Tractrix horn calculators

[greg928gts]

greg928gts

Did you get my email from last night? It is the holiday and I realize you may be out of pocket or maybe don't have access to email.

jc

Tired from working. I will look at it tomorrow sometime, can't think right now. I was a mason today.

Greg

[DrWho]

So are Roy and Edgar in full agreement? I know I keep saying this, but I need to revisit Post's thesis. From what I'm reading between the lines, I don't think a straight up tractrix area expansion would yield max power transfer in a rectangular horn because no way is the wavefront perfectly spherical. It can't be if your polar response is say 90x60 (that's more of an oval). Thoughts?

[Edgar]

So are Roy and Edgar in full agreement?

Roy and Edgar are in full agreement that, "how each distributes the area is related to how each thinks the wave is propagating down the horn and how each thinks the loading should be. in all cases, assumptions are made but real world measurments can reveal some errors in our thinking."

I know I keep saying this, but I need to revisit Post's thesis. From what I'm reading between the lines, I don't think a straight up tractrix area expansion would yield max power transfer in a rectangular horn because no way is the wavefront perfectly spherical. It can't be if your polar response is say 90x60 (that's more of an oval). Thoughts?

I'm not familiar with Post's thesis, but then I have to admit that horns are a side interest for me and I'm always learning new stuff about them. All that aside; even in a round tractrix horn the wave front is not perfectly spherical. The only horn that supports a truly spherical wave front is conical with a circular cross section. Earl Geddes published papers on this sort of thing.

It really comes down to what you want to optimize. Nowadays, when Watts are super-cheap, do you really care about maximum power transfer? In the pro audio world, pattern control is most important -- they want everybody in the audience to hear essentially the same thing. In your living room you don't care much about pattern control -- you just want the best sound quality possible at a single listening location.

People have been moving away from exponential horns and toward tractrix horns because tractrix horns sound better. Since the frequency response and loading characteristics of similarly sized exponential and tractrix horns differ only by small amounts, the differences in their sonic quality must be due to something else. Again, Geddes enters the picture and claims that the sonic differences are due to "higher-order-modes" -- resonances within the horn body due entirely to the shape of the horn itself. Maybe there is something to that. I honestly don't know.

Edgar (Greg)

[DrWho]

I think tractrix assumes planar to spherical as it travels down the horn. Regardless, I was suggesting that the ideal area expansion should change slightly based on the shape that you want your exit wavefront to be. Max power transfer is all about reducing distortion by making the driver work less hard, not about the power it takes to drive to the SPLs you desire. However, I would argue that you can show that distortion in an amplifier is inversely proportional to its gain (for a given topology). So really, you want to get by with as little volts as possible. And then polar response deals with the fact that about 90% of the sound that arrives at the listening position is reflected, not direct. Due to the Haas effects, we put more emphasis on the direct sound, but the tonal response of the reflected sound still affects our perception quite a bit. If you can have both, then why not?

[Edgar]

I think tractrix assumes planar to spherical as it travels down the horn.

Hmmmm ... I think that an infinitely long tractrix would have a point source, just like an infinitely long exponential, hyperbolic, etc.

Regardless, I was suggesting that the ideal area expansion should change slightly based on the shape that you want your exit wavefront to be.

Exactly. It comes back to those assumptions again.

Max power transfer is all about reducing distortion by making the driver work less hard, not about the power it takes to drive to the SPLs you desire. However, I would argue that you can show that distortion in an amplifier is inversely proportional to its gain (for a given topology). So really, you want to get by with as little volts as possible.

Ah, but amplifier distortion is typically orders of magnitude smaller than speaker distortion.

And then polar response deals with the fact that about 90% of the sound that arrives at the listening position is reflected, not direct. Due to the Haas effects, we put more emphasis on the direct sound, but the tonal response of the reflected sound still affects our perception quite a bit. If you can have both, then why not?

Again, it's about what you want to optimize. There is a whole school of speaker design that says that the sound should be omnidirectional, which would maximize the room reflections that you note. There is yet another school of speaker design that says that the sound should be tightly controlled, which would minimize the room reflections. The fact that superb-sounding speakers are available from both camps tells me that neither assumption is 100% correct (or incorrect).

I am not disagreeing with you ... just playing Devil's advocate.

[gaspr]

There is yet another school of speaker design that says that the sound should be tightly controlled, which would minimize the room reflections.

I would argue that the only way to truly minimize room reflections would be to make the room itself totally absorbtive. Not practical or desireable to most...

