Eavesdropping! (Physics-Sound)

You are trying to overhear a juicy conversation, but from your distance of 21.0m , it sounds like only an average whisper of 25.0dB . So you decide to move closer to give the conversation a sound level of 75.0dB instead.

How close should you come?

$dB = 10*log(I / I_0)$

$25 =10*log(I_1/I_0)$

$I_1/I_0 = 10^2.5$


$I_2/I_0 =10^7.5$

$I_2/I_1 =10^7.5-2.5 =10^5$

We know that $I = C/R^2$ (because the sound wave front is spherical) where $C$ is a constant

$I_2/I_1= (R_1/R_2)^2 =10^5$

$(21/R_2)^2 =100000$

$R_2^2 =21^2/100000 =0.00441 m$

$R_2 = \sqrt{R_2^2} =6.6 cm$