Driver preference for Frugal horns

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Scottmoose

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Re: Driver preference for Frugal horns
« Reply #20 on: 31 May 2015, 11:39 am »
Thanks for the graph. In FR terms, should be a reasonable candidate for back loading, details depending on requirements / circumstances as always of course.

FullRangeMan

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Re: Driver preference for Frugal horns
« Reply #21 on: 31 May 2015, 12:03 pm »
Back loading means Frugal Horn?
Frugal is a elegant and simple project.
I dont like other horns models(front side firing), just back or side firing.
How would be the bass(under 100Hz) with Frugal?
Thanks

Scottmoose

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Re: Driver preference for Frugal horns
« Reply #22 on: 31 May 2015, 07:22 pm »
No, back loading is a generic cover all for any type of back loaded enclosure, be it a reflex, back horn, quarter-wave et al. They're ultimately all related on a very basic level; it's largely a matter of degree.

Depends on the driver, and what exactly you mean by 'how would the bass be', since that is quite a broad subject. ;) As noted, the Omega unit mentioned will not physically fit FH3, which instantly rules it out even if the driver didn't need a larger cabinet from an operational perspective (which it does). It will probably go in the larger FHXL, but I can't speak for performance details since as I mentioned, I'll need to get my main computer back up and running. Unfortunately my health isn't great at present, so I'm limited in what I can do.

FWIW, a couple of broad points regarding back-horns that might be of some general interest:

-A back horn does not possess a compression chamber per se: the listening room is actually the compression chamber for a back horn. As far as enclosures are concerned compression chambers are the sealed chamber loading the rear of a driver in a front loaded horn, generally with the object of reactance annulling. The chamber often (but not invariably) employed on back-horns is a low-pass filter chamber: the objects of the two are dissimilar. In terms of the physics, such designs are ultimately extreme variations on the bass reflex theme.

-Back horns do not require a low pass chamber; the presence of a low pass chamber does not define whether a horn is a horn. A horn at the most basic level is simply a pipe that expands toward the terminus. Ideally it will be impedance matched down to it's QW cut-off frequency (F0), but most are not due to space constraints, so the bandwidth F0 - Fc will be provided by resonant action unless of course it's a boundary loaded design, in which case the room is a physical part of the horn and has to be factored in.

-It's a myth that back-horns require a driver with a low Q. That is a misunderstanding from the early days of audio, when power cost a fortune, so high sensitivity, highly damped drivers were produced for use with low-output amps that possessed variable output impedance. Driver specs. appropriate for a back-horn are basically the same, or similar, to those suitable for a bass reflex box. A back horn of course can be a more efficient load, and has a wider gain BW, so a slightly lower Q (once adjusted for amplifier output impedance or any series R present) can be used. More important is the mass corner, since although a back horn generally has a wider gain BW than other back-load variations, there's a limit to how high you can run them before GD becomes a problem. Very low Q drivers, uncorrected, aren't much use unless they have a concomitantly low resonant frequency, or you can 'fill in' the gap between the upper corner frequency of the horn and the mass corner roll-off of the driver with a short front low-midrange horn.


FullRangeMan

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Re: Driver preference for Frugal horns
« Reply #23 on: 1 Jun 2015, 09:19 am »
Thanks Scoot for your extensive reply, I appreciated.
W/this Omaga driver Iam prone to use it in:
BR 60L
FH XL
Passive Radiator (which one?)
If possible I would want use a floor standing enclousure.
I dont like stand mount loudspeakers.
« Last Edit: 2 Jun 2015, 11:58 am by FullRangeMan »

planet10

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Re: Driver preference for Frugal horns
« Reply #24 on: 1 Jun 2015, 06:00 pm »
Sorry, late to this thread.

What are the best overall sounding drivers that work well in the Frugal horn enclosure?  Thanks:)

A note on spelling: A frugal horn is any horn on the frugal-horn site. A Frugel-Horn is one of the 3 similar designs: the original Frugel-Horn Mk3, the larger Frugel-HornXL, and the unreleased Frugel-Horn Lite.

Those frugel horns that aren't Frugel-Horns should use the drivers they were designed for. The Frugel-Horns on the other hand are designed to support a broad range of drivers.

