Physical explanation of how horn speakers work

[cwujek]

I'm looking for broad information regarding how horn speakers work. This is for an academic project, so sources to cite would be awesome. Any books, periodicals, or web sites would be very helpful. This webpage has been very helpful, but I need materials that I can cite with credibility. The more the better. I know the bare basics, I'm looking for some deeper descriptions/explanations. Thanks,

Chris

[Scottmoose]

Here's a few to get you started:

Lord Rayleigh: The Theory of Sound. First published in the 19th century, and still decent (first person to derive conical horn math). 2 volumes. Still in print & easy to get 2nd hand.

Leo Beranak -Acoustics

Harry Olson: Acoustical Engineering

Martin King: www.quarter-wave.com

Any of Don Keele & W. M. Leach's relevant papers, which are all available online.

[GM]

Greets!

While by no means a complete listing nor any any particular order, but between these and their bibliographies you should be fairly 'up to speed' :

GM

-------------

L.F. Horn Design & Driver Parameters

[001] Title: Design Factors in Horn-Type Speakers
Publication: AES-J, Vol. 1, No. 4, pp. 276 (1953)
Author: Daniel J. Plach
Abstract: Maximum efficiency in a horn unit can be
achieved only if a conjugate match exists between
driver and horn. This match is possible only if the
unloaded resonance of the driver is greater than horn
cutoff frequency. Since the throat resistance of a
finite

[002] Title: On the Specification of Moving-Coil
Drivers for Low-Frequency Horn-Loaded Loudspeakers
Publication: AES-J, Vol. 27, No. 12, pp. 950 (1979)
Author: W. Marshall Leach, Jr.
Abstract: A procedure is presented for the design
from specifications of moving-coil drivers for
low-frequency horn-loaded loudspeakers. The method
permits specification of the upper and lower system
cutoff frequencies, the volume of the cavity behind
the driver,

[003] Title: Comments on Reactance Annulling in
Horn-Loaded Loudspeaker Systems
Publication: AES-J, Vol. 29, No. 7, pp. 523 (1981)
Author: Edward F. McClain, Jr.

[004] Title: Author's Reply to "Comments on Reactance
Annulling in Horn-Loaded Loudspeaker Systems"
Publication: AES-J, Vol. 29, No. 7, pp. 523 (1981)
Author: W. Marshall Leach, Jr.

[005] Title: Optimum Horn Mouth Size
Publication: AES-P, No. 933, Cnv. 46 (1973-09)
Author: D. B. Keele, Jr.
Abstract: Loudspeaker exponential horn computer model
studies indicate that there is an optimum mouth size
for a horn of specific cutoff to minimize mouth
reflections. Evaluation of the reflection coefficient
at the horn's mouth reveals how large the mouth must
be

[006] Title: Low-Frequency Horn Design Using
Thiele/Small Driver Parameters
Publication: AES-P, No. 1250, Cnv. 57 (1977-05)
Author: D. B. Keele, Jr.
Abstract: The design formulas for low-frequency horns
which yield various physical and performance related
horn data can be recast in a form which utilizes the
Thiele/Small direct-radiator driver parameters. This
conversion simplifies computations of items such a

[007] Title: Suitability of Low-Frequency Drivers for
Horn-Loaded Loudspeaker Systems
Publication: AES-P, No. 1251, Cnv. 57, (1977-05)
Author: Richard H. Small
Abstract: The efficiency, bandwidth and power
capacity of low-frequency horn-loaded loudspeaker
systems are directly affected by the parameters of
the driver used. Three new composite driver
parameters, formed by simple combination of the basic
parameters, give a

[008] Title: A Two-Port Analogous Circuit and SPICE
Model for Salmon's Family of Acoustic Horns
Publication: ASA-J, Vol. 99 No. 3, pp. 1459-1464
(Mar-1996)
Author: W. Marshall Leach, Jr.
Abstract: A two-port electroacoustic analogous
circuit model for finite-length acoustic horns
belonging to Salmon's family of horns is described.
An implementation of the circuit model for use with
the PSpice simulator software is given.
Internet:
http://users.ece.gatech.edu/~mleach/papers/hornmod.ht
ml

