How to calculate sound intensity when given decibels

[DMOC]

Homework Statement

When a person wears a hearing aid, the sound intensity level increases by 30.0 dB. By what factor does the sound intensity increase?

Homework Equations

B = (10 dB) log (Ia/Ib)

Ia = sound intensity
Ib = threshold of human hearing (1.0 * 10^-12 W/m^2)

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.

 

[Delphi51]

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.

 

[rock.freak667]

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

 

[DMOC]

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!