If I have two identical speakers facing me which are adjacent to eachother, playing the same music at the same volume, would it be any louder than having just one speaker at the same volume?

If not, where does this extra energy go? Will the sound travel twice as far?


In short, yes, it will be louder.

In the simplest case, if you were able to duplicate the exact signal everywhere in space, you would actually get 4 times the intensity - sound waves add linearly, but intensity adds quadratically. For two uncorrelated sources (if you played different white noise signals through each speaker) you would only get a factor of 2. In the real world, where not everything is exactly in phase everywhere in space will be something in between. (I'll add a sketch of the math later).

But you probably know, it doesn't sound 4 times louder. That's because your ears hear logarithmically - exponential increases in intensity are heard as linear increases in volume. Volume is typically measured in dB (a logarithmic scale), here is a reference that can calculate the dB of coherent and incoherent sources.


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