[009] Title: Simplified Loudspeaker Measurements at
Low Frequencies
Publication: AES-J, Vol. 20, No. 1, pp. 28 (1972)
Author: Richard H. Small
Abstract: The effective free-field frequency response
and harmonic distortion of a direct-radiator
loudspeaker system can be measured at low frequencies
without establishing free-field radiation conditions.
The technique is based on measurement of the
acoustical p

[010] Title: Direct Radiator Loudspeaker System
Analysis
Publication: AES-J, Vol. 20, No. 5, pp. 383 (1972)
Author: Richard H. Small
Abstract: The low-frequency performance of
direct-radiator loudspeaker systems can be accurately
specified and is quantitatively related to the basic
parameters of the system components. These systems
function at low frequencies as low-efficiency
electroacoustic

[011] Title: Direct Low-Frequency Driver Synthesis
from System Specifications
Publication: AES-J, Vol. 30, No. 11, pp. 800 (1982)
Author: D.B. Keele, Jr.
Abstract: The usual procedure for direct-radiator
low-frequency loudspeaker system design leads to the
calculation of the driver's fundamental
electromechanical parameters by an intermediate
specification of the Thiele-Small parameters. A
reformulation of the syn

[012] Title: Comments on "Direct Low-Frequency Driver
Synthesis from System Specifications"
Publication: AES-F, Vol. 32, No. 7, pp. 543 (1984)
Author: Thomas L. Clarke

H.F. Horn and Phase Plug Design

[013] Title: Phase Plug Modelling and Analysis:
Circumferential Versus Radial Types
Publication: AES-P, No. 1140, Cnv. 55 (1976-10)
Author: Clifford A. Henricksen
Abstract: Mechanical modeling of a simple phase plug
yields an electrical-mobility equivalent circuit; a
single-frequency notch filter. This applies directly
to "normal" circumferential-slit configurations. The
analysis is then applied to a radial-slit phase plug,

[014] Title: Phase Plug Modeling and Analysis: Radial
Versus Circumferential Types
Publication: AES-P, No. 1328, Cnv. 59 ( 1978-02)
Author: C. A. Henricksen
Abstract: Mechanical modeling of a simple
two-dimensional phase plug and diaphragm yields an
electrical mobility equivalent circuit; a two-pole,
low-pass filter. At higher frequencies, this analysis
becomes incomplete, and a model presented by Merhaut
(1975) is us

[015] Title: An Application of Bob Smith's Phasing
Plug
Publication: AES-P, No. 1384, Cnv. 61 (1978-11)
Author: F. M. Murray
Abstract: The war of the phasing plugs still rages
after more than 25 years. Compression driver phasing
plugs have vacillated between annular rings, salt
shakers, teardrops, and now radial slots again. When
Bob Smith provided simple design criteria for

[016] Title: The Dual Coil Inductively Coupled
Loudspeaker System Performance Optimization and the
Application of an Acoustic Phase Correction Plug
Publication: AES-P, No. 2780, Cnv. 86 ( 1989-03)
Author: Boaz Elieli
Abstract: Analysis of the dual coil inductively
coupled loudspeaker system using an electrical
equivalent circuit is presented, and some of the
practical design aspects relating to the system
optimization are discussed. The application of an
acoustic phase correct

[017] Title: Ultimate Performance of Wide-Range
High-Frequency Compression Drivers
Publication: AES-J, Vol. 24, No. 8, pp. 639 (1976)
Author: Clifford A. Henricksen
Abstract: Performance equations are developed from an
electric mobility model of a typical electromagnetic
compression driver. The analysis is independent of
impedance and relates ultimate performance to
material, air, and phase-plug variables.

[018] Title: An Investigation of the Air Chamber of
Horn Type Loudspeakers
Publication: ASA-J, Vol. 25, No. 2, Pg. 305-312,
Mar-1953
Author: Bob H. Smith
Abstract: The front air chamber design is treated as
a boundary value problem which yields a solution of
the wave equation for the general case in which the
horn throat enters the air chamber in a
circumferentially symmetrical manner.


[020] Title: Acoustical Studies of the Tractrix Horn.
I
Publication: ASA-J, Vol. 26, No. 6, Pg. 1024-1033,
Nov-1954
Author: Robert F. Lambert
Abstract: Acoustical properties of the tractrix horn
are modeled, measured and compared in a two part
article.

