Anatomy & Physiology of an Acoustic Horn

[Klipscheritage]

Acoustic Horn - "A tube of varying cross section having different terminal areas, which change the acoustic impedance to control the directivity of the sound pattern." Audio Terms Explained

Greeting Folks, I've been thinking of horns lately... Horn loaded speakers sound so much better. Paul Klipsch realized this many years ago... Anyway, I tend to over think things > I like too understand how things work... So I been thinking of horns thinking they are worthy of further discussion.

The First Law of Thermodynamics (Law of Conservation of Energy) This law suggests that energy can be transferred from one system to another in many forms. However, it can not be created nor destroyed. With this principle in mind it begs the question what lost in the conversion that takes place in a horn? Usually there is a price tag that comes with any benefit - you improve one thing but to the demise of another. With the horn it all seems like benefit. A few years ago my brother and I made some Bushhorn speakers to see how they sounded it was amazing what kind of clean bass we derived from a simple Fostex driver. In addition to my question of what is lost I also ask what happens to the sound and specifically the soundwaves? When I think of this I tend to think in terms of phase and alignment like a turbulent river that has been altered to flow In laminar with the same amount of kinetic energy present just packaged better. Without tons a mathematical formulas and computations can anybody contribute to the understanding of what a horn does and how it does it?

Scott

[PrestonTom]

Scott,

Good Question.

At the driver end of the horn you have a small volume & high pressure. This helps minimize the impedance mis-match between the driver's material and the air. It is the impedance mismatch that causes the inefficient transfer (so the 2nd law still holds). The displacement of the driver is relatively small (so the driver remains in its linear range). As the volume increases (traveling down the horn away from the driver and towards your living room), the impedance becomes more like the open space of your living room. In essence, the horn acts to "transform" the impedance. What is critical here is the issue of efficiency. As this increases, distortion decreases. All this, and you get a nice low frequency response also.

Good Luck,

-Tom

[Klipschguy]

Hi Scott,

Wecome to the Klipsch forum. Some good folks around here.

The impedance tranformer thing is interesting. When you read about horns in cone & dome loving publications, they tend to dismiss horn efficiency as a "loss of directivity for the sake of efficiency." They say horn efficiency is only the result of narrowing the directivity of a driver. Of course there is more to it. Anybody got a Dope from Hope article on the subject??

Andy

[WMcD]

I post articles but with the new search function being so lame, they are diffiuclt to find. I'll give one of my numbered explanatons. This is more fluid dynamics and wave mechanics than Thermo.

1) One is that the transfer of energy between two systems is maximized when the driving source impedance and the load impedance are equal. Source impedances are generally resistive, so we'd like a resistive load, and we'd like that at all frequencies.

[Edit. It is interesting that a you have to get to a 6 to 1 mismatch before losing half of the maximum power, which is 3 dB. But that means if you put the driving impedance in the middle of the impedance wiggles of the driven, the driven impedance can go to 6 time or 1/6 th before getting outside the plus or minus 3 dB window.]

2) In free space, the air load on a diaphragm (or a circle) doesn't get resistive until the circumfrence is about a half wavelenght. {Edit. I should have said two wavelengths.} This means that we'd like very large diaphragms. But they are relatively heavy (another issue). So even 15 inch bass radiators don't influence enough air at bass frequencies. They are good at 800 Hz. The same applies to midrange direct radiators

3) The condition in 2) somewhat descibes that when you push on air in free space, it runs way to the side where there is low pressure. The air does not push back, and you can't pump it much because you can't build up any pressure in front of it.

4) Generally speaking, you could think of a 15 inch driver as a bunch of seven 5-inch speakers arranged with a the last one in the middle of the ring. I you drive only the center diaphragm, the pressure runs away to non-driven ones. If you drive the ring too, Then the air from the center hits the pressure formed by the inside of the ring of speakers around it. .So at least for the center, the air pressure is contained. If pushes back on the diaphragm (pumping) and is propelled outward too. So you get pumping.

5) The principle in 4) is just to show that generally, a large diaphragm is better, and for understandable reasons.

6) We can increase pumping effectiveness by putting the diaphragm so it faces into a tube. Now the walls of the tube prevent the air from running away. It is trapped and pushes on the diaphragm and also gets forced down the tube. This is like Newton's third law. For every action there is an opposite reaction, which is to say pushing against the diaphragm allows the diaprhagm to push back.