For the Frugel-Horn Mk3 (part of our FH3 flat-pak info) these are the usual candidates, but other drivers have been used successfully -- almost any 4-4.5" driver should work with the FH3:

<boilerplate>

if you have the power the A7.3 (minimum 10W recommended) delivers more than any of the others -- more detail, finesse, top end, and DDR*. It is the least robust of the lot.
*(DDR = Downward Dynamic Range. That attribute of a hifi component that gives it the ability to resolve very low level information in the presence of much larger signal.  Shows up, if on the recording, as more subtle detail in instruments & voice, better & more 3D image/soundstage & more)

The FE126eN2 is the goto driver for most people with low power SE amps. It commonly gets used with 2-10 watts or more.

The EL70eN (no longer available) can be looked at as a budget paper cone A7, giving up some finesse, some top, but with the best bass of the lot.

The FF125wKeN can be considered as part way between EL70 & FE126, the FF105wKeN a bit smoother, with slightly better top-end and less bass quantity

Both the A7 and FE126 are very revealing of an amps shortcomings, FF105 & FF125 gain an edge if the amp doesn't want its deficiencies shown up.

A7.3eN is some 7-8 dB less efficient than FE126, FF125 between EL70 & FE126. A7p about the same as FF125

With FE126 the FH3 ideally has corners to load into, at least walls to help support the bass. The others are not bass shy and one tunes the bass they produce by adjusting the damping below the driver (as well as using room placement).

FE126, FF105, & FF125 both get special pre & post EnABL treatment to help with specific rough edges that stock versions of these drivers are criticized for -- but they are still Fostex. A7p gets some special pre EnABL treatment.

A7PeN stands out in that it needs more break-in than any of the others.
</boilerplate>

The FHXL was designed specifically for the Alpair 10p/10.3 as a start. We also have it with Fostex FF165wk. Others have reported success with FE168eS & FE166En. This design is fairly new, i expect other drivers will be found to work successfully.

The unreleased (soon) Frugel-Horn Lite works with 3" drivers. Scott has simmed it with a wide range of drivers, we have built it with FF85wKeN, and it is really superb. It does not go really low, but low enuff to produce the 2nd harmonic of low notes and trick you into thinking the low bass is there.

dave

planet10

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Re: Driver preference for Frugal horns
« Reply #25 on: 1 Jun 2015, 06:09 pm »
I wonder if anyone has tried a Frugal horn build with a straight front and back?

The original drawings had a perpendicular front, we never built one of those.

A fellow in Ireland, has cut the back flare off (a necessary part of the full design) and is trying to commercialize it. For what it was worth it did get a positive review in one UK magazine for sonics, less so for cosmetic detail.

At least one set has been made with the rear curve* replaces with a straight section.

*(functionally this was originally developed by Ron Clarke to make a high aspect ration horn mouth behave more like an ideal square/circle.)

We did build a prototype Twin FH3 with perpendicular front.



These are a 2 way with the CSS VWR126X MTM kit.

If you are interested in the perpendicular front FH3 or the Twin email me.

dave



Ultralight

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Dave Re: Driver preference for Frugal horns
« Reply #26 on: 1 Jun 2015, 07:41 pm »
Dave,

Fantabulous reply!  I'm sure you've posted this elsewhere but it is the first time I've read this.  Wonderful summary - looks like the Alpair 7.3 is your preferred choice if one has sufficient power.

Two follow up questions on the Alpair 7.3p vs FE126.

1. Which has better low volume (say 55db which is quite soft) dynamic response and detail/transients?  I keep hearing that higher efficiency speakers (for example) will do better with low volume listening.  While lower efficiency drivers need to be played at louder levels to come alive. 

2. As to damping below the driver, does that affect only the QUANTITY of the bass region, or does it actually also impact the EXTENSION of the bass region?  For example, will having LESS damping allow the bass to extend deeper?

Also, has anyone run in such a large or bass absorptive room that they used zero damping material? Curious.

Thanks again for a fantastic post.

UL

Sorry, late to this thread.

A note on spelling: A frugal horn is any horn on the frugal-horn site. A Frugel-Horn is one of the 3 similar designs: the original Frugel-Horn Mk3, the larger Frugel-HornXL, and the unreleased Frugel-Horn Lite.

Those frugel horns that aren't Frugel-Horns should use the drivers they were designed for. The Frugel-Horns on the other hand are designed to support a broad range of drivers.

