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Re: Horn stuff and a post back for Tom

Hi Wayne
Sorry for the delay, the holiday is over and there is work to do.
I had a chance to take a high res measurement of the cube I had here which I have not scanned into the computer but will.
That box is gone but I have a different model here now which I will be measuring and will send some from that as well.

Regarding driver delay and acoustic phase:
Beginning with the simplest case, a woofer that is acoustically small and has a flat amplitude response in a sealed box..
This driver is "simple" in that it is minimum phase over most of its pass band (well below break up) and its mechanical system is also simple, a
spring loaded mass, electrically damped with a small radiation resistance.
To be flat in response the radiator must have an "acceleration response" where the motion quadruples with each octave decrease in frequency.
THe drivers moving mass reflected through the transduction and the series resistance provide the "filter slope" it takes to get that response.
Since it is the moving mass acting as a capacitor in the equivalent circuit, the Phase is also that of a 1st order filter which is nominally at -90
degrees. So, when one measures a woofer, one finds that the 90 degree phase lag IS like you say, a variable time delay as 90 degree in phase is
a different amount of time at 20 HZ than 200 Hz.
Below and above mid band, the phase becomes "inductive" when the box/suspension spring dominates and when the series inductance
dominates.
Looking at the electrical terminals, one also finds the same shape phase curve but since the electrical side is separated by the Rdc, it has a
different phase magnitude (but the general shape of the acoustic phase and electrical phase are the same while the driver is minimum phase)
AS the system is only a parallel L,R,C and series R,L, the acoustic output and electrical load can only have up to a + - 90 degree shift, it is only a
second order system.
What your saying is correct then that the speaker, especially a point source direct radiator "moves around in time", it in effect moves front to
back depending on frequency.

Use a laser velocimeter to monitor the cone's motion (because light has no delay here to speak of) and apply a signal, complex in frequency to
the driver.
What one finds is at first, nothing happens, there is no motion.
One finds the speaker has a delay equal to some distance in time and from that delay, the acoustic phase cannot deviate more than the + -90
degrees as dictated by the equivalent circuit.

A highly loaded horn is resistance dominated and so one finds that by the time one has a 50% efficient horn, that the acoustic phase is around
zero degrees mid band. Over the region the acoustic phase is zero degrees, the driver does not move in time with a change in frequency.
Flat amplitude AND zero degrees phase are the conditions needed to preserve the waveshape of the input signal, no wonder
so many like horns.
See the response and phase of the BT-7's for example (4 are around 45% efficient)

In the Unity, I can't do anything about the phase response of the woofer, one is stuck with that and in that case the closest one can come is to
match the time /phase at and around crossover.

One last thing, the conical horn above some frequency (set by the wall angle and mouth size) has a constant directivity.
Since over a wide range of frequency the "illuminated angle" (to put it in terms of light) is constant so the intensity at any point in the coverage
exactly reflects the source strength.
The acoustic power of ALL compression drivers rolls off above a few KHz, Plane wave tube measurements show this and so does the response
when on a CD horn.
Understand, the conical horn has nothing to do with the roll off, it simply does not concentrate the sound into a smaller angle like curved wall
horns do. The roll off on the low frequency side IS due to the rapid expansion rate of the horn at the apex where the driver is coupled to the
acoustic system. It is the expansion rate which governs the "high pass" part of the horn.
Got to run

Tom



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