[Audio Empire]

On Mon, 27 Aug 2012 05:53:17 -0700, Dick Pierce wrote
(in article ):

Audio Empire wrote:
On Sun, 26 Aug 2012 05:03:05 -0700, Doug McDonald wrote
(in article ):
On 8/24/2012 10:13 PM, Audio Empire wrote:
Tweeters just can't move the volume of air that a human
of trumpet player can, and the difference cane be easily heard.

I take it you are saying that the tweeters were actually being
overdriven, and could not reproduce the peaks. Correct assumption?

Not really. The tweeter thing is a theory of mine. It's just that tweeters
are small out of necessity in order to be fast, but they can't move as much
air as larger drivers or as is necessary to reproduce instruments with
high-level harmonic content above 8-10 KHz, even when playing at their
absolute loudest.

The quantity that determines how loud something is "volume
velocity," not simply volume or displacement, which is what
most people are really talking about when they say "moving air."

For a given diaphragm area and a fixed linear displacement,
the sound pressure generated goes as the square of the
frequency. Conversely, for a given diameter, the amount
of excursion needed to radiate a certain sound pressure
level goes as the inverse square of frequency.

Consider the following: a 10" woofer moving about 0.08"
at 50 Hz generates a sound pressure level of about 100 dB
1 meter away. That same woofer, if it COULD, at that
excursion, would be producing 192 dB SPL. It'd need in
the realm of several billion watts of power to do so.
This suggests the obvious: woofers do not good tweeters
make.

Now, take our lonely little, diminutive 1" tweeter. At
10,000 Hz (10 kHz, to reproduce that same 100 dB SPL
1 meter away, would have to move all of 0.0002". That's
a mere 200 millionths of an inch, or nearly 400 times
LESS than the woofer (at 50Hz) to produce the same sound
pressure level.

The reason is, again, that the amount of sound for a given
diameter and excursion, goes as the SQUARE of frequency
or, equivalently, the amount of excursion needed for a
given sound pressure level goes as the inverse square of
frequency.

10,000 Hz is 200 times the frequency of 50 Hz, and the
square of that is 40,000. But there's a factor of 100
difference in the emissive area between a 10" woofer and
a 1" tweeter. It therefore goes that a 1" tweeter
requires 100/40,000 times the excursion at 10 kHz that
a 10" woofer does at 50 Hz.

Most instruments can be fairly realistically reproduced,
and that is because the high-frequency harmonics that they produce are
extremely attenuated compared to their fundamentals.

Except that for most tweeters, the limitation in output comes
not at the HIGH end of their range, but at the LOW end.

Once again, remember that the excursion, for a given emissive
area and sound pressure, goes as the inverse square of
frequency. In order to produce that same 100 dB SPL at, say
2 kHz that it can at 10 kHz, the tweeter has to move
(10 kHz/2kHz)^2 or 25 times as much at 2 kHz as it does at
10 kHz.

So, counter to your intuition (and, for that matter, many
peoples' intuition) producing the high frequency stuff is
EASY compared to the low frequency stuff.

"Yes, but," you or someone else might say, "it's all about
how FAST the tweeter is." Well, it turns out that while that
sounds intuitively correct, it's physically wrong. For the
same sound pressure level, the linear velocity of a given
diaphragm goes as the reciprocal of frequency, NOT directly
as frequency. That means that the same tweeter that's moving
X cm/sec at 2 kHz only has to move 1/5th that speed at 10 kHz
to produce the same sound pressure level.

In fact, we can directly calculate what those velocities
are by differentiating the excursion WRT time. Doing so
gives us an equation for peak velocity of Vpk = wX,
where w is radian frequency (2 pi times F) and x is the
excursion. At 10 kHz:

Vpk = 2 pi 10 kHz * 0.0002 in
Vpk ~= 13.2 in/sec

while at 2 kHz, and the same 100 dB sound pressure level:

Vpk = 2 pi 2 kHz * 0.0053 in
Vpk ~= 66 in/sec

"But why, then" it might be asked, "don't tweeters just keep
going up and up in frequency if they have an excursion that
goes as the inverse square of frequency and a velocity that
goes as the inverse of frequency?"

Because there are other limitations that come to play at high
frequencies. The first is physical size: as the wavelengths
get shorter at high frequencies, and as they start to approach
the size of the radiating area, you now get to the point where
one point in the diaphragm is a significant portion of a
wavelength (or, at high enough frequencies, MANY wavelengths)
distant from another part. Even assuming the radiating area
was infinitely rigid (reality is FAR from that), those path
length differences would lead to cancellations.

Second is the fact that the diaphragm is anything but rigid.
At high enough frequencies, that diaphragm is doing anything
BUT moving as a rigid piston.

Third is electrical: all loudspeaker drivers exhibit elect-
rically reactive properties whose effects come to dominate
as the frequency goes higher. Actual power can only be
produced through resistive loads: a portion of the resistive
load of ANY driver of ANY kind is the reflected resistive
portion of the acoustical radiation impedance. As the series
inductive reactance of a voice coil increases with increasing
frequency, or as the shunt capacitance of an electrostatic
system decreases with increasing frequency, the effect is
an inevitable low-pass filter effect.

Few instruments have the strong harmonic content produced
by a trumpet and perhaps a few other instruments.

Look first at what made it through the air from the
bell of the trumpet to the diaphragm of the microphone (look,
specifically, at the absorptive attenuation of air above 20 kHz).
Then look at what came out the the microphones that managed
to pick up what was left. These two factors alone count for an
enormous amount of very high-frequency losses in recording.



Well, thank you for that exacting primer on how tweeters work. It was very
informative. But it would have served this discussion better to explain to us
what the mechanism is that keeps even the finest speakers from being able to
convincingly reproduce trumpets and some other instruments. Most of us know
what these instruments sound like live - even in a concert hall, or even a
band concert in the park where there is some distance between the instrument
and out ears. No speaker ever made gets it right. The fact that a $195,000.00
pair of speakers can get just about every other aspect of reproduction
correct and still not be able to come within a country mile of getting the
trumpets to sound real must have a cause, some limitation that can't be
overcome by any current transducer technology.