Dr Toole over at Harman has done many interesting listening tests where the test subjects would almost always identify speakers with poor polars, as having a lower quality sound. Many of these test subjects were just ordinary folks with minimal training in how to listen. He claims that reflected sound must contain as much of the freq spectrum of the direct sound as possible to sound "right" to most people's ears. Check out his white papers at Harman...

[bodcaw boy]

So are Roy and Edgar in full agreement? I know I keep saying this, but I need to revisit Post's thesis. From what I'm reading between the lines, I don't think a straight up tractrix area expansion would yield max power transfer in a rectangular horn because no way is the wavefront perfectly spherical. It can't be if your polar response is say 90x60 (that's more of an oval). Thoughts?

all equations leave some degrees of freedom. in this case the area slice can be any geometry you want. why would that affect the loading?

roy

[bodcaw boy]

So are Roy and Edgar in full agreement?

Roy and Edgar are in full agreement that, "how each distributes the area is related to how each thinks the wave is propagating down the horn and how each thinks the loading should be. in all cases, assumptions are made but real world measurments can reveal some errors in our thinking."

I know I keep saying this, but I need to revisit Post's thesis. From what I'm reading between the lines, I don't think a straight up tractrix area expansion would yield max power transfer in a rectangular horn because no way is the wavefront perfectly spherical. It can't be if your polar response is say 90x60 (that's more of an oval). Thoughts?

I'm not familiar with Post's thesis, but then I have to admit that horns are a side interest for me and I'm always learning new stuff about them. All that aside; even in a round tractrix horn the wave front is not perfectly spherical. The only horn that supports a truly spherical wave front is conical with a circular cross section. Earl Geddes published papers on this sort of thing.

actually that is not true. the conical equation assumes a plane wave traveling down the conical area horn in order to arrive at the assumed real and imaginary acoustical impedance.

It really comes down to what you want to optimize. Nowadays, when Watts are super-cheap, do you really care about maximum power transfer? In the pro audio world, pattern control is most important -- they want everybody in the audience to hear essentially the same thing. In your living room you don't care much about pattern control -- you just want the best sound quality possible at a single listening location.

max power transfer helps keep distortion down.

People have been moving away from exponential horns and toward tractrix horns because tractrix horns sound better. Since the frequency response and loading characteristics of similarly sized exponential and tractrix horns differ only by small amounts, the differences in their sonic quality must be due to something else. Again, Geddes enters the picture and claims that the sonic differences are due to "higher-order-modes" -- resonances within the horn body due entirely to the shape of the horn itself. Maybe there is something to that. I honestly don't know.

i arrived at tractrix and later modified it in order to achieve what i thought were important acoustic, electrical and mechancial goals. if ever another equation was ever "discovered" or synthesized that achieved and exceeded what we get now, i would be all over it. higher order modes are just a fancy way of saying that you are getting harmonically related reflections in the horn.

Edgar (Greg)

take care,

roy

[bodcaw boy]

I think tractrix assumes planar to spherical as it travels down the horn. Regardless, I was suggesting that the ideal area expansion should change slightly based on the shape that you want your exit wavefront to be. Max power transfer is all about reducing distortion by making the driver work less hard, not about the power it takes to drive to the SPLs you desire. However, I would argue that you can show that distortion in an amplifier is inversely proportional to its gain (for a given topology). So really, you want to get by with as little volts as possible. And then polar response deals with the fact that about 90% of the sound that arrives at the listening position is reflected, not direct. Due to the Haas effects, we put more emphasis on the direct sound, but the tonal response of the reflected sound still affects our perception quite a bit. If you can have both, then why not?

exactly, that is why i have noticed that speakers with inconsistent power response (related to polar response) will tend to sound very different in different rooms. toole did an interesting paper on that.

take care,

roy

[bodcaw boy]

Again, it's about what you want to optimize. There is a whole school of speaker design that says that the sound should be omnidirectional, which would maximize the room reflections that you note. There is yet another school of speaker design that says that the sound should be tightly controlled, which would minimize the room reflections. The fact that superb-sounding speakers are available from both camps tells me that neither assumption is 100% correct (or incorrect).

I am not disagreeing with you ... just playing Devil's advocate.

what should the goal of the speaker be?

[bodcaw boy]

There is yet another school of speaker design that says that the sound should be tightly controlled, which would minimize the room reflections.

I would argue that the only way to truly minimize room reflections would be to make the room itself totally absorbtive. Not practical or desireable to most...