For the Frugel-Horn Mk3 (part of our FH3 flat-pak info) these are the usual candidates, but other drivers have been used successfully -- almost any 4-4.5" driver should work with the FH3:

<boilerplate>

if you have the power the A7.3 (minimum 10W recommended) delivers more than any of the others -- more detail, finesse, top end, and DDR*. It is the least robust of the lot.
*(DDR = Downward Dynamic Range. That attribute of a hifi component that gives it the ability to resolve very low level information in the presence of much larger signal.  Shows up, if on the recording, as more subtle detail in instruments & voice, better & more 3D image/soundstage & more)

The FE126eN2 is the goto driver for most people with low power SE amps. It commonly gets used with 2-10 watts or more.

The EL70eN (no longer available) can be looked at as a budget paper cone A7, giving up some finesse, some top, but with the best bass of the lot.

The FF125wKeN can be considered as part way between EL70 & FE126, the FF105wKeN a bit smoother, with slightly better top-end and less bass quantity

Both the A7 and FE126 are very revealing of an amps shortcomings, FF105 & FF125 gain an edge if the amp doesn't want its deficiencies shown up.

A7.3eN is some 7-8 dB less efficient than FE126, FF125 between EL70 & FE126. A7p about the same as FF125

With FE126 the FH3 ideally has corners to load into, at least walls to help support the bass. The others are not bass shy and one tunes the bass they produce by adjusting the damping below the driver (as well as using room placement).

FE126, FF105, & FF125 both get special pre & post EnABL treatment to help with specific rough edges that stock versions of these drivers are criticized for -- but they are still Fostex. A7p gets some special pre EnABL treatment.

A7PeN stands out in that it needs more break-in than any of the others.
</boilerplate>

The FHXL was designed specifically for the Alpair 10p/10.3 as a start. We also have it with Fostex FF165wk. Others have reported success with FE168eS & FE166En. This design is fairly new, i expect other drivers will be found to work successfully.

The unreleased (soon) Frugel-Horn Lite works with 3" drivers. Scott has simmed it with a wide range of drivers, we have built it with FF85wKeN, and it is really superb. It does not go really low, but low enuff to produce the 2nd harmonic of low notes and trick you into thinking the low bass is there.

dave

planet10

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Re: Dave Re: Driver preference for Frugal horns
« Reply #27 on: 1 Jun 2015, 07:46 pm »
1/ I'd give the drivers with bettter bass do better at low volumes

2/ It is mostly about bass level, but more damping below the driver will also reduce the ripple inherent in a quarter-wave design -- much of that ripple is removed by the damping in the point. I would not build one without at least the damping in the point.

When we did the 1st showing of the FH3 with A7 it was a quick swap from the FE126e and there was no front damping. Even pulled out 4 ft from the wall there was clearly toomuch bass but it was big & round and tuneful.

dave

Ultralight

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Re: Dave Re: Driver preference for Frugal horns
« Reply #28 on: 1 Jun 2015, 07:52 pm »
Thanks Dave,

That was quick. We must be both online. I'm about to go through security for my flight but quick follow-up.

1. I'm sorry, I'm unclear.  Are you saying that the Alpair 7.3 will be better than the FE126 at low volume?

2. I'm not sure what 'ripple' is - does it relate to extension? From your reply, I am understanding it to mean damping affects quantity rather than extension. 

I do wonder if FH3 can reach pretty flat down to 35hz in small rooms. or does one need FHXL.   I guess this is a new question.

Thanks again Dave.

UL 

1/ I'd give the drivers with bettter bass do better at low volumes

2/ It is mostly about bass level, but more damping below the driver will also reduce the ripple inherent in a quarter-wave design -- much of that ripple is removed by the damping in the point. I would not build one without at least the damping in the point.

When we did the 1st showing of the FH3 with A7 it was a quick swap from the FE126e and there was no front damping. Even pulled out 4 ft from the wall there was clearly toomuch bass but it was big & round and tuneful.

dave

planet10

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Re: Dave Re: Driver preference for Frugal horns
« Reply #29 on: 1 Jun 2015, 08:09 pm »
Are you saying that the Alpair 7.3 will be better than the FE126 at low volume?

That is my experience.

Quote
I'm not sure what 'ripple' is - does it relate to extension?

Every undamped quarter-wave design (horns/TLs/voigts etc) has a series of harmonics coming out the terminus. You want the lowest one and none of the rest. Various techniques are used to suppress those higher harmonics because they go in and out of phase with the front and cause a rippled response.

Damping is one way of doing this, but it is not abrupt so if you overdamp you can kill the ripple but at the expense of bass extention from the fundemental quarter wave action.

