The paper considers receiving acoustic horns designed for particle velocity amplification and suitable for use in vector sensing applications. Unlike conventional horns, designed for acoustic pressure amplification, acoustic velocity horns (AVHs) deliver significant velocity amplification even when the overall size of the horn is much less than an acoustic wavelength. An AVH requires an open-ended configuration, as compared to pressure horns which are terminated at the throat. The appropriate formulation, based on Webster’s one-dimensional horn equation, is derived and analyzed for single conical and exponential horns as well as for double-horn configurations. Predicted horn amplification factors (ratio of mouth-to-throat radii) were verified using numerical modeling. It is shown that three independent geometrical parameters principally control a horn’s performance: length l, throat radius R1, and flare rate. Below a predicted resonance region, velocity amplification is practically independent of frequency. Acoustic velocity horns are naturally directional, providing maximum velocity amplification along the boresight.

1.
G. W.
Stewart
, “
The performance of conical horns
,”
Phys. Rev.
16
(
4
),
313
326
(
1920
).
2.
H. F.
Olson
and
I.
Wolff
, “
Sound concentrator for microphones
,”
J. Acoust. Soc. Am.
1
,
410
417
(
1930
).
3.
N. H.
Fletcher
and
S.
Thwaites
, “
Obliquely truncated simple horns: Idealized models for vertebrate pinnae
,”
Acustica
65
,
194
204
(
1988
).
4.
Acoustic Vector Sensors, www.microflown-avisa.com (Last viewed October 3,
2011
).
5.
M.
Shujau
,
C. H.
Rits
, and
I. S.
Burnett
, “
Designing acoustic vector sensors for localization of sound sources in air
,” in
Proceedings of the 17th European Signal Processing Conference (EUSIPCO 2009)
,
Glasgow
,
Scotland
(August 24–28,
2009
), pp.
849
853
.
6.
M. J.
Berliner
and
J. F.
Lindberg
, Eds., “
Acoustic particle velocity sensors: Design, performance, and applications
,”
AIP Conf. Proc.
368
,
1
448
(
1995
).
7.
D. M.
Donskoy
and
B. A.
Cray
, “
Horns as particle velocity amplifiers
J. Acoust. Soc. Am.
130
(
5
),
EL311
EL315
(
2011
).
8.
A. G.
Webster
, “
Acoustical impedance and the theory of horns and of the phonograph
,”
Proc. Natl. Acad. Sci. U.S.A.
5
,
275
282
(
1919
).
9.
W. M.
Hall
, “
Comments on the theory of horns
,”
J. Acoust. Soc. Am.
3
,
552
561
(
1932
).
10.
V.
Salmon
, “
A new family of horns
,”
J. Acoust. Soc. Am.
17
(
3
),
212
218
(
1946
).
11.
E.
Eisner
, “
Complete solutions of the ‘Webster’ horn equation
,”
J. Acoust. Soc. Am.
41
(
4
),
1126
1146
(
1967
).
12.
G. R.
Putland
, “
Every one-parameter acoustic field obeys Webster’s horn equation
,”
J. Audio Eng. Soc.
41
(
6
),
435
451
(
1993
).
13.
Apparently Webster’s paper (Ref. 8) was the first published work which introduced the concept of the acoustical impedance. Webster, as well as Stuart (Ref. 14) later, defined it as the ratio of acoustic pressure to displaced volume rather than volume velocity as is customary now. The expressions for the four-pole coefficients in this paper are modified accordingly.
14.
G. W.
Stewart
and
R. B.
Lindsay
,
Acoustics
(
Van Nostrand
,
New York
,
1930
), pp.
137
148
.
15.
Handbook of Mathematical Functions
, edited by
M.
Abramowitz
and
I.
Stegun
,
Natl. Bur. Stand. (U.S.)
, Applied Mathematics Series 55 (U.S. Government Printing Office,
1972
), pp.
358
496
.
16.
H.
Levine
and
J.
Schwinger
, “
On the radiation of sound from an unflanged circular pipe
,”
Phys. Rev.
73
(
4
),
383
406
(
1948
).
17.
L. L.
Beranek
,
Acoustics
(
McGraw-Hill
,
New York
,
1993
), pp.
118
133
.
You do not currently have access to this content.