[021] Title: Acoustical Studies of the Tractrix Horn.
II
Publication: ASA-J, Vol. 26, No. 6, p.1024-1033,
Nov-1954
Author: Robert F. Lambert
Abstract: Acoustical properties of the tractrix horn
are modeled, measured and compared in a two part
article.

[022] Title: Theater Loudspeaker System Incorporating
an Acoustic-Lens Radiator
Publication: SMPTE-J, Vol. 63, p. 82, Sep-1954
Author: John G. Frayne
Author: Bart N. Locanthi
Abstract: This paper describes a two-way loudspeaker
system for presentation of stereophonic sound in
motion-picture theaters. The systems presented use
divergent acoustic lenses to achieve a wide
dispersion pattern for high frequencies.

[023] Title: Refracting Sound Waves
Publication: ASA-J, Vol. 21, No. 21, p. 471, Sep-1949
Author: Winston E. Kock
Author: F.K. Harvey
Abstract: Structures that refract and focus sound
waves are described. These include path length delay
element and obstacle arrays that function as the
acoustical convergent and divergent lenses.

[024] Title: A Modeling and Measurement Study of
Acoustic Horns
Author: Post, John Theodore
Publication: Thesis (Ph.D.)--The University Of Texas
at Austin, 1994. Source: Dissertation Abstracts
International, Vol. 55-06, Sec. B, Pg. 2246, UMI Co.
Abstract: Although acoustic horns have been in use
for thousands of years, formal horn design only began
approximately 80 years ago with the pioneering effort
of A. G. Webster. In this dissertation, the
improvements to Webster's original horn model are
reviewed and the lack of analytical progress since
Webster is noted. In an attempt to augment the
traditional methods of analysis, a semi-analytical
technique presented by Rayleigh is extended. Although
Rayleigh's method is not based on one-dimensional
wave

[GM]

Part 2:

[025] Title: A theoretical and experimental
investigation of the throat impedance characteristics
of constant directivity horns
Publication: ASA-J, Vol 92, No. 5, Nov-92, p.
2509-2520
Author: McLean, James S.
Author: Post, John T.
Author: Hixson, Elmer L.
Abstract: none
URL:
https://pubster.aip.org/cgi-bin/krs1-order?JNAME=The+
Journal+of+the+Acoustical+Society+of+America&CODEN =JA
SMAN&VOLUME=000092&ISSUE=000005&ISSUEDATE=November +19
92&PAGERANGE=2509-2520&TITLE=A+theoretical+and+experi
mental+investigation+of+the+throat+impedance+chara cte
ristics+of+constant+directivity+horns

[026] Title: Rayleigh's horn equation
Publication: ASA-J, Vol. 94, No. 3, Sep-1993, p.1803
Author: Post, John T.
Author: Hixson, Elmer L.
Abstract: none
URL:
https://pubster.aip.org/cgi-bin/krs1-order?JNAME=The+
Journal+of+the+Acoustical+Society+of+America&CODEN =JA
SMAN&VOLUME=000094&ISSUE=000003&ISSUEDATE=Septembe r+1
993&PAGERANGE=1803-1803&TITLE=Rayleigh's+horn+equatio
n

[027] Title: Measurement of throat impedance and
far-field directivity for acoustic horns
Publication: ASA-J, Vol. 96, No. 5, Nov-94, p. 3290
Author: Post, John T.
Author: Hixson, Elmer L.
Abstract: none
URL:
https://pubster.aip.org/cgi-bin/krs1-order?JNAME=The+
Journal+of+the+Acoustical+Society+of+America&CODEN =JA
SMAN&VOLUME=000096&ISSUE=000005&ISSUEDATE=November +19
94&PAGERANGE=3290-3290&TITLE=Measurement+of+throat+im
pedance+and+far-field+directivity+for+acoustic+horns

[105] Title: Computer Simulation of Horn-Loaded
Compression Drivers
Publication: AES-J, Vol. 35, No. 7, pp. 556 (1987)
Author: Earl Geddes
Author: David Clark
Abstract: Numerous investigators have performed
analyses of horns and compression drivers. Driver
models have typically used a plane-wave tube or
infinite horn as a termination to avoid the
complexities of finite horns. The present approach
models driver and â?¦

