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?

Answer 1

Given: a = 2a

f = `"f"_0/4`

Formula: I ∝ a²f²

 To find: I_new = ??

I_new ∝ 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"`