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Suppose I have four identical speakers, say 8 ohms each. There are two ways I can combine them:

  • Two in series would be 16 ohms, and running them in parallel with another identically connected pair would result in 8 ohms.

  • Two in parallel would be 4 ohms, and running them in series with another identically connected pair would result in 8 ohms.

Except for being able to handle 4 times as much power, would the resulting setups have identical sound and electrical characteristics as an individual speaker?

The two setups have identical wiring except for a cross connection in one but not the other. In theory there will never be any current in that connection, but in practice, is one way better than the other?

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Electrically, yes. Acoustically no. You also have to take into consideration the physical effects of having multiple point-sources of audio, specifically the way that each point-source interacts with the other. IF you are placing these four speakers inside a single cabinet, then there are other acoustic effects relating to bass porting and cabinet volume to consider. You might want to look at 'line arrays' and the acoustic characteristics of these devices.

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