Design of Acoustical Horns

[fletchbm]

I am trying to understand what dimensions drive the frequency of large acousitcal horns. Can anyone shed some light on the critical dimensions(i.e. area vs length)

 

[electricpete]

I believe that the resonant frequencies of a horn are dependent upon the lenght, and not the width, flare etc. Those other parameters affect the timbre, but not the pitch.

I know that the harmonic series of tones which can be formed on a horn will be separated by an octave, then a fifth, then a fourth, then a major third, then a minor third etc. This corresponds to factor of 2, then 3/2, then 4/3, then 5/4 etc. From this pattern it is evident that it is a series of tones of frequency f, 1f, 2f, 3f, 4f etc where f is the fundamental frequency.

I believe that the fundamental frequency is given as f = v/L where v is speed of sound in air and L is length of horn. 2nd harmonic would be v/(L/2), 3rd harmonic v/(L/3). These are frequencies at which the length of the horn is an integer multiple of the wavelength.

I'm going from memory and a little rusty, so please double check it.

 

[DanT]

Horn type loudspeakers are meant to act as acoustic tranformers to better match the imedance of the &quot;light&quot; air to the relatively massive speaker piston. Result is greater sound radiation at lower frequencies (<1000 Hz?). Conical horns are easier to make, but not so efficient as exponential horns. Real horns indeed have resonances that add messy numps and valleys to the nice performance curves of infinite horns. Most books on acoustics have stuff on horns.

 

[MJKing]

Hello fletchbm,

You might find some useful info at

http://www.quarter-wave.com

where there are many different MathCad acoustic models available including horn loudspeakers.

Hope that helps,

Martin

 

[electricpete]

My answer was geared toward identifying the RESONANT frequency of BRASS horns (musical instruments). If you are looking at the FREQUENCY RESPONSE of LOUDSPEAKER horns, then I am sorry for going on the wrong track.

 

[Rob45]

I think what you will have is a quarter-wave device.

The resonances will be given by f = nc/4L where L = length of the tube, c = speed of sound, and n = 1,3,5,...

I don't have the first clue how this relates to musical notes! <grin>

 

[MJKing]

Rob45,

The equation you site is only accurate for straight geometries where the cross-sectional area is constant along the length. When the cross-sectional area changes along the length (like in a horn) this equation is no longer applicable. The frequency of the first resonance of a horn will be significantly higher then your equation would have you believe. I also believe that the horn harmonics (n = 3, 5, 7, ...) will be higher in frequency but not as far off as the first.

Hope that helps,

Martin

 

[electricpete]

You may be right on the quarter wavelenght... not sure exactly whether it's 1/4 or 1/2 or one full wavelenth.

I do know that the harmonic series on a horn does NOT follow a pattern of ratio's matching 1/1, 3/1, 5/1, 7/1, etc. The harmonics achievable on a brass horn are in frequency ratio's of 1/1, 2/1, 3/1, 4/1, 5/1 etc.

The pattern you describe of 1/1, 3/1, 5/1, 7/1 frequency ratio's is applicable to clarinet and other similar instruments.

The difference is whether the instrument is considered open at one or two ends. Clarinet (and flute and others) have a closed wall at one end with air entering peripherally or vibrating reed on the side creating a boundary condition equivalent to closed end. Horn has mouthpiece which creates boundary condition of an open end.

 

[MJKing]

I think we are saying the same thing. By n = 3, 5, 7, ..., I was refering to the standing wave mode shape and not the frequencies, I was not clear. In other words 3/4 of a stretched sine wave, 5/4 of a stretched sine wave, 7/4 of a stretched sine wave and so on. I use the word stretched to indicate that the shape is not a pure sine wave but one that is distorted and having nodes (or crossings) at not equal increments along the length. Typically acoustic horns are analyzed with one end closed and one end open hence quarter wavelength mode shapes. The frequency ratios will not follow the simple formula given above.

Hope that helps,

Martin

 

[electricpete]

Hi Martin.

One fact: The frequencies which can be played on a muscial brass horn (trumpet, trombone, tuba, baritone horn, french horn) with a fixed fingering (valve) position fall in a series as follows: f0, 2*f0, 3*f0, 4*f0 5*f0 etc, at least as close as a muscial ear can detect.

Ratio of 2 coresponds to an octave. The second tone which can be played is an octave above the first.

Ratio of 3/2 corresponds to a fifth. The third tone which can be played is a fifth above the 2nd.

Ratio of 4/3 corresponds to a fourth. The fourth tone which can be played is a fourth above the third.

etc.