6.1) If work is force times distance, we do more work if we have have a force to work against. That is why we want to trap air. Of course if work is constant, this means we move the diaphram over a smaller distance. More of the last below.

7) The stuff in 6) says we can get more energy out of the diaphragm if we force air down a tube. The problem is, we run into the same problem of having a small surface, or diaphragm area, at the other end of the tube.

8) So what we need is a tube which has a very big other end (mouth of the horn). It must grow in size in such a way that the small end (mouth) doesn't know the difference. Classically that is an exponential expansion or exponential horn. It works down to only a certain point, the bottom of which is called the Fc of the horn. (There is more to this.)

9) How big does the other end of the horn-pipe have to be? We're back to the diaphragm size issue. We don't have to have a paper diaphragm at the mouth of the horn. The issue is how much air (area) is there (again, it must resist change)

10).. However, now we have an efficent driver situation at the small end. The horn mouth is big, and the big end is larger than a direct radiator. It doesn't have any mass. Everybody is happy about energy transfer based on acoustics.

11) There is the directivity issue. This is most seen in midrange and tweeter where we have many wavelenghts of size to play with before things get too big, measured in inches.

12) Remember, if we half the frequency, every structure gets half the size in terms of wavelength. So it is like Alice in Wonderland Every structure gets bigger and smaller in terms of frequency

13) We can play with the geometry of the horn to make it directional in ways we like. That is a very big issue.

14) Were are the losses, you ask. Acousticly, they are in the flexing of the walls or absorption by the structure.

15) We have not talked about electical issues. Basically, the strength of the motor has to match the size of the throat. This is a complicated issue described in 1). If you work out the math, the voice coil resistance has to match the throat size; but the effect of the acoustic throat on the electical system is set by the motor strenght.

16) The effect of 15) is that half of all the electical energy in a lossless system is consumed by the voice coil resistance. So the most perfect horns are 50 percent effecient. But direct drivers are less so.

17) It is worth noting that bass horns have to be very large. We can deal with that by putting the mouth in a corner of the room. There are several ways of thinking of this. The most common is that the corner is a cone and thus is an extension of the bass horn. Another is that we have pressure reflections from the two walls plus floor (a mirror effect which makes the mouth seem bigger).. The latter sounds like the tube condition at the throat. All of these are different ways of saying the same thing. More in 19) below.

18) The math (if you want to go into it) is a bit easier to see with something like the LaScala bass horn. It has a 15 inch driver looking into a half square foot throat. (I'm not going to go into the restriction). Every foot down the horn the area doubles because of the exponential area expansion.. It is three feet long. It winds up with a four square foot mouth. (This would be a very big direct driver but still not enough for resitive loading by our rules).

19) A corner provides the extra flare of the horn. Or this can be considered as 1./8 th of free space. This is another visual geometry problem. However, consider that you can have a building with many rooms and floors. At a bottom corner of a given room there is an intersection of the floors of the four rooms on one level, and the ceilings of the four rooms below. So that is 1/8 of free space. We don't really care whether there are other rooms. It is just enough that there are such walls in one room, which is our room..

20) Are we really dealing with 1/8 of open space with the bass system? No. Actually the bass horn is radiating into a box. The box is our living room. This creates many issues of room modes and pressure within the room. At very low frequencies the room is less than a wavelength.

21) Another issue is that there is probably another bass horn in another corner. Again we have the issue outlined in 4) above. There is a nearby source of pressure.

22) These higher numbered paragraphs explain how all our bass horns are small, but do deliver good bass response.

Best,

Gil

[WMcD]

Whoops, I didn't get back to 6.1

It is the center of PWK's work and why horns have low distrortion levels. It is not that the horns (as structures) have low distortion. It is that the drivers which operate into horns have lower distortion. This is because the efficiency of the good match allows the diaphragm to move less even though it is doing more work.

We have go-arounds about amplifiers and whether some topologies have no distortion, or the right distortion. PWK's theory is that the basic movement of the driving diaphragm causes the worst type of distortion. That is Doppler distorttion which is a type of intermod.

This is typically explained as the train with a whistle. We hear a frequency shift as the train goes by. So as a diaphram moves with bass (a moving train), any treble (the whistle frquency) moves around.

In the train analogy there is no imperfect amp, or over driven speaker. No cause of distortion except for motion .

Best,

Gil

[edwinr]

Very interesting Gil and Tom. I never really understood the philosophy behind horns - but I have an idea now. I guess speakers mounted on very large baffles (but no box) still allows the driver to pressurize the air somewhat, because the air cannot run to the side - or have I got this wrong?

