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A time-aligned top end - Part II


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Doesn't the horn operate by transforming high pressure high velocity at the throat into low pressure low velocity at the mouth?

Yes. But it isn't the speed of sound that is important - it is the higher efficiency of the driver's cone/diaphragm in pushing that air which is the difference (i.e., better "impedance matching" of the driver to air).

If so, won't this make the alignment distance shorter than simple driver to driver length, and vary also as a function of amplitude?

Noted above, the speed of sound in air ( the "c" or the celerity of sound) doesn't really change very much. It is really a function of temperature, and much less a function of pressure, and temperature changes inside compression drivers and horns are not significant until the SPL gets to be a significant fraction of atmospheric pressure (i.e., wave pressures exceeding a few PSI, corresponding to very, very high SPL in dB).

but I'm wondering if that length is overstated because of the time the wavefront in the mid horn might be going supersonic.

Supersonic flow through pipes and orifices (like horns and slots) is not occurring. That is something that requires mass flow of air around a properly shaped body being pushed with a LOT of force, and that isn't occurring here. In fact, the speed of sound is the limiting factor in air (mass) flow through internal spaces--the flow just will not go any faster. For a discussion of supersonic flow, here is a reference.

Note the words "flow" instead of "wavefront". This is an important distinction: there is no net mass flow inside horn-loaded speakers unless air is being blown through the device while the drivers are operating.

Chris

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Doesn't the horn operate by tranforming high pressure high velocity at the throat into low pressure low velocity at the mouth?

Exponential horns transform hi pressure and lo velocity air at the throat into lo pressure and hi velocity air at the mouth.

Is the velocity a real elevation in the speed of sound within the high pressure end of the horn that is normalized at the mouth?

Does this mean the wavefront is spending all of its time traveling the length of the horn at supersonic speed, slowing to match normal sonic speed at the mouth?

If so, won't this make the alignment distance shorter than simple driver to driver length, and vary also as a function of amplitude?

In a typical mid horn/tweeter set, wouldn't virtually all of this shortening be occuring in the midhorn?

Does this allow the midhorn wavefront to catch up somewhat to the tweeter?

No to all. Sound are oscillatory vibrations that are propelled by succeeding vibrations at the speed of sound. The velocity referred to earlier is particle velocity.

http://en.wikipedia.org/wiki/Particle_velocity

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Hmmm...

Cask05 says high velocity at the throat, low at the mouth

Don Richards says low velocity at the throat, high at the mouth

I'm thinking that the driver feels the throat's constricted low volume and delivers higher pressure than it would in free space. The higher pressure means the air is at a higher density but I find conflicting explanations of density's effect on speed of sound in air all over the internet.

I was imagining that the wavefront is transmitted through the air by two components. One is the direct banging of molecules, the other is the free space travelling of banged molecules toward their subsequent encounter. This is not the net flow of molecules through the horn, just local pressure and rarification propagating the wavefront energy through the horn.

I was also guessing that direct molecular banging is faster (more efficient and immediate) than the travelling between bangs; and this would account for the higher speed of sound with greater density at the same temperature. The speed of sound in air is 343m/s, in water 1493m/s, in copper 3560m/s, in iron 5130m/s, and in diamond 12000m/s (interesting for those of us that play records). I thought because the proportion of time spent travelling between bangs is less in higher density, higher density increases the speed of sound. I found aerospace sites that agree with my thinking, but Wikipedia states, "...the speed of sound is proportional to the square root of the ratio of the elastic modulus (stiffness) of the medium to its density." Which is to say that the speed of sound is independent of density for a particular medium like air - speed of sound in air is proportional to temperature, not density. So I'm not sure what is the case here...

So then, what is the velocity about? What is it the velocity of? Every horn theory I find states outright that horns do not amplify the sound, only match impedance to the free air at the mouth. Amplifiation of sound is increasing the amplitude of the waveform, so that is not happening in the horn. If the veolocity in question is the actual movement of molecules back and forth to comprise the wavefront propagation, I'm seeing a problem with that. The wave at the throat has the same fequency as at the horn mouth... the only way to incease the velocity of the molecules involved would be if the amplitude of the wave at the horn mouth was bigger than at the throat... but appearently that is not what is happening. I'm not sure what to think.

