# How to find the total dB of two sounds?

## Homework Statement

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?

A2∝I
dB=10log(I/I0)

## 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

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

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?

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?
because Intensity is proportional to the root of amplitude.

because Intensity is proportional to the root of amplitude.