Sub output: Is it the woofer size or the rated RMS

>In any subwoofer output, how important is the Watt output versus the woofer size?

Speaker efficiency is at best proportional to cabinet size and inversely proportional to the cube of the low frequency cut-off.

So all else equal, it's going to take 4X the power to maintain a given output level and bass extension in a 1 cubic foot box (like a Sunfire sub-woofer) versus a 4 cubic foot box.

You can't compare power without comparing box size.

>In any subwoofer output, how important is the Watt output versus the woofer size?

This also depends on the frequency range of interest.

The air you need to move quadruples with each octave decrease in frequency.

A driver with twice the area (say a 15" driver versus a 10" driver) can play 6dB louder. A longer stroke often goes with the larger diameter; if that doubled from 12 to 24mm you'd get a total of 12dB more output at low frequencies given enough amplifier power to use the excursion.

At higher frequencies you're limited by the power needed to overcome the stiffness provided by the air spring in the box + suspension; and at the highest frequencies you're limited by the power needed to accelerate the driver.

>A driver with twice the area (say a 15" driver versus a 10" driver) can play 6dB louder. A longer stroke often goes with the larger diameter; if that doubled from 12 to 24mm you'd get a total of 12dB more output at low frequencies given enough amplifier power to use the excursion.

Also note that since drivers are rated based on total basket diameter and that doesn't grow as much with the rest of the driver the surface area differences are greater with smaller drivers.

An 8.5"/22cm driver can have nearly twice the area of a 7"/18cm driver. (220 vs. 126 cm^2)

>One correction - membrane of 18" speaker should be 10.5 times heavier because it should be 3.24 times thicker and the area is 3.24 times larger. That is probably why definition is getting poor (too heavy).

It's entirely about extended frequency response, which only matters when you're using the driver at high frequencies as in a musical instrument amp. It's not an issue for sub-bass drivers in multi-way audio playback systems.

In spite of the name, bass guitars generate harmonics out to 5 kHz which is well into tweeter territory. Punch can be an 800 Hz phenomenon.

No matter what you do with the motor, larger diameter speakers without a phase plug have reduced power response (total power output in a sphere at a given frequency) at high frequencies the problem being that their radiating diameter is large compared to the wave lengths being reproduced so the sound from two points can be out of phase and cancel or at least add incoherently for less total output. For instance, a hypothetical 18" diameter cone (maybe a 21" driver) would have the 90 degree off-axis output 180 degrees out of phase at 376 Hz (sound travels at 1130 feet/second in air; 1130/2/1.5 = 376)

The force generated by the motor is a product of the magnetic field strength
(B), length of wire in the magnetic gap (L), and current flowing through the wire. Current is voltage divided by impedance. Voltage is fixed - it's just the instantaneous musical signal.

There are limits to how strong you can make the magnetic field especially given money, space, and or weight budgets - 40 pounds of motor isn't cheap or small so to overcome more moving mass (Mms) means a longer wire (L). More wire means more resistance which reduces current at all frequencies. You can increase the voice coil wire diameter for less resistance to compensate at the expense of weight and a wider magnetic gap which in turn means less field strength. Wire coils form inductors, and more turns mean more inductance. Inductor impedance is proportional to frequency (2 pi f * L) so current is less at high frequencies with the net effect being a heavy speaker cone + strong motor has less high frequency output.

On-axis this is compensated some by the driver coupling more efficiently to the air as its diameter becomes large relative to the wave length produced.

Cross the sub-woofer over at 40-120Hz and it's not an issue. With a good motor design you can even mate a 15" mid-bass to a wave guide at 1Khz.

>Drew -- doesn't your response overlook bass damping, inertia of the cone and the other parts of the moving assembly, and the ability of the cone to stop quickly when the input signal stops? All of which I think support what Kijanki was saying.

Bass damping is a separate issue which also isn't related to driver size.

It's determined entirely by the transfer function.

