Question

You are trying to overhear a juicy conversation, but from your distance of 15.0m, it sounds like only an average whisper of 25.0 dB. So you decide to move closer to give the conversation a sound level of 70.0 dB instead.How close should you come.

Answer 1

sound intensity is proportional to the inverse of distance squared.

10^7/10^2.5 = 15^2/d^2

d^2= 15^2*10^-4.5

d= 15*10^-2.25= 15*.0056= 8 cm

check my thinking.

Answer 2

You have to convert the dB to intensity and then use the relationship between intensity and distance.
So first use:
I=Io*10^(B/10dB) with Io being 10^-12
once you find the intensity for each dB (25 and 80 in this case) you use the relationship:
I1/I2=r2^2/r1^2
following the equations closely should give you the answer in meters and you just have to convert to centimeters. For this particular problem you should get around 3 cm.