Horn contour accuracy - how important?

[Defo]

How important is it to have an exact expansion rate to a given contour of a horn?

For instance; exponential, hyperbolic, and tractrix looks almost the same with tiny differences in expansion rate... Is there really any audible difference?

[GM]

Depends on the pass-band, the different expansions cause varying degrees of throat and mouth distortion over an increasing BW with decreasing M factor that's easily audible in our acute hearing BW and why some folks put a lot of effort into how the throat mates to the driver and the mouth to the surrounding air.

Once this is done, so much of the horn's length is already accounted for, so in this case the M factor becomes mostly moot and it's not uncommon to just connect them with a straight line, i.e. a waveguide (WG).

GM

[Defo]

Originally Posted by GM

Depends on the pass-band, the different expansions cause varying degrees of throat and mouth distortion over an increasing BW with decreasing M factor that's easily audible in our acute hearing BW and why some folks put a lot of effort into how the throat mates to the driver and the mouth to the surrounding air.

Once this is done, so much of the horn's length is already accounted for, so in this case the M factor becomes mostly moot and it's not uncommon to just connect them with a straight line, i.e. a waveguide (WG).

GM

Thanks for the reply. Whats the M factor? Expansion rate?

Given a 2" throat Le-Cleach/tractrix horn, would it be a bad idea to adapt the throat to a 1" like shown in the drawing below? The black line is the horn with a 2" throat and the red lines are with adapter.

[GM]

You're welcome!

Right, Prof. Leach uses 'M' in lieu of the 'T' factor of days gone by where 0.5 = Hyperbolic, 1.0 = exponential and hypex for anything in between.

Assuming it's an accurate representation, then in theory the discontinuity at the splice point will cause reflections back to the throat and why the adapter is normally attached at the throat, but this increases HF beaming/throat distortion due to the low M(T) factor.

Seems to me that 'best' in this case would be to use one of the 'new' duplex compression drivers to ~ 'have your cake and eat it too'.

GM

[Defo]

Originally Posted by GM

Assuming it's an accurate representation, then in theory the discontinuity at the splice point will cause reflections back to the throat and why the adapter is normally attached at the throat, but this increases HF beaming/throat distortion due to the low M(T) factor.

GM

Wouldnt this mean spherical horns have less HF beaming/throat distortion due to a higher M(T) factor then say... tractrix? Why is tractrix horns more common? Is throat distortion the same thing as higher order modes? (HOM's)

Would a cone shaped "phase plug" like in the picture below reduse HF beaming in such horns?

[GM]

Correct. My understanding is that HOMs are reflections generated within the horn that resonate like a 'horn within a horn' which if massive enough can modulate the driver, so I don't view them as horn 'honk' generators per se, though they can exacerbate them if throat distortion due to an acoustically poor transition between driver/horn is present.

Consider the old Altec 311, 511, 811 sectoral horns, they match the horn to the driver and gradually transition it to a conic radial to get good HF directivity - so far, so good - then abruptly neck it down as required to create an expo radial to make it load with some degree of directivity over a wide BW which causes massive reflections back to the driver's phase plug that its tiny filter chamber can't cushion enough.

Factor in a relatively poor mouth termination that adds a second layer of reflections back to the transition and on back to the throat to create a delayed three stage 'horn within a horn' and little wonder that it 'honks' with a slow decay rate long after the signal stops, though bell/mouth damping and an XO point slope that rolls off the 'honk' portion of its LF BW reduces it to a fairly benign expo WG and a throat foam insert that extends past the conic/expo transition will damp down the worst of the HOMs, though most folks don't feel the need for the latter once the other two 'fixes' are done.

Folks like how its low distortion mouth sounds, but to take max advantage of it requires it be fairly limited in gain BW to keep excessive beaming of its otherwise hypex flare to a minimum.

IME it can certainly help with a point source driver, but haven't tried it with a compression driver nor do I recall seeing one other than as part of the driver. Seems like there wouldn't be enough room for one considering the small throats typically used though.

GM

[gedlee]

Originally Posted by GM

Correct. My understanding is that HOMs are reflections generated within the horn that resonate like a 'horn within a horn' which if massive enough can modulate the driver, so I don't view them as horn 'honk' generators per se, though they can exacerbate them if throat distortion due to an acoustically poor transition between driver/horn is present.

HOM are basically as you say, but because they are delayed in time relative to the main wave - they travel a longer path - they can be quite audible long before they are a significant acoustic effect.

The minimization of HOM has been shown to reduce (elliminate) horn honk and since the coutour has a major effect on HOM's we must assume that the contour also has an audible effect.

There are, of course, other considerations.

[Jmmlc]

Hello Defo,

I don't like the presentation of the different profiles on the graph you shown.

See in atatched file a comparison of different profiles of horns having the same acoustiacla cut-off.

Best regards from Paris, France

Jean-Michel Le Cléac'h

Originally Posted by Defo

How important is it to have an exact expansion rate to a given contour of a horn?

For instance; exponential, hyperbolic, and tractrix looks almost the same with tiny differences in expansion rate... Is there really any audible difference?

[AndrewT]

Hi Jmmlc,
I'm surprised that the two Tractrix profiles are so much smaller (240/270radius) than the three other profiles (370/380radius) that are very similar in diameter (@ the mouth or @ the 90degree diameter).

[Jmmlc]

Hello Andrew,

This is easily understandable when we consider the main hypothesis on which is based the tractrix :

tractrix = propagation of cap spherical wavefronts having a radius :

radius = c / (2 . pi. Fc)
with c = speed of sound
and Fc = the acoustical cut-off frequency of the tractrix horn

As we can see Voigt choose empirically a mouth perimeter equal to one wavelenth at the cut-off frequency. (This is probably related to the common idea that's there is no need for a horn to have a mouth over a wavelength of the lowest frequency to cover.)

Then if you take the Kugelwellen horn which also uses an hypothesis of cap spherical wavefronts, that radius is 2 time the radius of the Tractrix.

No hypothesis about the shape of wavefronts is made for the Le Cléac'h but we can see that the profile of the Kugelwellen horn is very much similar on a large part of the profile.

Best regards rom Paris, France

Jean-Michel Le Cléac'h

Originally Posted by AndrewT

I'm surprised that the two Tractrix profiles are so much smaller (240/270radius) than the three other profiles (370/380radius) that are very similar in diameter.