Dr Toole over at Harman has done many interesting listening tests where the test subjects would almost always identify speakers with poor polars, as having a lower quality sound. Many of these test subjects were just ordinary folks with minimal training in how to listen. He claims that reflected sound must contain as much of the freq spectrum of the direct sound as possible to sound "right" to most people's ears. Check out his white papers at Harman...

i read his paper and it was very interesting. esstentially, by making sure that as much of the freq spectrum of the direct sound is reflected, in equal amounts, you are removing an "equalizer".

take care,

roy

[Edgar]

actually that is not true. the conical equation assumes a plane wave traveling down the conical area horn in order to arrive at the assumed real and imaginary acoustical impedance.

Again, we are talking about two different things. You are talking about the assumptions made to derive the expressions that describe the acoustical impedance, while I am talking about the actual shape of the wave front as it propagates down the horn. In the real world, neither assumption is exactly correct.

Greg

[Edgar]

what should the goal of the speaker be?

To sound good, of course! []

[mikebse2a3]

what should the goal of the speaker be?

To take an electrical input from the amplifier and transform it into an Acoustical Wavefront with maxumium efficiency (I would also add that all things being equal Highest Sensitivity available is important also especially in a system's context) and least distortion (of all forms ie:Frequency Amplitude, Phase, IM and etc.....) over as wide a frequency bandwidth as necessary to maintain an accurate transform.

Also in the goal IMO, The best loudspeaker designs should also have consistant (without abrupt shifts) polar frequency responses which offers a very predictable interaction with the room/listener so that maximum performance can be acheived with what we know at this time about the way a listener perceives sounds from the direct and indirect sounds from the loudspeaker/room/listener integration.

mike tn

[bodcaw boy]

what should the goal of the speaker be?

To take an electrical input from the amplifier and transform it into an Acoustical Wavefront with maxumium efficiency (I would also add that all things being equal Highest Sensitivity available is important also especially in a system's context) and least distortion (of all forms ie:Frequency Amplitude, Phase, IM and etc.....) over as wide a frequency bandwidth as necessary to maintain an accurate transform.

Also in the goal IMO, The best loudspeaker designs should also have consistant (without abrupt shifts) polar frequency responses which offers a very predictable interaction with the room/listener so that maximum performance can be acheived with what we know at this time about the way a listener perceives sounds from the direct and indirect sounds from the loudspeaker/room/listener integration.

mike tn

i agree with what you have written but still what should the goal of a loudspeaker be? my answer: to recreate the event; to be a reproducer (not a producer) of the acoustic event.

take care,

roy

[bodcaw boy]

actually that is not true. the conical equation assumes a plane wave traveling down the conical area horn in order to arrive at the assumed real and imaginary acoustical impedance.

Again, we are talking about two different things. You are talking about the assumptions made to derive the expressions that describe the acoustical impedance, while I am talking about the actual shape of the wave front as it propagates down the horn. In the real world, neither assumption is exactly correct.

Greg

that is why, if you try to get closer to the real world, then the tractrix loads the best, not the conical.

roy

[bodcaw boy]

what should the goal of the speaker be?

To sound good, of course!

that's one goal. what if the event was recorded not to sound good.......

[Edgar]

what if the event was recorded not to sound good.......

Not quite sure what "recorded not to sound good" means. I do like your definition that it should be a reproducer, not a producer, of sound. I look at everything as an engineering problem, so "to sound good" to me means creating the most accurate reproduction of sound possible within whatever external constraints apply.

Greg

[mikebse2a3]

that's one goal. what if the event was recorded not to sound good.......

That's why I want a loudspeaker that can maintain it's neutral accuracy of reproduction when placed in a properly treated acoustical enviroment! Then I can reproduce very good recordings with accuracy and great sound.

I can also take recordings that have obviouse flaws and sometimes very successfully apply EQ correction for what I personelly perceive as a more realistic (accurate would be debateable) reproduction.[]

In other words by starting with very accurate reproducer I have the option of a very accurate reproducer on it's own or a very accurate reproducer that is very adaptable to EQ changes that can help less than ideal recordings! This ability to adapt with an inaccurate system IMO would be much less likely!

mike tn

Edit: Just to be clear whether the recording was intentionally or unintentionally made to sound bad I do realize that when I choose to take my EQing and applying it that I have crossed the line into making my system into a producer of sound. But with all the variables that go into making a recording I will argue that EQing for pleasure and possibly a more realistic(as opposed to accurate) sound is an option I want available in my system. Having an accurate reproducer is essential IMO for me to be able to accomplish this goal.

[greg928gts]

Are there any Klipsch speakers, past or present, that are producers, more so than reproducers?

Greg