I'm not trying to reinvent the wheel. I spent some time looking for answers and found nothing that clearly settles this, although I'm sure it must be well known in the field. I did find some differences in opinion about the shape of the wavefront; some saying the wave begins with a particular radius of curvature that is constant throughout the length of the horn (leading to Tractrixs), others saying the wavefront is initially a plane wave but tranforms to spherical by the time it reaches the mouth (leading to exponential). The latter clearly requires that the speed of sound of the wavefront center on axis is greater than that off axis. Both assume that the wavefront maintains a right angle to the horn wall (but don't offer an explanation of that either). How can this still be a mystery?

Anyone that has a definitive reference on the mechanics of horns and sound, please feel free to attach or link it. I'm not looking for engineering articles that gloss aucoustic impedance and then jump into cut off frequency and cavity volumes. I would like to read something more fundamental at the physical molecular level, hard math is OK.

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Anyone that has a definitive reference on the mechanics of horns and sound, please feel free to attach or link it. I'm not looking for engineering articles that gloss acoustic impedance and then jump into cut off frequency and cavity volumes. I would like to read something more fundamental at the physical molecular level, hard math is OK.

See this link. Note that understanding Webster's horn equation expanded beyond the most simplified level requires at least partial differential equations and vector mechanics to represent (among other techniques).

Some of your statements above mix mechanics of solids and particles with those of gases: a gas behaves as a continuum. I'd look more closely at the difference between gases and solids, for instance, the speed of sound in an ideal gas is:

<br /> c = \sqrt{\gamma \cdot {p \over \rho}}\,<br />

where:

γ is the adiabatic index (isentropic expansion factor)--the ratio of specific heats of a gas at a constant-pressure to a gas at a constant-volume(Cp / Cv), arising due to the assumption of sound waves inducing adiabatic compression, in which the heat of the compression does not have time to escape the pressure pulse, thus contributing to the pressure induced by the compression.

p is the pressure.

ρ is the density

Chris

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There are several different types of horns used these days, all with different strengths and weaknesses. Here is a history of horns that explains the workings of horns and their differences:

http://www.pispeakers.com/Pi_Speakers_Info.pdf

If you want all the math and theory then get a copy of Sound System Engineering, third edition, by Davis and Petronis. I have not been able to find any of the third edition online, so you may need to buy one or get it at a library.

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Another link on simulation of folded horns using something known as "Boundary Element Method" (BEM) is provided below:

http://community.klipsch.com/forums/storage/3/1110109/JAES_V52_10_PG1029.pdf

Note that the figures on page 7 of this article show non-spherical and non-flat geometries, and wavefronts which are not normal to the nearest boundary.

Once you dive below the surface of the classic "one-dimensional" Webster horn equation, the math and accompanying physics get to be very challenging to explain using simplified conceptual models. Computational grid models like this one (BEM) show the most detail that I've seen.

Chris

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Here's an article that explains the difference between horns designed to maximize efficiency and waveguides designed for optimal pattern control:

http://community.klipsch.com/forums/storage/3/1322842/How%20Horns%20Work%20Revisited%20by%20Dr.%20Earl%20Geddes%20(compressed).pdf

Here's 2 articles on horn theory that are pretty good:

http://www.audioxpress.com/magsdirx/ax/addenda/media/kolbrek2884.pdf

http://www.audioxpress.com/magsdirx/ax/addenda/media/kolbrek2885.pdf

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Thanks for the links... I notice that the 2nd audioexpresslink - (Distortion section), provided by Don, the author confirms that, "You can see that the speed of sound increases with increasing pressure". The context within which he mentioned this is the discussion of how the wave is distorted to take on a second harmonic because, basically, air is single-ended. Identical magnitudes of positive and negative pressure change result is different changes in volume - bigger for increases in pressure, less for reductions. The higher speed at higher pressure tends to advance the positive half of the wave over the negative half leading to a change in the waveform itself showing the identical change that occurs when 2nd harmonics are added; same as how single ended amps deliver the positive wave half at greater amplitudethan the negative half.