[Stovebolt6]

I remember reading a PWK quote somewhere that went something like this:

A direct radiator is like a piston moving up and down in a lake, just a lot of sloshing around. If we put a cylinder around that piston, now we can get some work done!!!

Dan

[Klipschguy]

Gil,

That was a great post! That got my gears turning this morning.

How do the mass of air in a port vs. horn relate? (I may be wrong, but doesn't the mass of the air in a port ideally have the same mass as the cone driving it?) If most of the resistance in a horn is at the throat, is the mass of the air in the throat and the mass of the diaphragm related like the port issue?

Andy

[D-MAN]

Couple of things, the port (assuming a reflex-type loudspeaker) acts as an inert mass of air (more or less) until a specific frequency is resonated when the heretofore inert mass of air starts to vibrate like a piston (at the specific frequency it is physically "tuned" for). The driver, enclosure volume and port volume are specifically and inextricably linked to form a Helmholtz resonator tuned to resonate at a particular frequency. The air through the port doesn't actually transmit AS a soundwave from one end to the other, but the vibrating mass of air CREATES a soundwave at the enclosure exit boundary or flange (commonly called the baffle, in other words) by acting as a vibrating "plug" or piston-head of air (like a cone of the same diameter would do). That is why the port is only "active" at a certain frequency. If it wasn't specifically tuned along with the enclosure and driver, it would merely act as a flanged duct, which would transmit plane waves.

The horn, while containing a larger air mass volume (of course) is not an inert mass of air NOR is it particularily resonant at any frequency. It does transmit soundwaves from one end to the other. The small end (throat) gradually expands in a mathematical manner of a length and width until it presents an appropriate size of vibrating sheet of air to the atmosphere (the mouth) for its specific bandwidth. The gradual change between high-pressure, low velocity at the throat to the low pressure, high velocity at the mouth caused by the expansion rate and overall pathway length is why the horn is known as an acoustical transformer.

DM

[Klipschguy]

That makes a lot of sense D-Man. Thanks. You know I've taken a bunch of physics, but you know, it doesn't matter if you can "work the problems" - you have to be able to visualize it before you can grok it.

Andy

[edwinr]

I always thought a port acted as some kind of pump outlet. Obviously not.

[IB Slammin]

I always thought a port acted as some kind of pump outlet. Obviously not.

Please be kind with corrections if I am wrong.

In a total enclosure, only the front side of the cone or diaphragm moves air and produces sound. The back side of the cone is compressed and contained inside the box.

With a port, or reflex, the back side of the cone is in play, and fires thru the port. The size and lenght of the port along with cabinet volume, allows one to synchronize the front side with the back side at the point of exit, moving more air with the same amount of watts in. ?? Definition of bass-reflex?

Terry

[IB Slammin]

I always thought a port acted as some kind of pump outlet. Obviously not.

Please be kind with corrections if I am wrong.

In a total enclosure, only the front side of the cone or diaphragm moves air and produces sound. The back side of the cone is compressed and contained inside the box.

With a port, or reflex, the back side of the cone is in play, and fires thru the port. The size and lenght of the port along with cabinet volume, allows one to synchronize the front side with the back side at the point of exit, moving more air with the same amount of watts in. ?? Definition of bass-reflex?

Terry

EDIT: 17) It is worth noting that bass horns have to be very large. We can deal with that by putting the mouth in a corner of the room. There are several ways of thinking of this. The most common is that the corner is a cone and thus is an extension of the bass horn. Another is that we have pressure reflections from the two walls plus floor (a mirror effect which makes the mouth seem bigger).. The latter sounds like the tube condition at the throat. All of these are different ways of saying the same thing.

Back to a recent thread about port coupling. When we push the bass horn back into the corner, the rubber to the wall, to extend the last fold down the corner walls,....... Is that so different than coupling a reflex port to the floor, or placing them in a side orientation so that they discharge down the lenght of the corner side walls?

Terry

[D-MAN]

Guys, very little air movement is going to occur in a port that is not at (or near) it's specific tuned frequency. Also the back of the cone is active at all times (so is the front). The acoustic load is different at different frequencies, of course, for both the front and the back of the cone, which cannot be divided in reality.

That's why a ports response curve is a pronounced peak at the tuned frequency. The air mass in the port tends to resist modulation UNLESS it is at or very near the tuned frequency. It acts like a PLUG more or less.

DM

[Colin]

nice, as usual, very nice Gil