Previous work has demonstrated that structural vibrations of brass wind instruments can audibly affect the radiated sound. Furthermore, these broadband effects are not explainable by assuming perfect coincidence of the frequency of elliptical structural modes with air column resonances. In this work a mechanism is proposed that has the potential to explain the broadband influences of structural vibrations on acoustical characteristics such as input impedance, transfer function, and radiated sound. The proposed mechanism involves the coupling of axial bell vibrations to the internal air column. The acoustical effects of such axial bell vibrations have been studied by extending an existing transmission line model to include the effects of a parasitic flow into vibrating walls, as well as distributed sound pressure sources due to periodic volume fluctuations in a duct with oscillating boundaries. The magnitude of these influences in typical trumpet bells, as well as in a complete instrument with an unbraced loop, has been studied theoretically. The model results in predictions of input impedance and acoustical transfer function differences that are approximately 1 dB for straight instruments and significantly higher when coiled tubes are involved or when very thin brass is used.

1.
W.
Kausel
,
D. W.
Zietlow
, and
T. R.
Moore
, “
Influence of wall vibrations on the sound of brass wind instruments
,”
J. Acoust. Soc. Am.
128
,
3161
3174
(
2010
).
2.
T. R.
Moore
,
E. T.
Shirley
,
I. E.
Codrey
, and
A. E.
Daniels
, “
The effects of bell vibrations on the sound of the modern trumpet
,”
Acta Acust. Acust.
91
,
578
589
(
2005
).
3.
G.
Nief
, “
Comportement vibroacoustique des conduits: Modelisation, mesure et application aux instruments de musique a vent
” (“Vibroacoustic behavior in ducts: Modalisation, measurement and application to musical wind instruments”), Ph.D. thesis, Laboratoire d'acoustique de l'universite du Maine, Le Mans, France (
2008
).
4.
G.
Nief
,
F.
Gautier
,
J.-P.
Dalmont
, and
J.
Gilbert
, “
Influence of wall vibrations on the behavior of a simplified wind instrument
,”
J. Acoust. Soc. Am.
124
,
1320
1331
(
2008
).
5.
G.
Nief
,
F.
Gautier
,
J.-P.
Dalmont
, and
J.
Gilbert
, “
External sound radiation of vibrating trombone bells
,” in
Proceedings of Acoustics'08
,
SFA, Paris, France
(
2008
), pp.
2447
2451
.
6.
J.
Backus
and
T. C.
Hundley
, “
Wall vibrations in flue organ pipes and their effect on tone
,”
J. Acoust. Soc. Am.
39
,
936
945
(
1966
).
7.
A.
Morrison
and
P.
Hoekje
, “
Internal sound field of vibrating trombone bell
,”
J. Acoust. Soc. Am.
101
,
3056
(
1997
).
8.
J.
Whitehouse
, “
A study of the wall vibrations excited during the playing of lip-reed instruments
,” Ph.D. thesis,
Open University
,
Milton Keynes, United Kingdom
(
2003
).
9.
P.
Hoekje
, “
Vibrations in brass instrument bodies: A review
,”
J. Acoust. Soc. Am.
128
,
2419
(
2010
).
10.
W.
Kausel
, “
It's all in the bore! – Is that true? Aren't there other influences on wind instrument sound and response?
,”
J. Acoust. Soc. Am.
121
,
3177
(
2007
).
11.
W.
Kausel
,
V.
Chatziioannou
, and
T.
Moore
, “
More on the structural mechanics of brass wind instrument bells
,” in
Proceedings of Forum Acusticum 2011
,
European Acoustics Association
,
Aalborg, Denmark
(
2011
), pp.
527
532
.
12.
B.
Gorman
,
M.
Rokni
,
T.
Moore
,
W.
Kausel
, and
V.
Chatziioannou
, “
Bell vibrations and how they affect the sound of the modern trumpet
,” in
Proceedings of the International Symposium on Musical Acoustics 2014
,
Institut Technologique Europen des Mtiers de la Musique
,
Le Mans, France
(
2014
), pp.
