What are the steps for reducing sound intensity by 20 decibels?

[ongobongo]

Homework Statement

A man stands 3m from a siren. How far does he have to move to reduce the intensity level by 20 decibels?

Homework Equations

Intensity level = 10log(I/Io)
the inverse square law

The Attempt at a Solution

i know the answer is 30m because 10 times the distance drops the intensity by 20 dB although i don't understand how to use the equations to answer such a question, what are the steps involved

 

[tiny-tim]

welcome to pf!

hi ongobongo! welcome to pf!

start with 20 = 10 log(I/I₀)

 

[ongobongo]

hi thanks for the hint but honestly i can't make heads or tails of the equation

 

[tiny-tim]

simplify 20 = 10 log(I/I₀)

 

[ongobongo]

I=10*10
√100 = 10
10*3 = 30m

 

[tiny-tim]

I=10*10
√100 = 10
10*3 = 30m

yeees … i think you've got it, but i can't really tell

shouldn't your proof have an I₀ in it somewhere? and some reference to logs?