...An old Tom Danley forum post, with parts i think that fit that discussion......
> > Hi all
> >
> > I am not sure how many Joes are in the "its all magic" camp and how many
> > are interested in how things really work but so far as how a woofer
> > really works, this has been known for some time. Authors like Benson,
> > Heyser have written very good books and papers on the subject.
> > At least from being able to model / predict the performance of a real
> > speaker from its electroacoustic equivalent circuit, there are no
> > missing links or mysteries, just a few things mfr.'s chose not to
> > explain and or things some choose not to look at..
> > Perhaps this explanation will help.
> >
> > The number one misconception about woofers is that moving mass has
> > something to do with "speed" of response or its high frequency limit.
> > It does not, at least directly.
> > What mass effects is efficiency and also the shape of the low frequency
> > roll off.
> >
> > A radiator that is small compared to the wavelength it is producing,
> > experiences an increasing acoustic load with increasing frequency (one
> > of the few places on sees a frequency dependent resistance with out a
> > reactance). That radiator in an infinite baffle, driven at a constant
> > velocity
> > will produce a +6 dB oct rising response because its radiation
> > efficiency increases with frequency.
> > To make a driver like this have "flat response", we must roll off the
> > voltage response 6 dB per octave, one pole.
> > This is done by having a much larger amount of mass or weaker motor such
> > that above some point velocity control is lost and then with increasing
> > frequency, the velocity falls 6 dB oct. It is this range, where the
> > velocity falls 6 dB /oct that one has flat response.
> > Electrically, this speaker looks like and acts like an R/C filter, the R
> > is the coil R+the amplifier source R and the C is the moving mass of the
> > speaker reflected through the motor, which looks /acts like a capacitor.
> >
> > Since the moving part is the C, it is the voltage across it (the voltage
> > /velocity output) which falls 6 dB /oct, which is canceled out by the
> > changing radiation resistance and now gives flat response. The -90
> > degree phase shift of the slope is not canceled out as the radiation
> > resistance is pure resistance. Changing the size of the C (moving mass)
> > has no effect on the slope angle, just its level and starting point.
> >
> > 99% of the people do not realize that when a point source has flat
> > response, its mid band acoustic phase lags behind the input signal by
> > about -90 degrees (once all fixed time delays are accounted for). This
> > broad band lag is equal to a time delay who's amount increases with
> > decreasing frequency. This -90 degree operation is how some of the
> > simpler measuring systems "determine" acoustic phase, it is a Hilbert
> > transform of the amplitude and at low frequencies for a simple piston,
> > this is a safe assumption.
> >
> > Consider how a normal "perfect" speaker spreads out a signal in time.
> > Make an imaginary signal that has equal amplitude content from 100 Hz to
> > 25 Hz, a specific waveshape which has this property.
> > Take an imaginary perfect flat response speaker who's upper and lower
> > cutoffs are way past our needed bandwidth.
> > This mass controlled "flat" response speaker has a -90 degree lag or
> > delay, at 100 Hz the phase shift is equal to a source 2.83 feet behind
> > the speaker cone, at 50 Hz, the delay is equal to 5.66 feet, at 25 Hz is
> > equal to 11.32 feet and so on.
> > This test signal's wave shape defines the input "time" of each frequency
> > component.
> > When reproduced, the highest frequency component at 100 Hz emerges from
> > the radiator 2.5 ms AFTER the signal arrived at the driver terminals.
> > At 50 Hz, this component emerges 5 ms AFTER the signal hit the terminals
> > and at 25 Hz, the signal emerges after 10 ms and so on.
> > With the driver spreading the signals frequency components out in time,
> > it is simply not possible to retain the same waveshape as the input
> > signal, lower frequencies arrive progressively later in time than the
> > original signal.. Any signal reproduced is done so with the spectrum
> > rearranged in time by the drivers acoustic phase response.
> >
> >
> > If one had a driver which had a very strong motor or a normal motor but
> > very low moving mass, one gets an "over damped" response.
