Design of Acoustical Horns
Design of Acoustical Horns
(OP)
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)
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Design of Acoustical Horns
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RE: Design of Acoustical Horns
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.
RE: Design of Acoustical Horns
RE: Design of Acoustical Horns
You might find some useful info at www.quarter-wave.com where there are many different MathCad acoustic models available including horn loudspeakers.
Hope that helps,
Martin
RE: Design of Acoustical Horns
RE: Design of Acoustical Horns
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>
RE: Design of Acoustical Horns
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 When the cross-sectional area changes along the length (like in a horn) this equation is no longer applicable.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
RE: Design of Acoustical Horns
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.
RE: Design of Acoustical Horns
Hope that helps,
Martin
RE: Design of Acoustical Horns
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.