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Let the source propagate a sound waves w...

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 ?

Text Solution

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Intensity of sound wave = `I_("old")`
Amplitude is doubled = 2A =`A_("new")`
frequency is reduced to are fourth
`f_("new") =1/f f`
Intensity `I_("new")` = ?
`I=2pi^(2)rho v f^(2) A^(2)`
`I_("old") propto f^(2)A^(2)`
`I_("new") propto 1/4 I_("old")`
`I propto A^(2)/f^(2)`
`I_("new") propto (4A^(2))/(1/16f^(2))`
`I_("new") propto I_("old")`
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