also: lamèd From Hebrew לָמֶד (lamedh)

[WMcD]

Typically horn flare rates (areas)are described by the term "cut-off" frequency aka "Fc"; at freques below this this the horn just about stops working.  You put Fc into the exponential equation  

  however,  PWK often used the term "lamedh" (I'll use "Ld") to describe the horn area expansion;  It is the lengh of travel down the horn in which the area doubles  (or halves).  Therefor the expansion works like animals / bacterium doubling every time period.

  If my math is correct, the cuttoff wavelength (I'll call it "Lc) is 18.1 times the length to double.

     We can examine the LaScala's two paths (combined) and notice the area at the throat is 0.5 ft^2; then the paths go across the back to the interior corners where the area is 1 ft^2; then toward the front for a foot to where the area is 2 ft^2; then another foot to the mouth where the combined area is 4 ft^2.  Therefore we see the Ld is 1 foot or 12 inches.  The Lc is thus 18.1 * 12 and we dived the velocity of sound 15,00 in/sec by that wavelength to get an Fc of 62 Hz.

      We can check the PWK article on the K400 horn and notice that the length to double is given as 2.75 inches.  The math like the above shows that it's Fc is 270 Hz.  PWK was really getting it to go as low as possible to where the bass bin on the Khorn is running out of steam! 

     Good night all, WMcD

[Woofers and Tweeters]

5 hours ago, WMcD said:

WMcD

Hello Gil,

 

Thanks for the information. I have wondered about the formulas used to make speakers sound as great as they do.

I hope you're doing well. Glad to see you posing again and please keep posting when you can. 

James

[WMcD]

 It is instructive to look at US Patent 4,210,223 (Note this is corrected)which concers the big MCM bass horn woofer.  The Length to double area is 23.3 inches which gives an Fc of 31.95 Hz.  You can find the document at USPTO.GOV or Google Patents.

There is in that patent document some design information.  And Klipsch and Gillim use the 18.1 figure (so I was correct!)

  Many thanks toJames and also to John A for helping me through this stroke time.

WMcD 

[Deang]

Glad to see you back Gil. 

[mikebse2a3]

This place is much better with you Gil … 🙂

[Woofers and Tweeters]

2 hours ago, WMcD said:

Many thanks to James and also to John A for helping me through this stroke time.

WMcD 

Glad to help. You have been so much help on here for many years.

I saw this thread this morning and thought it was one from years ago. It made my day when I saw it was a new one from you. Glad you're back.

[JohnA]

Hey Gil! 

 

Good to see you posting again.  Musta worked out the computer issues. 

 

Do you like tablets?  Sometimes they are easier, but typing is slower, one or 2 fingers.  But I love the pinch/zoom. 

[babadono]

Oh how wonderful to see you back here Gil. God Bless you.

[babadono]

Don't know too much(if anything) about the math behind horns..but sure love how they sound.

[WMcD]

Since I've been writing about US Patents . . .  Please consider the bass horn shown in the Klipsch Papers i.e. Bell Labs' Symposium.  I shows up in US Patent 1,970, 926 titled "Sound radiator" to E.C. Wente and assigned to Bell Labs.  (It is likely the same IMHO)  It seems best charactized as a giant re-entrant horn (like a bull horn) in a box.  It does not seem adaptable to home construction.  But take a look.  It claims  300 to40 Hz with a 5 square foot mouth and 3' 8" depth.  Stackable.

'Good Night, WMcD

[JohnA]

 

Weird.  Built in halves and bolted together.  Wente stated horns with large mouths became directional.  Is that true? 

[WMcD]

I took another look at the Symposium bass horn and see the throat is 50.27 in^2; the mouth is 3,600 in^2; the length is 131.76 inches (approx).  From those I calculate the Fc to be 34.83 Hz.  Thanks to John A for the graphic.

Good Night All, WMcD

[Bill W.]

I would love to hear one of those to understand their capabilities, seems like a groundbreaking achievement in their day.

[Dave MacKay]

I've been reading an old (1972) book (How To Build Speaker Enclosures by Badmaieff and Davis). A topic that I found to be of interest was how the area of the mouth of an exponential horn determines the lowest frequency that the horn can reproduce. I tried applying the logic to my vintage La Scalas, but the answers I get don't seem to be very satisfactory. 

 

I measured the area of the mouths of:

   a) the lens used with the K-77M tweeter (4" x 1.5")

   b) the K-400 horn used by the squawker (16.75" x 5.75")

   c) the La Scala bass bin (22.25" x 22")

 

I then used those areas to figure out what the circumference of a circle with the same area would be (i.e., Radius=sqrt(Area/pi) and Circumference = 2pi*Radius). The thinking is that the lowest wavelength the horn can support should match the circumference,

 

I divided the speed of sound (1125 ft/s) by the wavelength to get the frequency (in Hz).

 

Here's what I came up with for the lowest frequencies supported by the different horns:

   a) lens used with the K-77 tweeter ---> 1555 Hz

   b) the K-400 horn used by the squawker ---> 388 Hz

   c) the La Scala bass bin ---> 172 Hz

 

I thought the the K-400 got its name because it was intended for use down to 400 Hz, so the figure for it (i.e., 388 Hz) seems reasonable. However, from what I've read on this forum, I thought that the La Scala bass bin was supposed to be good to about 104 Hz, which is well below the 172 Hz that I calculated.

 

I'd be grateful if anyone would care to help me understand this better.

[JohnA]

Memory is a ethereal thing, but I recall that the K-400, on a baffle, had an fc of 273 Hz.  I also thought the *length* of the horn controlled its fc and the mouth area determined the response ripples it had (or didn't).  I seem the remember the La Scala bass horn had an fc of about 70 Hz and acted more like a woofer in a corner from 70 to 55 Hz or so.

[boom3]

Sorry to chime in late, i seem to do that a lot...Dinsdale's three-part article on horn design, in Wireless World, March 1974 is one of the best compact explanations of horn design. I had the Badmaieff and Davis book years ago, too. Learned a lot from it in my early days of speaker tinkering. Don Davis worked for Paul Klipsch back in the 50s.

 

More math-heavy approaches, and some different perspectives on horn design,  may be found in D.B. Keele's articles in the Journal of the Acoustical Engineering Society (JAES). Keele also worked for Klipsch at one time.