common misconception out there, that heavy woofers must be "slow",
and light woofers must be "fast". If a woofer A's moving mass
is higher than woofer B's, then woofer A is probably going to be
sloppy, or slow and inaccurate. Can't keep up with the bass
line. Woofer A simply can't respond as fast as woofer B.
Well, on surface this might sound like a logical assumption.
However, it is in fact incorrect! More to the point, moving
mass has precious little to do with woofer speed or signal response!
And we'll prove it...
Go back to good old Newtonian physics... We're going to
start with the famous law:
F=ma (eq 1)
Or force equals mass times acceleration. Anyone who's been
through introductory physics (or watched a bit of PBS) should be
familiar with the equation above. It's pretty much the bedrock
equation of Newtonian physics - it's number 2 of the Big 3 Newtonian
equations (the first being about interia, and the third being about
Now, let's look at a loudspeaker... What do we have?
We have a coil of wire which creates an alternating magnetic field
which interacts with the static magnetic field in the gap (see our
page on DVC subs for a bit more
information on this). How does the alternating magnetic field
of the coil come into being? Well, the magnetic field is
created by passing a current through the voice coil. As the
current through the voice coil changes, the magnetic field created
by the coil changes. This field interacts with the static
magnetic field of the permanent magnet, and you get a force - the
cone moves in and out. Just like two permanent magnets will
attract/repel each other depending upon how they are oriented.
And a bigger current means more force. Just like
bigger/stronger permanent magnets mean stronger
Additionally, what if we make the field of the permanent magnet
stronger? Well, that's call the B field in the gap.
Increase B, we increase the force as well. Or, what if we
could somehow make the magnetic field from the voice coil stronger?
We can - increase the number of turns of the voice coil (increase
the Length of the wire in the gap). Guess what - in both
cases, we increased the BL of the speaker (yes, this is the BL of
the T/S parameters - now you know where it comes from!).
Now, let's go back to equation 1... Let's define each of
the terms in that equation so we know what we're talking about:
|m = mass (moving mass)|
|a = acceleration|
So, what is the Force (NO Star Wars jokes, please!). From
above, we see that the force on the cone is the motor force factor
(BL) times the current. So, let's rewrite equation 1 in these
terms that are applicable to the loudspeaker:
= ma (eq 2)
So, the Motor Force Factor BL
times the current i equals the moving mass of the
driver m times the acceleration of the driver a.
Note that we have italicized i and a.
There's a reason for it!
Now, back to the original question -
transient response of a driver. What is transient response?
Simply a measure of how fast the driver can respond to the input
signal. That means that - inherently - there is a time
dependency on the driver. How much TIME elapses before the
driver responds. So, let's look at equation 2, and cancel
out all terms that are not based on time. After all, if a
quantity is time-invariant, then it won't affect time-variant
effects like transient response (think of this as a simple
Or, to put it in an analogy, does the 1/4 mile time of a vehicle
depend upon where you start? No, the distance over which you
measure is still 1/4 mile. So whether you start in front of
your house and go straight 1/4 mile, or motor on down to the
dragstrip and go 1/4 mile doesn't really affect the car's 1/4 mile
time. The 1/4 mile time is strictly dependent on how fast the
car can accelerate from a dead stop over a 1/4 mile length.
looking at equation 2 we see that:
|BL is time invariant, assuming small excursions
(assume an ideal motor with a flat BL curve; I know, most
drivers don't have that, but assume that it does, like our XBL2
enabled motors). So BL is essentially a constant.|
|i is the current into the driver (we used
italics to indicate a parameter that is time-variant).
This is the music, or test tone sweep, or whatever signal is
coming from the amp. It's an AC waveform so by definition
it changes with time.|
|m is mass. Well, if the moving mass of the
driver is changing as you operate, you've got big problems!
The weight of the cone, dustcap, former, voice coil, surround,
and spider are pretty much fixed. The don't change either.
So m is essentially a constant.|
|a is the acceleration. This is what
we're after. After all, acceleration IS the transient
response - it's what dictates how fast the driver can change
speed, which also means it dictates how fast the driver can move
from position to position. And note that it's in italics,
too. After all, acceleration in the time-variant parameter
we care about here!|
So, let's rewrite equation 2, and replace the time-invariant
parameters with a simple "C" to indicate a constant (a parameter
that does not change with time):
Ci = Ca
(eq 3) or i :: a (eq 4)
(note: the "::" symbol is the mathematical
symbol for proportionality; that is, i is proportional to
Interesting! This says that
acceleration of a driver - how fast it can change position - is
strictly a function of the current through the driver. In
fact, if you could make the current change infinitely fast, then
the driver would accelerate infinitely fast, and we'd have
infinite transients - zero time to change between states.
Infinite frequency response.
So, now that we know that current
is the driving force (pun somewhat intended) behind driver
acceleration, let's look at what limits how fast we can ramp
current through the driver. Because if we are not
restricted in how fast we can change the current, then we are
not restricted in how fast the driver can accelerate - transient
response is not limited at all.
So, back to that loudspeaker
model... A loudspeaker is a coil of wire wound on a former
that attaches to the cone. The current flows through the
coil, creating an alternating magnetic field that interacts with
the static magnetic field of the permanent magnet. So,
what could limit current flow? Well, what does a voice
coil look like?
How about an inductor? You know, those
coils of wire (hey, isn't that what a voice coil is) that you
use in crossovers? Guess what - a voice coil IS an
inductor! In fact, an inductor stores its energy in the
magnetic field (as opposed to a capacitor which stores its
energy in the electric field). It is this magnetic field
of the voice coil "inductor" that interacts with the permanent
magnet field we talked about above. Hey, a loudspeaker is
an inductor hung on the end of a cone in a static magnetic
So, what about an inductor will alter the way current
flows? Well, inductors don't like to have the current
flowing through them change. They like to hold the current
constant. They will allow you to change the current
flowing in them, but the bigger the inductor (or, the higher the
measured inductance) the longer it will hold the current before
it starts to change (I'll leave it to the reader to go research
inductance on their own, to learn why this happens).
voice coil is an inductor. And we see that inductors don't
like to change current. But we also see from equation 4
above that we need to change the current if we want to change
the acceleration. So, the voice coil doesn't want us to
change the current. How good is it at holding the current?
Depends upon the inductance! The higher the inductance of
the driver, the longer it can hold the current flowing through
it. Which means the more time elapses before it starts to
respond to the amplifier's applied voltage. Which means we
have slower transient response.
Guess what - we just answered
the original question! It turns out that transient
response of a woofer is not a function of the moving mass, as is
commonly espoused (one of the most infamous audio myths).
In actuality, it is based upon the inductance of the driver.
And the greater the inductance, the slower the driver - the
lower the transient response.
Mass isn't the problem -
inductance is. So if you want faster transient response,
ignore that moving mass parameter that some manufacturers push -
look at the inductance! And if they don't list the
inductance, ask yourself why - is there something they don't
want to show? Inductance is the key to driver transient
response - ask for it when transient response comes up!