Driver offset can be used to kill one of the unwanted harmonics, usually the 1st or 2nd unwanted one -- if you get rid of the first then you can see that there becomes less challenge for damping to kill the rest.

Folds in the line without any deflectors create a volume expension which act as a low pass filter.

Horns with a  air-cavity/pre-chamber have a LP caused by the volume of the air cavity.

The FHs do not have an air-cavity as they are tapped horns, but they do have a choke (thanx Paul Klipsch) just before the major flare that does much the same.

The taper affects the placement of the harmonics and thus can have a secondary affect.

I've probably missed some.

I should also note that some of these techniques were brought to light by MJK's modeling software.

Quote
I do wonder if FH3 can reach pretty flat down to 35hz in small rooms. or does one need FHXL.

Corner loaded in the right room at reduced levels, maybe. FHXL will reach that low.

dave

FullRangeMan

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Re: Driver preference for Frugal horns
« Reply #30 on: 2 Jun 2015, 12:02 pm »
Thanks Dave for your reply.
I would like the FH-XL that Scott mention.
Do you already listen an Omega FR with a FH?
About FHXL vs the factory project BR 60L, what I would expect?
Thanks
« Last Edit: 2 Jun 2015, 01:24 pm by FullRangeMan »

Scottmoose

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Re: Driver preference for Frugal horns
« Reply #31 on: 2 Jun 2015, 01:06 pm »
AFAIK Dave hasn't tried an Omega driver in FHXL -as far as I know, they seemed to be available for about ten seconds then vanished -not sure what happened, but they don't seem to be available as separate units any longer. So it would be difficult to say how it would compare for that reason, and in that it's an apples / oranges comparison anyway: the designs have different form factors, different gain bandwidths, different response and loading characteristics. You'd probably (probably) find FHXL controls the driver more as it functions over a wider gain BW, and power-response is different for the same reason as the box will be operative up to ~ 250Hz - 300Hz. A BR may (may) have a slightly flatter response curve, but this is variable with the room, so YMMV. BTW, it's 'Scott', not 'Scoot' -I'm not well enough to do much in the way of scooting. ;)


Expanding a bit on what Dave said above (Olson rather than Klipsch ;) ) re 'ripple' in a back-horn, on a technical level it's the result of there being a disparity between the 1/4 wave fundamental (F0) which is a function of axial length (all expanding pipes are 1/2 wave resonators with a 1/4 wave fundamental), and the -3dB frequency to which the horn is impedance matched (Fc), which is a function of terminus size. If Fc is > F0, then like any other pipe, the impedance mismatch at the terminus results in a shockwave being reflected back along the horn flare path, causing nulls / cancellations at specific frequencies that vary depending on the design. This can be partly addressed via damping and as a side-effect of internal acoustic low-pass filters of xyz type, be it a dedicated chamber, folding scheme or whatever. 

FH3 et al were designed as corner-horns; the room boundaries are a part of the horn expansion path. Optimally positioned, Fc = F0 in FH3 (more or less) so there's significantly less response deviation. With the MA drivers, gain is often excessive when corner-loaded, so they would need significantly more damping to reduce LF output. Most people are happy with them in 1/4 space, i.e. with floor & front-wall loading; the internal damping keeps the response reasonable, and the curved terminus helps with this also.

For the sake of interest, the commercial box Dave referred to above is essentially FH3 which the company have seriously compromised by sawing the back off, and turned what was a tapped hypex corner-horn with internal low pass into a decidedly sub-optimal tapped conical horn (aka TQWT). Because the cabinet is no longer operating properly, they've had to stick a wide front baffle onto it and add a shelving filter to get the response into line -which it would have been if they hadn't mucked it up in the first place. Sigh.

FullRangeMan

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Re: Driver preference for Frugal horns
« Reply #32 on: 2 Jun 2015, 02:12 pm »
Sorry Scott my incompetence at the keyboard, seems its against to me these last days.
I suspect I must content myself with a mid sized box in a stand.
I can order the stand in real wood though.
At the BR box my only doubt is the duct dimensions.
I suspent the dimensions are suited to the smaller box 40L, not sure.



planet10

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MJK

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Re: Driver preference for Frugal horns
« Reply #34 on: 2 Jun 2015, 03:48 pm »
Scott,

The following paragraph has a lot of statements that in my opinion and expereince are simply incorrect. 

