Here’s my question.
Guitar speaker cabinets come in 3 common sizes, those with
1, 2, or 4 12" speakers. Now, almost all of these cabinets
are rated at 8 ohms.
Now, ohm’s law says that if R and V stay constant, then I and
therefore P also stay constant, so you would assume the
same amount of power is going through these speakers.
Why are the 4 12" speakers which impede 8 ohms louder than
the 1 12" speaker which impedes 8 ohms?
A 4 12" speaker cabinet shouldn’t be any louder, but it should sound tighter. (All things being equal)
Loudness isn’t due to power, it’s due to voltage. Power mostly just lets you go quickly from low volume to jugh volume (called dynamic range). If the elements are wired in parallel, the voltage across each speaker element is constant, and equal to the supply voltage (that is, the voltage of the final amplifier output). Each speaker element is operating in phase, and so constructively interfere, thus, more elements, more volume.
They’re not wired all in parallel. They’re two series circuits wired
in parallel.
You’ve quadrupled the cone area, which will give a 6 dB increase in SPL.
You can also get a 6 dB increase over a single 8 ohm speaker by wiring two in parallel. You get a 3 dB increase from doubling the cone area, and another 3 dB increase from halving the impedance. Of course in this situation, you’re drawing twice as much power from the amp.
Or, if you wire two 4 ohm speakers in series, you get a 3 dB increase for the same power input.
well a 4x12 cab is 4 8 ohm speakers, with two pairs of speakers
in parallel wired in series.
like
- S - S -
| |
+ --- - S - S ----- -
Well, yes, I understand that, and I’ve already given you the answer: “You’ve quadrupled the cone area, which will give a 6 dB increase in SPL.”
SPL, by the way, stands for sound pressure level.
how much is 6 db?
okay another question.
How is two 16-ohms in parallel compared to 1 8-ohm?
Two 16 ohm speakers in parallel gives the same result as two 4 ohm speakers in series, i.e., a 3 dB increase in SPL.
How much is 3 dB?
A 3 dB increase is equivalent to a doubling in power. It’s the equivalent of increasing the amplifier output from, say, 50 W to 100 W.
A 6 dB increase is equivalent to a quadrupling in power. It’s the equivalent of increasing the amplifier output from, say, 50 W to 200 W.
So your 4 speaker set-up driven by 50 W sounds as loud as a single speaker driven by 200 W.
But twice as much power doesn’t mean twice as loud, and four times as much power doesn’t mean four times as loud.
A 1 dB increase in SPL is about the minimum that the human ear can detect. So 3 dB is definitely noticeably louder, but nothing like twice as loud.
An increase of 3 dB is a doubling of SPL. 10 dB is ten times the SPL.
As Desmostylus said, it depends on cone surface area. All things being equal, two 10 ohm elements in parallel will be twice as loud as one 8-ophm element, even though their total impedance is the same.
you mean 16 ohm elements?
Ignoring heat losses and frequency response differences and “antenna pattern” effects, input power translates directly to acoustic power.
In theory, ten watts of electrical power MUST always have the same loudness regardless of the number of transducers used. Anything else would violate the conservation of energy rule.
But we CAN’T ignore inefficiency (loss as heating), or different frequency curves, or different radiated patterns! These are where the differences lie.
For example, if you have a single small speaker being fed a couple of KHz pure tone, it acts as a “point source” of acoustic radiation, and the sound will spread in all directions uniformly. But if you have several speakers wired together, then they generate something resembling a plane wave. The sound will come out as a narrow beam. Broadside to the speaker array the loudness will be high, but at other listening locations it will be far less or even zero. The TOTAL might be the same as for a single speaker, but the sound isn’t spread uniformly any more.
As for frequency response differences, you have to measure the actual impedance of one speaker versus several. “Eight ohms” is just a rule of thumb, an average taken over a wide band of frequencies. Weird things can happen, and eight ohms might be a total mistake. For example, if you have two small speakers in separate cabinets in separate rooms, then their combined series impedance will give a certain value, but if you put them in a sngle cabinet, then together they behave as a woofer, as one much larger cone, and their impedance at low frequencies will be very different than the impedance of two widely-separated small speakers.
Hey, just build one of those huge electrostatic loudspeaker panels. That way you get millions of tiny speakers all hooked in parallel and arranged in a planar array. Is it a woofer or a tweeter? It’s a square window through which sound flows!
bbeatty’s explanation of why the larger cone area results in greater perceived loudness is correct.
Speaker efficiency is usually measured in dB @ 1 W @ 1 m.
For example a given speaker may have its efficiency expressed as 90 dB @ 1 W @ 1 m. That means that when driven by 1 W input power, the SPL will measure 90 dB 1 m in front of the speaker.
If you look at the efficiencies of speakers that are otherwise similar apart from size (e.g., speakers in a particular series from one maunfacturer), you’ll see a size/efficiency relationship something like this:
6": 87 dB @ 1 W @ 1 m
8": 89 dB @ 1 W @ 1 m
10": 91 dB @ 1 W @ 1m
12": 93 dB @ 1 W @ 1m
The greater efficiency with size doesn’t come from a greater thermal efficiency, but rather from a greater focussing efficiency. More sound is focussed forwards, where it’s being measured, and less to the sides, where it’s not being measured.
A similar effect is observed when you have 2 or more speakers. They form a phased array, which is capable of focussing sound in the forward direction.