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How to calculate sound intensity when given decibels

Tags: decibels, intensity, sound
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Jan13-09, 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.

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Jan13-09, 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.
Jan13-09, 09:08 PM
HW Helper
P: 6,202
Quote Quote by DMOC View Post

10^3 = (I/1.0 * 10^-12 W/m^2)
Right there is your answer. The wanted the factor, I/I0, not the intensity to give 30dB

Jan13-09, 09:32 PM
P: 100
How to calculate sound intensity when given decibels

So I got the right answer all was just that I had to realize that the question asked for what (Ia/Ib) was equal to, not just Ia.


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