intensity of sound at the same point?
Solution
Given: a = 2a
f = `"f"_0/4`
Formula: I ∝ a2f2
To find: Inew = ??
Inew ∝ a2f2
`"I"_"old" prop "a"_0^2 "f"_0^2`
`"I"_"new" prop (2"a"_0)^2 ("f"_0/4)^2`
`therefore "I"_"new" prop 4/16 "a"_0^2 "f"_0^2`
`=> "I"_"new" = 1/4 "I"_"old"`
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