Power series expansions in are derived for the pressure at the edge of a radiator, the reaction force on the radiator, and the total radiated power arising from a harmonically excited, resilient, flat, circular radiator of radius in an infinite baffle. The velocity profiles on the radiator are either Stenzel functions , with the radial coordinate on the radiator, or linear combinations of Zernike functions , with the Legendre polynomial of degree . Both sets of functions give rise, via King’s integral for the pressure, to integrals for the quantities of interest involving the product of two Bessel functions. These integrals have a power series expansion and allow an expression in terms of Bessel functions of the first kind and Struve functions. Consequently, many of the results in [M. Greenspan, J. Acoust. Soc. Am. 65, 608–621 (1979)] are generalized and treated in a unified manner. A foreseen application is for loudspeakers. The relation between the radiated power in the near-field on one hand and in the far field on the other is highlighted.
REFERENCES
1.
2.
L. E.
Kinsler
, A. R.
Frey
, A. B.
Coppens
, and J. V.
Sanders
, Fundamentals of Acoustics
(Wiley
, New York
, 1982
).3.
4.
A. D.
Pierce
, Acoustics: An Introduction to Its Physical Principles and Applications
(Acoustical Society of America through the American Institue of Physics
, New York
, 1989
).5.
H.
Stenzel
and O.
Brosze
, Guide to Computation of Sound Phenomena (Leitfaden zur Berechnung von Schallvorgängen)
, 2nd ed. (Springer-Verlag
, Berlin
, 1958
).6.
M.
Greenspan
, “Piston radiator: Some extensions of the theory
,” J. Acoust. Soc. Am.
65
, 608
–621
(1979
).7.
G. R.
Harris
, “Review of transient field theory for a baffled planar piston
,” J. Acoust. Soc. Am.
70
, 10
–20
(1981
).8.
H.
Stenzel
, “On the acoustical radiation of membranes (published in German as Über die akustische Strahlung von Membranen)
,” Ann. Phys.
7
, 947
–982
(1930
).9.
L. V.
King
, “On the acoustic radiation field of the piezo-electric oscillator and the effect of viscosity on transmission
,” Can. J. Res.
11
, 135
–155
(1934
).10.
A.
Schoch
, “Contemplations on the sound field of piston membranes (published in German as Betrachtungen über das Schallfeld einer Kolbenmembran)
,” Akust. Z.
6
, 318
–326
(1941
).11.
J. A.
Archer-Hall
, A. I.
Bashter
, and A. J.
Hazelwood
, “A means for computing the Kirchhoff surface integral for a disk radiator as a single integral with fixed limits
,” J. Acoust. Soc. Am.
65
, 1568
–1570
(1979
).12.
C. J.
Bouwkamp
, “A contribution to the theory of acoustic radiation
,” Philips Res. Rep.
1
, 251
–277
(1946
).13.
F.
Oberhettinger
, “On transient solutions of the “baffled piston” problem
,” J. Res. Natl. Bur. Stand., Sect. B
65B
, 1
–6
(1961
).14.
T.
Hansen
, “Probe-corrected near-field measurements on a truncated cylinder
,” J. Acoust. Soc. Am.
119
, 792
–807
(2006
).15.
D. A.
Hutchins
, H. D.
Mair
, P. A.
Puhach
, and A. J.
Osei
, “Continuous-wave pressure fields of ultrasonic transducers
,” J. Acoust. Soc. Am.
80
, 1
–12
(1986
).16.
R. J.
McGough
, T. V.
Samulski
, and J. F.
Kelly
, “An efficient grid sectoring method for calculations of the near field pressure generated by a circular piston
,” J. Acoust. Soc. Am.
115
, 1942
–1954
(2004
).17.
J. F.
Kelly
and R. J.
McGough
, “An annular superposition integral for axisymmetric radiators
,” J. Acoust. Soc. Am.
121
, 759
–765
(2007
).18.
T. D.
Mast
and F.
Yu
, “Simplified expansions for radiation from a baffled circular piston
,” J. Acoust. Soc. Am.
118
, 3457
–3464
(2005
).19.
T.
Mellow
, “On the sound field of a resilient disk in an infinite baffle
,” J. Acoust. Soc. Am.
120
, 90
–101
(2006
).20.
R. C.
Wittmann
and A. D.
Yaghjian
, “Spherical-wave expansions of piston-radiator fields
,” J. Acoust. Soc. Am.
90
, 1647
–1655
(1991
).21.
R. M.
Aarts
and A. J.E.M.
Janssen
, “On-axis and far-field sound radiation from resilient flat and dome-shaped radiators
,” J. Acoust. Soc. Am.
125
, 1444
–1455
(2009
).22.
M.
Abramowitz
and I. A.
Stegun
, Handbook of Mathematical Functions
(Dover
, New York
, 1972
).23.
T.
Hasegawa
, N.
Inoue
, and K.
Matsuzawa
, “A new rigorous expansion for the velocity potential of a circular piston source
,” J. Acoust. Soc. Am.
74
, 1044
–1047
(1983
).24.
N. W.
McLachlan
, “The acoustic and inertia pressure at any point on a vibrating circular disk
,” Philosophical Magazine and Journal of Science
14
, 1012
–1025
(1932
).25.
F.
Zernike
, “Beugungstheorie des Schneidenverfahrens und seiner verbesserten Form, der Phasenkontrastmethode (Diffraction theory of the knife-edge test and its improved version, the phase-contrast method)
,” Physica (Amsterdam)
1
, 689
–704
(1934
).26.
27.
B. R.A.
Nijboer
, “The diffraction theory of aberrations
,” Ph.D. thesis, University of Groningen
, The Netherlands, 1942
.28.
A. G.
Warren
, “A note on the acoustic pressure and velocity relations on a circular disc and in a circular orifice
,” Proc. Phys. Soc. London
40
, 296
–299
(1928
).29.
R. M.
Aarts
and A. J.E.M.
Janssen
, “Approximation of the Struve function occurring in impedance calculations
,” J. Acoust. Soc. Am.
113
, 2635
–2637
(2003
).30.
A. P.
Prudnikov
, Yu. A.
Brychkov
, and O. I.
Marichev
, Integrals and Series, Volume 2: Special Functions
, (Gordon and Breach Science
, New York
, 1986
).31.
G. N.
Watson
, A Treatise on the Theory of Bessel Functions
(Cambridge University Press
, Cambridge
, 1944
).© 2009 Acoustical Society of America.
2009
Acoustical Society of America
You do not currently have access to this content.