You are trying to overhear a juicy conversation, but from your distance of 15.0 , it sounds like only an average whisper of 35.0 . So you decide to move closer to give the conversation a sound level of 60.0 instead. How close should you come? (in cm)

Question

You are trying to overhear a juicy conversation, but from your distance of 15.0 , it sounds like only an average whisper of 35.0 . So you decide to move closer to give the conversation a sound level of 60.0  instead. How close should you come? (in cm)

drwls · Answer

You need to get closer to the speaker so that the sound power per area is increased by a factor 10^2.5 = 316. According ti the inverse square law, this will require getting closer by a factor sqrt (316) = 17.8. This will put you just abut 1 cm away from the speaker's lips.