How to find the total dB of two sounds?

1. Feb 7, 2015

Summer95

1. The problem statement, all variables and given/known data
The frequency of the two sounds is the same, and the observer is equal distance from either sound source. When one speaker is turned off the loudness is 70dB, what is the total loudness when it is turned back on?

2. Relevant equations
A2∝I
dB=10log(I/I0)

3. The attempt at a solution
$$10log(\sqrt{\frac{2A}{A}})=10log\sqrt{2}=1.5$$
and 70+1.5=71.5dB

but I do not see it done this way anywhere so I don't know what I'm doing wrong

2. Feb 7, 2015

Staff: Mentor

Intensity is amplitude squared, not the other way round. Where does the square root come from?

3. Feb 7, 2015

Summer95

The square root comes from the equation for dB which is 10log(I/I0)

But if you are doubling the amplitude that part becomes √2 right?

4. Feb 7, 2015

Summer95

because Intensity is proportional to the root of amplitude.

5. Feb 7, 2015