"Expanding a bit on what Dave said above (Olson rather than Klipsch  ) re 'ripple' in a back-horn, on a technical level it's the result of there being a disparity between the 1/4 wave fundamental (F0) which is a function of axial length (all expanding pipes are 1/2 wave resonators with a 1/4 wave fundamental), and the -3dB frequency to which the horn is impedance matched (Fc), which is a function of terminus size. If Fc is > F0, then like any other pipe, the impedance mismatch at the terminus results in a shockwave being reflected back along the horn flare path, causing nulls / cancellations at specific frequencies that vary depending on the design. This can be partly addressed via damping and as a side-effect of internal acoustic low-pass filters of xyz type, be it a dedicated chamber, folding scheme or whatever."

In acoustics texts where the one dimensional wave equation is derived and solved for a horn geometry, one of the first simplifications is that the horn is very long if not infinite. This means that sound waves travel only in one direction, from the transducer to the mouth, without any reflections. The mouth is sufficiantly large that the sound waves are efficiently emmitted out into the room over a broad frequency band and no sound is reflected back into the horn. So mathematically a horn is an expanding geometry with an adequate mouth area to not generate reflections, sound only travels in one direction.

In reality getting a horn big enough to satisfy this definition for bass frequencies is not going to happen in the compact enclosures that we typically refer to as BLH's. At low frequencies the mouth is always too small and reflections occur leading to standing wave resonances. These standing wave resonances are all odd harmonics of a 1/4 wavelength, there is no physics or math that will support a 1/2 wavelength resonance in an expanding geometry where one end is open and the other end closed. There are no shockwaves, only reflections from a mouth that is too small. The peaks and nulls are easily explained by the transmission line models which are all quarter wave based. The BLHs are all too small for the coupling volume math derived for horns to be applicable, treating the design as a transmission line is a better way of sizing this coupling volume. The ultimate proof is found in the electrical impedance curve of an empty BLH enclosure, if there are multiple peaks then it is behaving as a TL and not as a horn.

At higher frequencies the BLH can start to act like a horn but by then the designer is typically looking to roll off the mouth output and go with the driver as the primary acoustic source. All varients of the FH family, and every other BLH I have found on the Internet with the exception of Nelson Pass' design, obey these simple laws of physics and are all really transmission line designs with or without the corner loading.

Martin

http://www.quarter-wave.com/Horns/TL_and_BLH_Physics.pdf


planet10

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Re: Driver preference for Frugal horns
« Reply #35 on: 2 Jun 2015, 05:43 pm »
No matter the theoretical detail, the Frugel-Horn enclosures work REALLY well.

dave

MJK

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Re: Driver preference for Frugal horns
« Reply #36 on: 2 Jun 2015, 06:51 pm »
I have no doubt that the FH design works very well. I heard a pair designed for the FF225WK driver using a custom worksheet I prepared just for the FH geometry. I have analyzed the FH concept in some detail and have a pretty solid understanding of how it works and what variables are important, a good design deserves that type of attention.

Unfortunately, in my opinion there is still a lot of misinformation and questionable physics being used to describe the behavior of designs we commonly refer to as BLHs. If you make strong statements you should be able to provide a solid technical basis for what is being stated. Every acoustics text I have looked at defines a horn consistent with my understanding and I know the authors are much smarter than I am on this topic.

Scottmoose

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Re: Driver preference for Frugal horns
« Reply #37 on: 2 Jun 2015, 10:40 pm »
I defer to you on all matters pertaining to physics Martin. You're an engineer / physicist, I am not. That said, in fairness, I think your primary complaint with my post above is partly loose phrasing on my part, and partly due to us having / applying differing definitions or criteria. I hope you and everyone else will accept my sincere apologies for the former. As for the latter, I believe that is a matter of interpretation, but strongly advise anyone reading to accept yours over my own.

Going through some of the errors you rightly identify (and apologies if I miss any; I haven't been well since mid-February and I'm currently on five different pain killers which aren't doing much for clear thinking):

-Agreed; 'reflection' is a better term than shockwave. My apologies for the laxity.

