Horn length.

[Hamilton]

I have a question concerning the effects caused by horn length. I'm visualizing a trumpet vs a tuba, but the frequency coming out of a horn would be determined by the crossover, I would think, and not the length of the horn.

Say we have two horns that will fit a common driver and both have equal dispersion, 60ºx60º, but one has a short throat while the other is long. What is the audio differences caused by throat length?

Thanks,
Hamilton

[10 Watt Street]

http://en.wikipedia.org/wiki/Horn_speaker

[Hoerninger]

I have a question concerning the effects caused by horn length. For an (exponential) horn there is a strict relationship between
- throat area (at the speaker),
- horn length x,
- area at distance x and
- flare constant (proportional to cut off frequency).
Normally the mouth area is determent by the cut off frequency. (The area increases by lowering the cut off frequency.)

Say we have two horns that will fit a common driver and both have equal dispersion, 60ºx60º, but one has a short throat while the other is long. What is the audio differences caused by throat length?
If the longer horn has the same flare rate it would not change the dispersion at higher frequencies but maybe at the lowest . For the lowest frequency the response would be smoothened (which should be tested in a concrete case.)
But nobody would make a horn longer than necessary because there would be greater problems with time alignment.

If the longer horn has a lower flare rate it would have a narrower dispersion at a given frequency. (But
for this you did not ask, I guess.)

Hope this helped.
__________
Peter

[Steve Schell]

It's a big question, but here are my initial thoughts...

Generally speaking the longer the horn the better its directivity and the lower the frequency it will work to before it loses control and the pattern widens out beyond what was intended. The response will also be much smoother down near the cutoff with the larger horn. In a finite horn (all of them), there is an impedance mismatch at the mouth and some energy will reverse direction and travel back up the throat to affect the loading seen by the driver. Depending on wavelength this may result in either a peak or a dip at a given frequency, resulting in ripples in the response in the octave above cutoff. The shorter horn will have a smaller mouth, which causes the ripples to be stronger as the wavefront has not expanded as much and has a greater impedance mismatch, which causes a greater proportion of the energy to travel back up the horn.

Horns are almost always compromised in length and mouth area, and this has been a major cause of their past unpopularity. Most of the shrieky, honky hi fi horn speakers of the past used really inadequate, nasty little midrange horns so that everything would fit in the walnut box. Designing in the largest possible midrange horn should be a goal for good sound. Crossing over considerably higher than the horn's flare frequency is also a good strategy to avoid most of the response ripples.

[Earl K]

,,,,snip ,,,, Depending on wavelength this may result in either a peak or a dip at a given frequency, resulting in ripples in the response in the octave above cutoff.

- The best reference book ( in my possession ) which illustrates these ripples ( graphed as Acoustical Impedance & Acoustical Reactance ) is Harry F. Olson(s)' "Acoustical Engineering" .



The shorter horn will have a smaller mouth, which causes the ripples to be stronger as the wavefront has not expanded as much and has a greater impedance mismatch, which causes a greater proportion of the energy to travel back up the horn.

- Just so people don't misinterpret this statement ( and then take it to the bank to slag short horns ) / /

- Olson nicely illustrates that the magnitude ( and frequency ) of these impedance ripples is directly proportional to ; the horn depth vs the horns' mouth area .
- This is illustrated on page 112 of the above mentioned book .

ie ; a short horn with a wide mouth minimizes the impedance ripples .


:)

[Steve Schell]

Hi Earl,

All good points. Olson's works are essential, and they are where I learned much of what I think I know about horns. He and his frequent collaborator Frank Massa were really brilliant engineers.

[Hamilton]

Thanks guys, I can see this is not so simple...

So does the area of the mouth determine the frequency, and the throat determine the degree of dispersion? Or am I backwards... :blink:

[Hoerninger]

Thanks guys, I can see this is not so simple... You are on the right way. ;)
There is still no "final maths" for horn calculaions. The lower frequency limit is determent by the flare rate, the way it widens. An ideal horn has infinite length. :banghead:
Because of the finite length there are reflections disturbing the sound quality. :biting:
For controlling dispersion there is a variety of shapes. The whole thing is still under investigation. :blink:

Some are talking about wave guides. You can consider the wall of a horn as an obstacle. If the geometrical dimension is small compared to the wavelength, then the sound will come around. If the wavelength is small compared to the geometrical dimension than the sound will be directed.
The dimensions of the mouth are important as well.
Most maths in this respect are simplifications.

Hope this was helpful. (http://pda.leo.org was my friend. :) )
____________
Peter