Originally Posted by sc00by4life
edited out to reduce post length....
I don’t think we are quite understanding each other. I am treating the hella tones as a “single” 118db source. I am not looking at them individually.
Ok so I think we can agree on the following points:
(1) treating one hellatones pair as a “single” 118dB source
(2) Assuming no manufacturing differences between two pairs they should have the same: amplitude, intensity (which is actually what we mean when we say power in this thread- given the equations you have provided), frequency output and phase of the signal
Now the important part of point 2 is that the frequency output and the phase in this case of the signal between two pairs is the same (ie: just to re-iterate there are no difference between our 2 sources – where 1 source equals one pair of hellatones).
Now two signals with equal frequency and a definite relationship between their phase (in this case there is a definite relationship because they are the same phase!) are coherent sources. if these conditions are not met then they are incoherent sources.
I believe you will agree with the above point because the sources are identical. Again to reiterate 1 source =118dB pair of hellatones
So now on to the main theory, if the two signals are incoherent you would be correct in adding the power/intensity and the 3dB increase would be correct. However because these are identical sources (ie: coherent) you cannot add the intensities, you must add the amplitudes (which means quadrupling the power/intensity as the power/intensity is proportional to the square of the amplitude.
Therefore for two identical (coherent) sources, adding two together gives you a 6dB increase.
(1) It is explained in section 3 "addition of two sounds" of the following reference (specifically read the first 2 paragraphs, the be sure to look at 3.2.1 where they work through the addition of two coherent sources and demonstrate that two identical sound sources added together results in a 6dB increase):
(2) the end of section 6.2 in the following source (they note below the equations if both are in phase coherent sources the increase is 6dB):
and the following is a quick calculator tool for adding two coherent (identical) sources together and you’ll see you get 124:
Amid the rims and tims, CAIs and exhaust threads this is actually a pretty interesting discussion