Horns, Waveguides and Acoustic Filter Chambers

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Check out this interesting link:
Acoustic Filters, Waveguides and Transmission Lines, by Daniel Russell of the Science and Mathematics department of GMI Institute.
On this forum, we recently discussed chambers for providing low pass functions. This paper adequately describes such a device, and also band stop and high pass chambers. The characteristics of each type of chamber are discussed, as well as the properties required and the specific methods of solutions for each.
It's a simple technical discussion about waveguides, and provides formulas describing their properties. Also included are the formula which describe acoustic chambers that provide high pass, low pass and band stop (notch filter) properties. The paper is written as a laboratory exercise for students of acoustics.
Also noteworthy, is the paper's discussion of waveguides. Most of us know the difference between waveguides and horns, but for those that don't - the paper describes what a waveguide is, and quantifies its properties.
In a sentence, a waveguide has a constant cross section area and presents a constant impedance at its resonant frequency. It does not provide any gain, and rather passes a set of frequencies which are the harmonics of resonance.
On the other hand, a horn has a significant increase of cross section area along its length. The horn provides a "transformer-like" impedance match, and therefore provides gain in our loudspeakers because it more closely matches the impedance of the motor diaphram with the mass of air which it is to drive.
When we've taken the pains to bend the wood to provide shape, we may make a catenoidal, expotential or hyperbolic horn. We may also form one of the hybrid shapes, which essentially combines some of the properties of two or more of these shapes.
But even if we do not bend the wood, we can form a conical horn having a linear increase in the ratio of area to length. This too, forms an impedance matching horn device which has characteristics determined by the same formula as is used for expotential horns. They are all part of the same "family" of horn shapes.
What does not do much good in a loudspeaker cabinet, is to have lengthy sections which have cross section areas that increase very little over their length. These closely resemble waveguides, and their performance also closely resembles that of a waveguide. Even if made sectional - with each section having a slightly larger area - then what we have resembles a set of waveguides placed in series.
While all horns have waveguide properties, these effects should be minimized if relatively linear impedance matching over the bandwidth is desired. The best way to do this is by obtaining a favorable area increase in addition to the necessary length. System performance is not improved by having the necessary length, but having only modest area increases. Likewise, multiple "pre chambers" with modest area increases - included so as to add length - should be discouraged.
Conical horn shapes are not any more waveguides than are expotential, hyperbolic or catenoidal horns are. They're all part of the same family of horns and have response characteristics determined by the same formula.
I think the confusion comes from the fact that many describe horns as being "waveguides" - even in the academic and professional communities. Especially those describing some "hybrid" forms - CD's or "sectional," Bi-radial and Quadradratic's, in particular - describe these units as "waveguides" because of their focus on direction control as opposed to impedance matching.
But this is merely using the word "waveguide" as a description of it's function - being that of a "guide for the acoustic energy" - and not an indication of response characteristics. Technically speaking, a waveguide is a device which has constant cross-section area over it's length, and which functions only as a transmission line.
Wayne

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Topic - Horns, Waveguides and Acoustic Filter Chambers - Wayne_Parham 04:58:43 01/04/01 (1)

Re: Horns, Waveguides and Acoustic Filter Chambers - Martin 09:09:47 01/04/01 (0)

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