don@umd5.UUCP (04/07/85)
*** REPLACE THIS LINE WITH YOUR MESSAGE *** Whatever for ??
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Sorry folks, but I went and confused electromagnetic waves with sound
waves .. Out of habit I suppose, since I work almost exclusively with RF
equipment. Thanks to those who have responded directly to me. The numbers
I calculated in my previous posting are all off by a factor of 1,000
(approximately that is). Still, 693 kHz is quite a limiting frequency for
a 10 inch speaker!!
--
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"Space, the final frontier .." Final, hell! It's the frontier of frontiers !!
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SPOKEN: Chris Sylvain
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UUCP: {seismo, rlgvax, allegra, brl-bmd, nrl-css}!umcp-cs!cvl!umd5!dondon@umd5.UUCP (04/07/85)
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The vote has been tallied .. My calculations are off by 10^6 as the speed
of sound is about 330 meters per second, and I mistakenly used the speed
of light which is about 300,000 KILOmeter per second. So the REAL cutoff
frequency of the waveguide model of a speaker is 693 Hz -- a reasonable
number. (I guess then that is why PA systems use a whole bunch of big
speakers -- LARGE effective diameter pushes the cutoff freq. higher)
So I can't sail the Nimitz through the holes in Phil's explanation,
(that's OK Phil, when all else fails call me "stupid"!) but I can still
possibly paddle a canoe through the holes (I've always been suspicious
of anyone who doesn't sprinkle in a little math to backup their argument,
so why don't you call me a "Doubting Thomas" instead?)
The waveguide model is now ruled out since wvaguides become VERY lossy
when operated above cutoff. Most speakers have woofer crossovers at 1,000 Hz.
Given the above and that (330 m/s) divided by (0.254 m) = 1,300 Hz, how is
the dispersal mechanism going to affect anything ? The woofer power will
already be decreased at the supposed limiting frequency of the speaker.
I have speakers whose tweeters are 0.064 meter in diameter. They work
quite well out to 16,000 Hz, but by what Phil said they shouldn't even
work at all beyond 5,200 Hz !! [(330 m/s) / (0.064 m) = 5,200 Hz; "speakers
cannot reproduce wavelengths shorter than their diameter ..."]
Please, someone (or Phil) clear this up....
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"Space, the final frontier .." Final, hell! It's the frontier of frontiers !!
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SPOKEN: Chris Sylvain (transient user of Don Preuss' account)
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UUCP: {seismo, rlgvax, allegra, brl-bmd, nrl-css}!umcp-cs!cvl!umd5!donark@alice.UUCP (Andrew Koenig) (04/09/85)
> Sorry folks, but I went and confused electromagnetic waves with sound > waves .. Out of habit I suppose, since I work almost exclusively with RF > equipment. Thanks to those who have responded directly to me. The numbers > I calculated in my previous posting are all off by a factor of 1,000 > (approximately that is). Still, 693 kHz is quite a limiting frequency for > a 10 inch speaker!! Ummm... try about 1.2 kHz.
pmr@drutx.UUCP (Rastocny) (04/09/85)
First let me clarify why I don't like to throw a lot of math and formulas out
on the net. I choose not to so that MORE people will understand what I'm
talking about, not just the EEs.
There is much to explain about how tweeters work than presented in the first
article. There are two basic problems with dynamic tweeters: 1) the rising
voice coil inductance with rising frequency, and 2) the dispersion effect
described in the previous article.
How do you get around these problems? You could use a small voice coil
(< 0.25") but that limits either the impedance (less wire in the VC) or the
power handling ability (smaller wire in the VC) of driver. You could also
change the shape of the piston from flat to hemispherical. This changes how
the piston pushes against the air and extends the piston's dispersion-bandwidth.
Most manufacturer's choose the latter.
Another technique used with leaf drivers is to increase dispersion in one plane
and reduce it in another. By making the driver long and narrow to maintain a
"large" piston area, you can increase dispersion at higher frequencies in
the narrow plane. This phenomenon is referred to as the slit effect. The trick
is to make the piston move back and forth uniformly. If the edge lags the
center, you get all kinds of phase distortion and a poor sounding driver.
The third problem with tweeters lies with first reflections. Wavelengths in
the tweeter's operating bandwidth are quite short. Anything projecting above
the piston plane near the edge of the piston can set up standing waves that
impair the drivers performance (screws, the edge of the driver assembly,
grills, other drivers, etc.).
|<--d1--->| |<---------d2---------->|
---|screw|---------|piston|-----------------------|grill|--
So in the above illustration, standing waves are generated whose wavelengths
are 2d1 and 2d2, 4d1 and 4d2, etc.
This is getting too long. There's too much involved to explain in this article
and I must get back to work.
