Why Does Doubling Sound Sources Not Simply Double the Decibel Level?

[somecelxis]

Homework Statement

A source prodeuces sound of intensity level of 30dB .If another source prodeuces sound at the same time , what's the resultant level?

Homework Equations

The Attempt at a Solution

the ans is 10 log (2$I_1$ / ($I_0$)) = 33dB , but why not = 10 log (4$I_1$ / ($I_0$)) .. beacuse when 2 sound waves superposed , the resultant amplitude is A+A= 2A , I is directly proportional to (A^2) ...

 

[olivermsun]

Are the two sounds correlated (e.g., in phase) with each other? The sum of the two will only have amplitude A + A (and therefore +6 dB) if they are perfectly in phase with each other. In general they're assumed uncorrelated (they have nothing to do with each other), and so you add the intensities and get +3 dB.

 

[somecelxis]

Are the two sounds correlated (e.g., in phase) with each other? The sum of the two will only have amplitude A + A (and therefore +6 dB) if they are perfectly in phase with each other. In general they're assumed uncorrelated (they have nothing to do with each other), and so you add the intensities and get +3 dB.

it's not 3db am i right? the intensity now it's 2I ?

 

[olivermsun]

33 dB is +3 dB relative to the original 30 dB, right?

Hint: log₁₀2 = ?