> > This term is from filter design meaning that it is not optimally flat,
> > excessively damped, rolling off too soon and gradually
> > Should the slope of the response reach 6 dB per octave, the driver is
> > operating in the Velocity controlled mode, while the response is not
> > flat, the acoustic phase DOES track the input signal (zero degrees) and
> > the different frequency components are not spread out in time.
> > The waveshape of the input signal is more closely replicated as the
> > frequency components are in the original "time" although the amplitudes
> > are off 6 dB/oct. Each 3 dB /oct change in the slope produces a 45
> > degree change in phase.
> >
> > An over damped response more closely retains the time information where
> > a flat amplitude response cannot.
> >
> > A proper LF horn can have flat acoustic response AND roughly zero degree
> > acoustic phase.
> >
> > For a person more sensitive to "time errors", they will likely find an
> > over damped system more realistic.
> > For a person more sensitive to "amplitude errors" the traditional "flat
> > response" system will be more satisfying.
> > For the person lucky enough to have heard a proper lf horn system, you
> > have heard that one can have "lightning fast" sounding bass and still
> > make your pant legs flap.
> >
> > A normal "flat" response point source speaker HAS this kind of delay
> > built right in and it is unavoidable (currently).
> > All conventionally driven point source speakers MUST have the phase
> > shift / delay if they are to have flat frequency response (dictated by
> > the falling velocity, acceleration controlled response needed to offset
> > the changing radiation resistance with frequency).
> >
> > Additional reactance's can alter this phase relationship.
> > For example above midband at the point in the impedance called Rmin, the
> > electrical series "L" is equal but opposite the reflected moving mass
> > (capacitive reactance) of the driver thus canceling each out and being
> > resistive (no phase shift).
> > Above that frequency, the series Inductance dominates and produces a
> > roll off with an inductive reactance.
> > At the bottom end to the response, for a simple sealed box, there is a
> > point where the parallel spring or "compliance" of the box and driver
> > are equal but opposite the moving mass and this point is also resistive
> > (at box resonance). Below that frequency, the spring constant dominates
> > (an inductive reactance) and the acoustic phase leads
> >
> > More complications from non perfect drivers and alignments..
> >
> > In pro sound it is a common practice to evaluate subwoofers with a kick
> > drum signal.
> > Such a signal has a wide spectrum however it makes a bad test signal for
> > a subwoofer alone.
> > Nearly always, the subwoofer with the best "snap" or attack is the one
> > with the greatest distortion and or the highest low cutoff.
> > Clearly, the ear hears the added hf content and judges it to be more
> > lifelike.
> > In actual operation, the subwoofer is mated with midbass speakers who's
> > job it is to produce the spectrum above the subwoofer.
> > Now, with the actual drum signal being produced in the upper ranges, the
> > subwoofers formerly desirable distortion spectrum interferes with the
> > real drum signal. Now, the subwoofer with the least distortion will
> > often have the best subjective sound.
> >
> > A subwoofer can be made with a under damped low frequency corner, this
> > puts a bump in the response right before roll off.
> > Subjectively, this can make a woofer sound even slower and the "decay"
> > of the too high Q takes more time.
> >
> > Remember that it is acceleration which produces sound, it is the
> > amplifier current which produces the force which produces the
> > acceleration.
> > While few of you may have a TEF machine or are able to measure real
> > acoustic phase, most of you can plot the current phase angle with
> > respect to the voltage drive signal for a woofer. The phase shift curve
> > of the current vs freq will have the same shape as the acoustic phase
> > shift (although the degrees are different). If one had a speaker that
> > was flat midband, one could look at the current phase in that range and
> > assume the acoustic phase magnitude was about -90 deg .
> > This acoustic phase IS time, it is essentially ignored in discussions
> > about how speakers sound, yet it accounts for most of what you guys and
> > others are talking about.
> >
> >
> > Tom Danley