How you get to a given Q (the ratio of stored to dissipated energy) isn't relevant to decay. Even convolving the input to a sealed or open baffle enclosure with a Linkwitz-Transform or shelving low-pass filters works (although with a small box the distortion from air-spring non linearities and power required make a large box more desirable).

Resonant devices (ports and passive radiators) rely on stored energy and may cause audible problems when within the musical power spectrum, but work fine to gain infrasonic extension.

Stored energy in the room is a much bigger problem than in sub-woofers built for flat response, with decay and the resulting amplitude response being very frequency dependant.

The relative significance of time and amplitude aberations is not well understood here. Stimulating fewer room resonances through directional bass works well (this implies dipoles which are dumping most of their power into an acoustic short circuit). Equalizing for flat steady state amplitude response seems to work. Sub-woofers at a null or two sub-woofers centered on the null work according to literature. Catch-throw arrays look real interesting.

Two sets of two (mounted push-pull to cancel even order harmonics) dipole sub-woofers equalized to a second order roll-off with poles at 20Hz (Q=.5) did produce the most natural bass I've heard from any room-loud speaker system in spite of having only 13x19x8' to work with and no acoustic treatments.

>Shadorne - I wasn't thinking of slap and 5kHz when I mentioned 10" woofer's bass definition - for that bass enclosures have tweeters. I was thinking of low frequencies. 10" woofer arrays have better controlled/damped (shorter) bass while 18" woofers tend to produce "woolly" bass. The question is what is cheaper - 18" woofer or 3 x 10" woofers (to obtain the same surface area).

You can't extrapolate from instrument speakers driven with a wide bandwidth signal (even with a tweeter you may be running the main driver out to 2Khz) that are engineered to break up in a pleasing way to hi-fi drivers run in a narrow bandwidth (not even out to 200Hz) containing entirely wave lengths that are much larger than the speaker that are supposed to be true to whatever signal you're feeding them.

>It seems to me that a bigger, thicker, heavier cone would have reduced "compliance," if that is the right term, and therefore require a greater degree of damping than a smaller, lighter cone.

By the time you've built a speaker with a given pair of high-pass poles it doesn't matter whether the driver in question is a 26 gram 8" mid-bass, 166 gram 12" sub-woofer, something smaller, or something bigger.

Most of the damping is electrical. For instance, the Peerless 830452 bass drivers in my Orions have an electrical Q of .22, mechanical Qms of 3.90, and total Qts of .21 (those drop a bit in the H-frames due to the mass of the air).

When you make the motor stronger to maintain efficiency in spite of the heavy cone and stiff air spring, it's stronger when braking too.

>Putting it another way, couldn't the smaller, lighter, more compliant driver get away with a higher-Q enclosure, which would partially offset its limitations in low frequency extension and volume?

No. Qs higher than .707 produce a pass-band peak which is audible.

While a reasonable psycho-acoustic trick to give the impression of missing octaves for tiny speakers you don't want it in sub-woofers where tightly spaced equal loudness curves make a small peak especially noticeable. High-Q resonances are what give box store sub-woofers that anoying one-note boom-boom quality.

>Shadorne - I was thinking of three 10" woofers versus one 18" woofer (same area).

That's a bad comparison, because the bigger driver can have more excursion. The bigger surround can move farther, bigger basket accomodates a bigger spider which can move farther, etc.

You'd need 6 long-throw 10" drivers (DPL10 with 333 cm^2 Sd and 19mm xmax) to match one healthy 18" driver (Maelstrom 18 with 1182 cm^2 Sd and 33mm amax).

>You'd need 6 long-throw 10" drivers (DPL10 with 333 cm^2 Sd and 19mm xmax) to match one healthy 18" driver (Maelstrom 18 with 1182 cm^2 Sd and 33mm amax).

It's probably a bad specific example (the DPL is a high-Q driver appropriate for dipoles and infinite baffles) but there just aren't a lot of high-quality 10" drivers out there.