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

AI Thread Summary
To reduce sound intensity by 20 decibels, the man must move from 3 meters to 30 meters away from the siren. The intensity level is calculated using the formula 20 = 10 log(I/I0), which indicates that a tenfold increase in distance results in a 20 dB decrease in intensity. The inverse square law applies, confirming that sound intensity diminishes with distance. The discussion highlights confusion around using logarithmic equations for sound intensity calculations. Ultimately, the correct distance for a 20 dB reduction is established as 30 meters.
ongobongo
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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
 
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welcome to pf!

hi ongobongo! welcome to pf! :smile:

start with 20 = 10 log(I/I0) :wink:
 
hi thanks for the hint but honestly i can't make heads or tails of the equation
 
simplify 20 = 10 log(I/I0)
 
I=10*10
√100 = 10
10*3 = 30m
 
ongobongo said:
I=10*10
√100 = 10
10*3 = 30m

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

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