Exponential Horn Question

[Bigdnfay1]

 Would a 2 dimensional horn (Increasing width and length only) be considered exponential? 

 

Big D

[Quiet_Hollow]

Conical.

[Bigdnfay1]

Let me rephrase.  Let's say 6 inch thick constant with increasing width and length.

Big D

[WMcD]

Would a 2 dimensional horn (Increasing width and length only) be considered exponential? 

 

Big D

I don't see why not, just as long as the area follows the exponential equation. This means the area has to double every X distance down the length. PWK called it Lamedh, the Hebrew for L. http://en.wikipedia.org/wiki/Lamedh.

This double every x is inherent in the exponential equation. You see it describing bacteria population which doubles every hour -- or a blob in science fiction which will grow to take over the county, then the state, then the nation, then the world.

The function doesn't have to double (2 times every x whatever) it can grow 1.05 times a year, as in growth of money funds with compound interest. But I'm getting off topic.

If the top and bottom and parallel and the side walls are diverging straight, you don't get a conical expansion. A conical expansion must have an area which is the square of the distance down the length. This is easier to do with a cone or a square pyramid, or even a rectangular pyramid. You might have seen diagrams where a single point of light is radiating into pyramidal areas (a fraction of space). The intensity drops as the square of the distance because it is falling on areas which increase as the square of the distance. Again OT, but can be interesting that you sort of know this stuff already but teachers don't put it all together in one lesson.

If the top and bottom are parallel and the side walls are diverging straight, you get something which approximates a hyperbolic horn. Baranek has a drawing of a hyperbolic megaphone which looks like this. You also see it as the matching section (throat to the bell section) of constant directivity horns which were started by Don Keele. Klipsch uses it in some of their THX systems.

WMcD

Edited April 26, 2015 by William F. Gil McDermott

[Deang]

Nice job Gil. Today, I learned something.

[Bigdnfay1]

What determines the X distance?  Say in a folded horn to reach a certain HZ the rate of expansion has to be a certain amount per a certain distance.

[John Warren]

What determines the X distance?  Say in a folded horn to reach a certain HZ the rate of expansion has to be a certain amount per a certain distance.

 

The lowest frequency desired determines all.  In other words, the area of the horn mouth must be a certain size to achieve a given low frequency.  If your horn is an exponential "transformer" you have only one X value that will give you the mouth area you need to meet the low frequency target and also meet the requirements of an exponential expansion.

 

You pick how low you want to go and everything else is determined.

Edited April 26, 2015 by John Warren

[Edgar]

If the top and bottom and parallel and the side walls are diverging straight, you don't get a conical expansion. A conical expansion must have an area which is the square of the distance down the length.

 

 

Yes, this is exactly correct. Conical expansion (top and bottom expanding as straight lines and left and right sides also expanding as straight lines) results in an area that expands as the square of the distance.

 

However, if only the top and bottom are expanding in a straight line while the sides are not expanding at all (or, similarly, if only the left and right sides are expanding in a straight line while the top and bottom are not expanding at all), then the area expands linearly with the distance. To achieve this same expansion rate with a 2-dimensional expansion would require a parabolic contour.

[Bigdnfay1]

Edgar, So an exponential folded horn would require contour at every section of the fold.

[Edgar]

Edgar, So an exponential folded horn would require contour at every section of the fold.

 

Techically, yes. But audio is very forgiving, so you can approximate any contour that you want with straight-sided sections, and not affect the performance significantly.

[Bigdnfay1]

 Edgar, hope this is not to confusing to figure out. a lot of crossing lines. Would this be a viable low-end folded horn concept?

Edited April 26, 2015 by Bigdnfay1

[Edgar]

 Edgar, hope this is not to confusing to figure out. a lot of crossing lines. Would this be a viable low-end folded horn concept?

 

Sure; as long as it's expanding, it's a horn. But with all of those folds and almost equal-length passages, at higher frequencies reflections and standing waves might be a problem.

[WMcD]

If the top and bottom and parallel and the side walls are diverging straight, you don't get a conical expansion. A conical expansion must have an area which is the square of the distance down the length.

 

Yes, this is exactly correct. Conical expansion (top and bottom expanding as straight lines and left and right sides also expanding as straight lines) results in an area that expands as the square of the distance.

 

However, if only the top and bottom are expanding in a straight line while the sides are not expanding at all (or, similarly, if only the left and right sides are expanding in a straight line while the top and bottom are not expanding at all), then the area expands linearly with the distance. To achieve this same expansion rate with a 2-dimensional expansion would require a parabolic contour.

Edgar is correct. Attached is the section from Acoustics by Leo Beranek which I was recalling.

OTOH, I'm sure I worked out a hyperbolic which comes very close.

WMcD

Parabolic Megaphone from Beranek Acoustics.pdf

[Bigdnfay1]

Thank You!

[WMcD]

What determines the X distance?  Say in a folded horn to reach a certain HZ the rate of expansion has to be a certain amount per a certain distance.

The answer is found in the attached U.S. Patent. As you can see, the cut-off wavelength is 18.1 times the length to double. This assumes the exponential equation. This is nice to know because PWK often used this to express the cut-off wavelength of his horns, rather than just coming out and saying fc in Hz.

Therefore, knowing the speed of sound is 13,500 inches per second we find: 13500/(18.1 x lamedh) = fc

For the K-Horn, length to double is 16 inches. (This is in the final two sections of the design where he used a rapid flare at the beginning of 8 inches to double, but in later versions it is uniform.) fc = 46.61 Hz (Oh and let me add that PWK describes the first section where two walls are parallel and the other two are diverging in straight lines as being parabolic, just like Edgar says.)

For the LaScala, it is 12 inches, by my estimation. It starts with (ignoring the reduced slot) about 1/2 square foot (78 inches square), doubles to 1 square foot, then doubles to 2 square feet, and doubles again to 4 square feet - - this is a total length of 3 feet. fc = 62 Hz

For the K-5, it is 2.25 inches. fc = 331 Hz.

For the K-400 it is 2.75 inches. fc = 271 Hz.

Now you know!

WMcD

US Patent on MCM Woofer.pdf

Edited April 26, 2015 by William F. Gil McDermott

[djk]

"Would a 2 dimensional horn (Increasing width and length only) be considered exponential? "

 

Parabolic.

 

I built wooden parabolic midrange horns in the late 70's, they had a septum down the middle and a 2-1/2" cone driver attached to the dual slot throat (the septum dividing the rectangle into two slots).

 

They sounded quite nice and ran from about 700hz to 7Khz.

 

These found their way into a Forte sized speaker. One fellow heard a pair I did for his sister, sold his JBL L-65 (Jubal) and made a set for himself.

 

The speaker measured dead flat on an Ivie 1/3rd oct analyzer, ±3dB or so out to 20Khz on the top end. An autoformer was used on the KSN 1034A  2-1/2" piezo cone driver, and on the KSN 1016 horn piezo tweeter. The mid was driven with a 1.5KΩ resistor in series with it, the tweeter had a 62Ω resistor in series with it.

[Marvel]

So a Smith horn or JBL 2397 would be a parabolic?

[djk]

I believe so, yes.

 

They have very low horn gain, but sound very natural.