215
218
.
13.
V.
Chatziioannou
and
W.
Kausel
, “
Modelling the wall vibrations of brass wind instruments
,” in
Proceedings of the COMSOL Conference 2011
,
Stuttgart, Germany
(
2011
).
14.
T. R.
Moore
and
J. J.
Skubal
, “
Time-averaged electronic speckle pattern interferometry in the presence of ambient motion. Part I: Theory and experiments
,”
Appl. Opt.
47
,
4640
4648
(
2008
).
15.
W.
Kausel
, “
Bore reconstruction of tubular ducts from acoustic input impedance curve
,”
IEEE Trans. Instrum. Meas.
53
,
1097
1105
(
2004
).
16.
D.
Keefe
, “
Acoustical wave propagation in cylindrical ducts: Transmission line parameter approximations for isothermal and nonisothermal boundary conditions
,”
J. Acoust. Soc. Am.
75
,
58
62
(
1984
).
17.
N. H.
Fletcher
and
T. D.
Rossing
,
The Physics of Musical Instruments
, 2nd ed. (
Addison-Wesley
,
New York
,
1990
), pp.
190
232
.
18.
D.
Keefe
, “
Woodwind air column models
,”
J. Acoust. Soc. Am.
88
,
35
51
(
1990
).
19.
R.
Picó
,
J.
Gilbert
, and
F.
Gautier
, “
The wall vibration effect in wind instruments: Effect induced by defaults of circularity
,” in
Proceedings of the International Symposium on Musical Acoustics, ISMA 2007
,
Univerisitat Politecnica de Catalunyia, Institut d'Estudis Catalans
,
Barcelona, Spain
(
2007
).
20.
G.
Nief
,
F.
Gautier
,
J.-P.
Dalmont
, and
J.
Gilbert
, “
Influence of wall vibrations of cylindrical musical pipes on acoustic input impedances and on sound produced
,” in
Proceedings of the International Symposium on Musical Acoustics, ISMA 2007
,
Univerisitat Politecnica de Catalunyia, Institut d'Estudis Catalans
,
Barcelona, Spain
(
2007
).
21.
V.
Chatziioannou
,
W.
Kausel
, and
T.
Moore
, “
The effect of wall vibrations on the air column inside trumpet bells
,” in
Proceedings of the Acoustics 2012 Nantes Conference
,
Nantes, France
(
2012
), pp.
2243
2248
.
22.
W.
Kausel
,
V.
Chatziioannou
,
B.
Gorman
,
M.
Rokni
, and
T.
Moore
, “
Vibro acoustic modeling of wall vibrations of a trumpet bell
,” in
Proceedings of the International Symposium on Music Acoustics, ISMA 2014
,
Le Mans, France
(
2014
), pp.
89
93
.
23.
A.
Braden
,
D.
Chadefaux
,
V.
Chatziioannou
,
S.
Siddiq
,
C.
Geyer
, and
W.
Kausel
, “
Acoustic Research Tool (ART)
,” http://sourceforge.net/projects/artool (Last viewed 05/18/2015).
24.
F.
Gautier
and
N.
Tahani
, “
Vibroacoustic behaviour of a simplified musical wind instrument
,”
J. Sound Vib.
213
,
107
125
(
1998
).
25.
G.
Widholm
,
H.
Pichler
, and
T.
Ossmann
, “
BIAS—a computer aided test system for brass instruments
,” Audio Engineering Society preprint No. 2834 (
1989
), pp.
1
8
.
26.
G.
Widholm
,
W.
Kausel
, and
A.
Mayer
, “
Brasswind Instrument Analysis System (BIAS)
,” http://bias.at (Last viewed 05/18/2015).
27.
See supplemental material at http://dx.doi.org/10.1121/1.4921270 for animation of the motion of the first axial resonance (predicted frequency is 994 Hz) and of the (2,1) elliptical mode shape (predicted frequency is 472 Hz).

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