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How to calculate sound intensity when given decibels 
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#1
Jan1309, 08:03 PM

P: 100

1. The problem statement, all variables and given/known data
When a person wears a hearing aid, the sound intensity level increases by 30.0 dB. By what factor does the sound intensity increase? 2. Relevant equations B = (10 dB) log (Ia/Ib) Ia = sound intensity Ib = threshold of human hearing (1.0 * 10^12 W/m^2) 3. The attempt at a solution I used the equation above, substituting into it: 30 dB = (10 dB) log (Ia/1.0 * 10^12 W/m^2) I divided both sides by 10 dB to get rid of the 10 dB on the right side of the equation. 3 = log (Ia/1.0 * 10^12 W/m^2) Then I converted this into regular exponential form without logs: 10^3 = (I/1.0 * 10^12 W/m^2) I get 1.0 * 10^9 for I, but my answer key says the answer is 1000. This is 10^3, which I seem to have, but I still have an unknown  I  in the equation. 


#2
Jan1309, 09:07 PM

HW Helper
P: 3,394

Your answer of I = 1.0 * 10^9 is correct.
But the question doesn't ask for I, it asks by what factor has I increased  presumably from 0 db which is the threshold of hearing. So divide your answer for I by the value of Ib. 


#3
Jan1309, 09:08 PM

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P: 6,202




#4
Jan1309, 09:32 PM

P: 100

How to calculate sound intensity when given decibels
So I got the right answer all along...it was just that I had to realize that the question asked for what (Ia/Ib) was equal to, not just Ia.
Thanks! 


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