(adsbygoogle = window.adsbygoogle || []).push({}); 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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# How to calculate sound intensity when given decibels

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