-We appear to be employing a different definition for the term 'horn'. I do not define a horn as a pipe that is impedance matched to its QW cutoff frequency (which is what is usually assumed in acoustics texts and what you are using). I simply define it as a pipe that expands toward the terminus, since expanding pipes to the best of my knowledge possess some element of 1/2 wave behaviour -a point GM also frequently makes, and is usually noted in texts on the subject of pipe resonance, e.g. http://hyperphysics.phy-astr.gsu.edu/hbase/waves/opecol.html#c1 In my own defence, I did make the point that there is usually a difference between the QW cutoff frequency (F0) defined by axial length and the frequency to which the horn (or expanding pipe if you prefer) is impedance matched down to (Fc), which is generally taken as a function of terminus size / circumference, with resonant action covering the F0 - Fc BW. So I entirely accept the fact that such designs should be developed as resonant types, always have & AFAIK, I've never intentionally suggested otherwise. If my prose lacked clarity & appeared to imply the opposite, then I owe you and everyone else who read it a most sincere apology.

-Since as far as I am aware boundary loading is at a simplistic level merely a continuation of expansion, FH3 (for e.g.) taken purely as Rm value when corner loaded should have a conservative Fc around the 87Hz point. To be frank, I rarely bother being overly precise in this regard since rooms differ so much, with construction, shape, furnishings etc. having such an impact on behaviour, in my view it becomes something of a moot point. You have far more knowledge and expertise on this matter than myself, so please accept my apologies once again for my inept phrasing before.

-The FH boxes do include an element of Ron's work on curved wavefronts rather than purely plane-wave (that's where the curves come from) & he was happy with the implementation. I imagine you have access to the same & a lot more data on this from other sources + your own work than I am ever likely to, and can refine / improve upon it if you so wish to an extent far beyond anything I could achieve.

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Re: Driver preference for Frugal horns
« Reply #38 on: 2 Jun 2015, 11:59 pm »
Quote
We appear to be employing a different definition for the term 'horn'. I do not define a horn as a pipe that is impedance matched to its QW cutoff frequency (which is what is usually assumed in acoustics texts and what you are using). I simply define it as a pipe that expands toward the terminus, since expanding pipes to the best of my knowledge possess some element of 1/2 wave behaviour -a point GM also frequently makes, and is usually noted in texts on the subject of pipe resonance, e.g. http://hyperphysics.phy-astr.gsu.edu/hbase/waves/opecol.html#c1 In my own defence, I did make the point that there is usually a difference between the QW cutoff frequency (F0) defined by axial length and the frequency to which the horn (or expanding pipe if you prefer) is impedance matched down to (Fc), which is generally taken as a function of terminus size / circumference, with resonant action covering the F0 - Fc BW. So I entirely accept the fact that such designs should be developed as resonant types, always have & AFAIK, I've never intentionally suggested otherwise. If my prose lacked clarity & appeared to imply the opposite, then I owe you and everyone else who read it a most sincere apology.

Scott,

Your definition is at odds with the acoustics texts I consulted, I think you are out on your own with this definition of a horn. The broad band increase in efficiency can only occur if the mouth is large enough to not reflect sound back into the horn, no standing wave resonances.

Consulting the site your referenced, look at the mode shape represented by the red curves. The red curve is the velocity profile along the length of the pipe, the shape is the same for the closed cylinder and the closed cone. It is a quarter wave mode shape. Because of the pipe geometry the fundamental resonant frequency is higher for the cone compared to the cylinder, no big surprise there. Click on the "Closed cone" link and look at the mode shapes on the next page; they are 1/4, 3/4, and 5/4 standing waves. The mode shape is the key and not the frequency equation.

Martin

Scottmoose

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Re: Driver preference for Frugal horns
« Reply #39 on: 3 Jun 2015, 07:49 am »
Martin,

Presumably it's at odds with textbooks on acoustics because it doesn't come from them. As I recall, GM has the same take, so I do have some company. Either way, we appear to be debating linguistic semantics in a similar way that people use the term 'transmission line' for a wide variety of differing loads. There doesn't appear to be any real disagreement as far as the physics are concerned; just over my prose style. For example, re increase in load efficiency only occurring above Fc: yes. I agree with you. I've always agreed with you. That is exactly what I was talking about when I said that if F0 is lower than Fc, then that portion of the BW is produced by resonant action. I took it as read that people understood the implications of '-3dB frequency to which the horn is impedance matched (Fc)' and the transition that occurs below this if the QW resonant frequency (F0) is lower -again, I apologise for my poor prose style.

Agreed -which is why I made the point that they have a 1/4 wave fundamental, but as far as I am aware, like an open pipe they produce both odd and even order harmonics, not just odd.