Let the source propagate a sound waves whose intensity at a point (initially) be l. 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 ?

Explanation

Intensity of sound wave (old) = `I_(1)`
Amplitude of sound wave `(A_(2)) = 2 A_(1)`
Frequency of the sound wave `f_(2) = (1)/(4) f_(1)`
Intensity of sound wave `I_(2) = ?`
`I_(1) prop f_(1)^(2) A_(1)^(2) , I_(2) prop f_(2)^(2) A_(2)^(2)`
`(I_(1))/(I_(2)) = (f_(1)^(2) * A_(1)^(2))/(f_(2)^(2) * A_(2)^(2)) = (f_(1)^(2) A_(1)^(2))/((1)/(16) f_(1)^(2) * 4 A_(1)^(2)) = (16)/(4) = 4`
`I_(2) = (1)/(4) I_(1)`