Yours for higher fidelity,
Phil Rastocny
AT&T-ISL
ihnp4!drutx!pmrklein@ucbcad.UUCP (04/10/85)
OK, folks. Here is a lot of information about speaker physics, specifically about the discussion concerning driver diameter and radiated frequencies. First of all, there is no "magic frequency" above which a speaker suddenly sounds like it's playing through mud. There is a gradual decline in frequency response, dispersion, and imaging. [It is of course an entirely separate discussion as to what the decline in quality of these really means.] The rule of thumb about wavelengths equalling diameter is pretty good, though, as it gives you a rough idea of the limitations of this aspect of speakers. To see why, consider a few effects that depend on this diameter vs. wavelength factor. First, interference, which is what most people have mentioned. Let's take the case where the wavelength emitted by the speaker is exactly its diameter. The first instance of complete destructive interference will occur when the path length difference between the far edge and the near edge of the cone is half the wavelength, or at 30 deg off-axis. As the frequency rises, this destructive interference occurs ever closer to the speaker's axis. Where does it become objectionable? Who knows. Probably 30 degrees off axis is too close to the axis. In any case, Diameter < max wavelength is good enough for a very rough initial guess. By the same token, just because a speaker is crossed over at 1000 Hz does not mean it does not contribute above 1000 Hz. Most crossovers are single or double slope so their contributions die out slowly. A speaker with a single slope crossover at 1000 Hz still contributes about 30% of the total power at 1500 Hz. If it is contributing zero at that frequency (not likely, but just for illustration), you're down about 1.5 dB from your ideal response with no interference. Not that bad, but still something to keep in mind when designing. At 1200 Hz it's down 2.3 dB. There are other reasons to keep the driver diameter small relative to its maximum significant radiated wavelength. Related to the above discussion, you are crossing over to another driver; the radiation from that one will interfere with this one for some frequency range above and below the crossover. The larger the speakers, the larger the distance between them, and the lower the frequency at which destructive interference gives you problems. You can minimize this problem by lining the drivers up vertically on the assumption that you will probably only be significantly off-axis horizontally, not vertically, but this is only a patch. Since this problem is closer to the ideal two-point-sources interference, it is potentially a worse problem. Another important problem (as I've mentioned before) is the breakup of the driver's cone. At some frequency, a speaker's cone will cease to act like a piston and will look like a very flexible medium to the motor driving it. One effect is that the cone will support standing waves all over it, making regions that are 180 degrees out of phase with their neighbors. This is REALLY bad. You can't do anything about this except cross over WELL BELOW this frequency; but how do you know where the frequency is? Maybe you can get it from the manufacturer. Maybe you can tell by frequency response curves given for the driver: if you see a lot of sharp dips and peaks at higher frequencies, it's a good bet that that's what happening. Cones can be made stiffer, can have a damping medium applied to them, and various other things, but again these are often patches that lead to other problems. Yet another problem, harder to quantify and highly variable from one type of driver to the next, is nonlinearities introduced by making that driver put out small but important higher frequency radiation on top of higher power, larger excursion lower frequencies. Theoretically it's no problem but in reality it is, with position-dependent nonlinearities in the voice coil/magnet motor. This is more of a problem if the range of frequencies you are trying to reproduce is very large, but again, it is highly variable depending on the particular driver design. It sounds like the grand solution is to cross over at very low frequencies, and all your problems are solved. Not true, although this is the approach I have taken in speakers I have built. The problem is that crossing over at low frequencies means that each driver's operating range is shifted as low as possible, and operates over a smaller range of frequencies. So you need more drivers. You also have to be careful about not putting too much power into the higher frequency drivers. I have built a pair of 4-ways that cover the range of about 32 Hz up to about 40 kHz like so (first-order crossovers throughout): 12" 32 - 300 6.5" 300 - 1600 1.5" 1600 - 6300 ribbon 6300 -> I haven't blown any drivers, but then I don't pump more than about 100 watts peak into the speakers and tend to keep the average power pretty low. Now some of these problems go away if it is possible to design steep crossovers that come out better overall than first-order ones. This is a very difficult problem, but judging from net.audio, the folks over at JSE seem to have been the first to my knowledge to do this succesfully. I would be very interested in finding out what their crossover topology is... Bill Mitchell, any ideas???? -- -Mike Klein ...!ucbvax!ucbmerlin:klein (UUCP) klein%ucbmerlin@berkeley (ARPA)
seifert@mako.UUCP (Snoopy) (04/10/85)
In article <464@umd5.UUCP> don@umd5.UUCP writes: > Most speakers have woofer crossovers at 1,000 Hz. Most contributors to this forum know that speakers vary much too widely to make absurd generalisations(sp?) such as the above. Sounds like you're talking about a two-way system, with conventional type drivers and enclosure. By the time you add up all the three-way, four-way, and up systems, the one-way systems by Bose, Ohm, and possibly others, the non-conventional stuff by Ohm (again), Magnapan, Quad, etc., I suspect that woofer crossovers near 1000 Hz (much less *at* 1kHz) are quite in the minority. You're getting closer, at least you're not off by several orders of magnitude this time. :-) _____ |___| the Bavarian Beagle _|___|_ Snoopy \_____/ tektronix!mako!seifert \___/
herbie@watdcsu.UUCP (Herb Chong [DCS]) (04/11/85)
In article <691@mako.UUCP> seifert@mako.UUCP (Snoopy) writes: >In article <464@umd5.UUCP> don@umd5.UUCP writes: > >> Most speakers have woofer crossovers at 1,000 Hz. > >Most contributors to this forum know that speakers vary much too >widely to make absurd generalisations(sp?) such as the above. > >Sounds like you're talking about a two-way system, with conventional >type drivers and enclosure. By the time you add up all the three-way, >four-way, and up systems, the one-way systems by Bose, Ohm, and possibly >others, the non-conventional stuff by Ohm (again), Magnapan, Quad, etc., >I suspect that woofer crossovers near 1000 Hz (much less *at* 1kHz) >are quite in the minority. it also depends on what you mean by "near". Herb Chong... I'm user-friendly -- I don't byte, I nybble....