Quote from Forum Archives on November 6, 2003, 3:45 pm

Posted by: donlc <donlc@...>

Chris wrote:

> If all other things were equal what are the differences, in sound, of a
> 1x12, 1x15, 2x10, 4x10?

By far, by way far, the differences *generally* have a lot less to do
with size than all the other factors: the nature of the driver, how it
is "tuned" in conjunction with the cabinet, and a fairly significant
but oft-overlooked point, the stiffness of the cabinet walls, to keep
the "rear pressure" inside where it belongs, rather than radiating
unwanted energy all over the place causing harm. (It's surprising how
much sound comes out the back and sides of a bad cabinet! And it's all
"wrong sound", in that it doesn't *belong* outside, doesn't fit.) And
we have cone flexure issues, damping issues, and lots of other things
that make a difference between cabinets. And then impedance issues
that relate to how efficiently we're using amplifier power, and that
sort of thing.

So... When you say "all other things equal," it's really *those*
things that are more interesting than driver size, in real life
practical terms. This 1x12 over here sounds a *gob* different than
that 1x12 over there. It's not the... uh... 1x12-osity that makes it
sound the way it does, it's the *rest* of the story.

That said, *if* all else could be equal, driver size has two primary
influences. One is volume: more cone area is louder. The other is
dispersion: the wider the source, the narrower the dispersion pattern
at a given frequency, or, we might say the dispersion pattern starts to
get narrow "earlier" (i.e. at lower frequencies) as the size goes up.
You can use different standards as you see fit; mine is such that a
rule of thumb makes it easy to compute: dispersion is "good" up to
waves that have a length the same size as the driver, and starts to
fall off at higher frequencies. By three times that frequency, there
is just no dispersion. You *might* be able to hear some if you are
standing smack in front of the cabinet, nice and close, but for all
practical purposes, it just ain't there.

In a multi-driver cabinet, you use the total width, e.g. in a 4x10, er,
ah, 2x2x10 if you get my drift, for purposes of dispersion, you
consider the width to be about 20". A 2x10 has a pattern that's the
same as a 10" driver on one axis, and a 20" driver on the other.

So what's that mean? If my standard is of any use, here are the basic
upper limits of a given driver, assuming 2" of lost diameter due to the
rim and the surround. The equation is

good = 12*1130 / (driver size in inches - 2)
gone = 3*good

10" -- good to 1695Hz, gone at 5085Hz.
12" -- good to 1356Hz, gone at 4068Hz.
15" -- good to 1043Hz, gone at 3129Hz.
2x10" -- good to 753Hz, gone at 2260Hz.

Two 2x10's stacked vertically, i.e. a 10x40 driver:

horizontal good to 1695Hz, gone at 5085Hz.
vertical good to 356Hz, gone at 1070Hz.

Nine 1x15's stacked vertically, with four inches of space between:

horizontal good to 1043Hz, gone at 3129Hz.
vertical good to 82Hz, gone at 246Hz.

The upper limits of these driver sizes reveals why it's so common to
find tweeters in bass cabinets: the big drivers just cain't do it.
It's not a matter of driver quality or cleverness of design or anything
-- it's a simple matter of the size of the wave, and how it "runs into
itself" as it radiates from different parts of the cone at different
angles. It's just *sizes*. But notice, for example, in a 4x10, where
the tweeter is probably crossed over at 2500Hz, there is a gap between
the upper limit of what the 10's can do (side-by-side) and the lower
limit of what the tweeter can do. There's a fairly noticeable midrange
hole in the response; you can hear it... the low driver and high
driver usually sound a little bit "disconnected" from each other. And
that region happens to be one that the human ear is hugely sensitive
to, so it really causes problems *if* what you're after is hi-fi sound.
If you do want hi-fi sound, there really needs to be a bridge in
driver size between the big dog(s) you're using for the low end, and
the tiny little tweeter for the upper end, like maybe a 8" or 6" or 5"
-- thus, you buy an Accugroove or some such, and say "Ahhh! I *get*
it, now! Smooth!" 🙂

- donl