If we assume he is correct about sound speed change with pressure, the question remains; is there a net differential pressure gradient within the length of the horn? On the one hand, one might think if there were, then there would have to be a net movement of air from the throat to the mouth to re-establish equilibrium; but that does not happen. On the other hand, one might interprete the "high pressure" felt at the throat by the driver as "virtual", and described as acoustic impedance...

Anyway, it sounds like we have confirmed that soundspeed is a function of pressure; what remains is to determine if the "pressure" gradient in the horn is real air pressure or just a shorthand misnomer for something else...

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Would these 2 drivers be considered time-aligned?

The drivers are aligned for one point in space. Now if you hook a passive crossover to them, they will no longer be getting aligned signals. It is more than just aligning the voice coils when you are using passive crossovers. Here is a little bit on alignment and lobing:

http://www.rane.com/note160.html

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That's why I said "close enough". Physical position is only one component and you can only come so close to where it no longer matters compared to the others factors involved. If you read all the pro stuff..........they ballpark their digital delays. Close enough is close enough.

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Anyway, it sounds like we have confirmed that soundspeed is a function of pressure; what remains is to determine if the "pressure" gradient in the horn is real air pressure or just a shorthand misnomer for something else...

I looked at my copy of Sound System Engineering last night and air density is what affects sound speed. Temperature affects the speed of sound only because temperature affects air density. There is plenty of math there that shows the degree with which this occurs. When the speed of sound changes due to an air density change wind instruments will go out of tune.

The pressure gradient through a horn or from any loudspeaker is real, just very small compared to the 14.7 PSI or so of air pressure present on the earth's surface. The changes in air density caused by sound are too small to affect the sonic speed significantly. We do not percieve these pressure changes as distortion but as normal sounds.

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I looked at my copy of Sound System Engineering last night and air density is what affects sound speed. Temperature affects the speed of sound only because temperature affects air density. There is plenty of math there that shows the degree with which this occurs.

That's a pretty impressive piece of equipment in your avatar (even 50 years later)...

Okay, back on topic...the formula for speed of sound © in an ideal gas is (repeated here again):

<br /> c = \sqrt{\gamma \cdot {p \over \rho}}\,<br />

where γ is (Cp / Cv), p is pressure, ρ is the density (in consistent units)

Note the ratio: p/ρ - this ratio is almost entirely a function of temperature (...look closely and you'll see it...). γ can be considered a constant.

"c" is also a function of the square root of the p/ρ ratio - which means that it is relatively insensitive to temperature changes.

Chris [;)]

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Here's an article that explains the difference between horns designed to maximize efficiency and waveguides designed for optimal pattern control: http://community.klipsch.com/forums/storage/3/1322842/How%20Horns%20Work%20Revisited%20by%20Dr.%20Earl%20Geddes%20(compressed).pdf

Thanks for this - I'd not seen it...it's not that old, BTW. I've ordered Giddes's book and expect to see it next week. I'll let you know if I find something that is of interest. One thing already - the argument about Higher Order Modes (HOMs) and horn shape, i.e., any small radii of curvature/internal edges in the horn's throat area isn't a good thing if one is trying to avoid HOMs. This discussion is intuitively satisfying and also seems to support my listening experiences with different types of horns - notably the early "flat, bi-radial constant directivity" JBL horn (i.e., the 2380A, which later was copied by P.Audio as their PH-4245 and the Chinese version of this horn) which sound a bit harsh to my ears.

Chris

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Ok horn experts. What's the down side of simply putting a round "pipe" between the tweeter horn and driver exactly long enough to position the tweeter driver right along side the mid-range driver? With a 1 inch horn and screw-in driver like the Selenium 220 it should be easy to do. It would simply be a 1 Inch I.D. pipe.

Al K.

post-2934-13819636976312_thumb.gif

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The Danley Synergy Horns (SH series) integrate the tweeter with all the other speaker's drivers (midrange, woofer).

Maybe there is good reason to integrate them into one horn? The delays have to be made correctly (according to Tom Danley).

Multiple_entry_horn.png

Chris

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