[107] Title: Calculation of Sound Radiation from an
Unbaffled, Rectangular-Cross-Section Horn Loudspeaker
Using Combined Analytical and Boundary-Element
Methods
Publication: AES-J, Vol. 38, No. 5, pp. 340 (1990)
Author: T. Shindo
Author: T. Yoshioka
Author: K. Fukuyama
Abstract: Methods are described for calculating the
sound radiation from an unbaffled,
rectangular-cross-section horn loudspeaker using a
minicomputer. The boundary-element method is used for
smaller horn loudspeakers and, in combination with
the analytical method ...

[109] Title: Prediction and Measurement of the
One-Parameter Behavior of Horns
Publication: AES-J, Vol. 39, No 5, pp. 315 (1991)
Author: K. R. Holland
Author: F. J. Fahy
Author: C. L. Morfey
Abstract: It is investigated to what extent aspects
of the performance of horns can be modeled using
Websterâ?Ts one-parameter horn equation. A computer
model, based on Websterâ?Ts equation, is described.
Its results are compared to measurements. It is shown
that a â?¦

[112] Title: Acoustic Wave-guides, In Practice
Publication: Vol. 41, No. 6, pp. 462 (1993)
Author: Paul D. Bauman
Author: A. B. Adamson
Author: Earl R. Geddes
Abstract: The acoustic wave-guide concept first
introduced in 1987 has gained little understanding
within the industry despite fundamental limitations
inherent in traditional horn theory. To illustrate
the practical feasibility of acoustic wave-guides,
measurements â?¦

Clifford A. Hendrickson & Mark S. Ureda, "The Manta-Ray Horns," Journal of
the Audio
Engineering Society, Vol. 26, No. 9, pp. 629-634 (1978)

Charles E. Hughes, "A Generalized Horn Design to Optimize Directivity
Control & Wavefront
Curvature," Audio Engineering Society, Pre-Print No. 5016 (F-6), (1999
Sept.)

The Physics of Musical Instruments, Second Edition
Springer-Verlag, Berlin (1998)
Neville H. Fletcher and Thomas D. Rossing
8.12 Curved Horns, pp. 220-222

Wave Propagation in Strongly Curved Ducts
ASA-J, Vol. 74, pg. 320-332, 1983
D.H. Keefe and A.H. Benade

Acoustical Aspects of Woodwind Instruments
Frits Knuf, Amsterdam, pg. 60
Reprinted by Northern Illinois University Press,
DeKalb, IL 1998
C.J. Nederveen (1969)

Propagation in any horn with flared walls is not 1P;
thus, Webster's equation is only an approximate
solution whose accuracy deteriorates with the flair
angle. Pressure across the isophase surface is not
uniform nor is the phase velocity between these
surfaces. I suspect that vector sum of spreading
velocity and forward propagation total to some "c"
that may be a function of frequency. You must cast
your formula in an orthogonal coordinate system for
the flair formula you are using. At a minimum, a 2p
model should yield better results. At high
frequencies, my conjecture is that sound propagation
follows the caustic in the case of a spiral. If this
were true, the process of transformation would be an
extremely important discovery.
When ever I think about your Cornu, hurricanes,
tornadoes, dust devils and toilet flushes come to
mind, which arouses the suspicion that their may be
an advantage to guiding sound propagation in this
fashion.
Well, enough speculation and on to some more
references regarding horn modeling:

Modeling of Horns and Enclosures for Loudspeakers
(PhD thesis)
Author: Gavin R. Putland
http://www.users.onaustralia.com.au/putland/phd/index
.html

Acoustics and Signal Processing Techniques for
Physical Modeling of Brass Instruments (Thesis,1999)
David P. Berners
http://www-ccrma.stanford.edu/~dpberner/

[SunRa]

Wow, GM, thank for these titles. I think it took you a while to gather them! Very nice...

[cwujek]

Perfect. Thanks a lot Scottmoose and GM, it will take me awhile to go through all those.....

[Bluto]

cwujek -

Read all those this afternoon. Not thorough enough. Far too simplistic .

LOL. Have a ball.

Bluto