An approximate time domain solution is derived for spherically spreading signals incident on an infinitely long rigid wedge. The solution is a short time approximation of the corresponding exact solution. The presented solution improves the accuracy of an approximate solution derived previously by the authors. The solution is extended to cylindrically spreading and plane wave incident signals. The solutions for all three types of incidence are recast in a unified form. The main advantage of this approximate solution is that it provides insight into the mechanism of diffraction. Specifically, it is shown that the time evolution of diffraction depends on a single time parameter–the diffraction delay time. Furthermore, a generator curve is presented that generates all diffraction impulse responses for all source and receiver locations, all wedge angles, and for all types of incident radiation. Finally, it is shown that any signal (irrespective of its time waveform or its type of spreading) incident on any wedge can be analyzed as an equivalent plane wave incident on a half plane. Thus, the diffraction field of a plane wave incident on a half plane (the simplest diffraction case) encompasses all wedge problems and can be considered a prototype diffraction problem.
References
1.
R.
Mehra
, N.
Raghuvanshi
, A.
Chandak
, D. G.
Albert
, D. K.
Wilson
, and D.
Manocha
, “Acoustic pulse propagation in an urban environment using a three-dimensional numerical simulation
,” J. Acoust. Soc. Am.
135
(6
), 3231
–3242
(2014
).2.
K. M.
Li
and H. Y.
Wong
, “A review of commonly used analytical and empirical formulae for predicting sound diffracted by a thin screen
,” Appl. Acoust.
66
, 45
–76
(2005
).3.
D. G.
Albert
and L.
Liu
, “The effect of buildings on acoustic pulse propagation in an urban environment
,” J. Acoust. Soc. Am.
127
, 1335
–1346
(2010
).4.
S. T.
Cho
and V. W.
Sparrow
, “Diffraction of sonic booms around buildings resulting in the building spiking effect
,” J. Acoust. Soc. Am.
129
, 1250
–1260
(2011
).5.
T.
Lokki
, A.
Southern
, S.
Siltanen
, and L.
Savioja
, “Acoustics of Epidaurus–studies with room acoustics modelling methods
,” Acust. Acta united Acust.
99
(1
), 40
–47
(2013
).6.
L.
Savioja
and U. P.
Svensson
, “Overview of geometrical room acoustic modeling techniques
,” J. Acoust. Soc. Am.
138
, 708
–730
(2015
).7.
R. R.
Torres
, U. P.
Svensson
, and M.
Kleiner
, “Computation of edge diffraction for more accurate room acoustics auralization
,” J. Acoust. Soc. Am.
109
, 600
–610
(2001
).8.
J.
Williams
and L.
Hall
, “Aerodynamic sound generation by turbulent flow in the vicinity of a scattering half plane
,” J. Fluid Mech.
40
(4
), 657
–670
(1970
).9.
D. G.
Crighton
and F. G.
Leppington
, “Scattering of aerodynamic noise by a semi-infinite compliant plate
,” J. Fluid Mech.
43
(4
), 721
–736
(1970
).10.
M. S.
Howe
, “A review of the theory of trailing edge noise
,” J. Sound Vibr.
61
(3
), 437
–465
(1978
).11.
M.
Roger
, S.
Moreau
, and K.
Kucukcoskun
, “On sound scattering by rigid edges and wedges in a flow, with applications to high-lift device aeroacoustics
,” J. Sound Vibr.
362
, 252
–275
(2016
).12.
F. J.
Sánchez-Sesma
, “Diffraction of elastic SH waves by wedges
,” Bull. Seism. Soc. Am.
75
(5
), 1435
–1446
(1985
).13.
H.
Medwin
and C. S.
Clay
, Fundamentals of Acoustical Oceanography (Applications of Modern Acoustics)
(Academic Press
, San Diego
, 1997
).14.
F.
John
, M.
Cimdins
, and H.
Hellbrück
, “Underwater ultrasonic multipath diffraction model for short range communication and sensing applications
,” IEEE Sens. J.
21
(20
), 22934
–22943
(2021
).15.
J. J.
Bowman
, T. B.
Senior
, and P. L.
Uslenghi
, Electromagnetic and Acoustic Scattering by Simple Shapes
, Revised ed. (North-Holland Pub. Co
., New York
, 1987
).16.
L. B.
Felsen
and N.
Marcuvitz
, Radiation and Scattering of Waves
(John Wiley & Sons
, 1994
), Chap. 6, pp. 660
–670
.17.
M. A.
Biot
and I.
Tolstoy
, “Formulation of wave propagation in infinite media by normal coordinates with an application to diffraction
,” J. Acoust. Soc. Am.
29
(3
), 381
–391
(1957
).18.
F. G.
Friedlander
, “The diffraction of sound pulses II. Diffraction by an infinite wedge
,” Proc. R. Soc. London, Ser. A: Math. Phys. Sci.
186
(1006
), 344
–351
(1946
).19.
G. E.
Barr
, “On the diffraction of a cylindrical pulse by a half-plane
,” Quart. Appl. Math.
25
(2
), 193
–204
(1967
).20.
R.
Ianconescu
and E.
Heyman
, “Pulsed field diffraction by a perfectly conducting wedge: A spectral theory of transients analysis
,” IEEE Trans. Antennas Propagat.
42
(6
), 781
–789
(1994
).21.
D.
Ouis
, “Diffraction by a hard half-plane: Useful approximations to an exact formulation
,” J. Sound Vibr.
252
(2
), 191
–221
(2002
).22.
U. P.
Svensson
and P. T.
Calamia
, “Edge-diffraction impulse responses near specular-zone and shadow-zone boundaries
,” Acust. Acta united Acust.
92
(4
), 501
–512
(2006
).23.
A. W.
Trorey
, “A simple theory for seismic diffractions
,” Geophysics
35
(5
), 762
–784
(1970
).24.
J. R.
Berryhill
, “Diffraction response for nonzero separation of source and receiver
,” Geophysics
42
(6
), 1158
–1176
(1977
).25.
P.
Menounou
, I. J.
Busch-Vishniac
, and D. T.
Blackstock
, “Directive line source model. A new model for sound diffraction by half planes and wedges
,” J. Acoust. Soc. Am.
107
, 2973
–2986
(2000
).26.
P.
Menounou
and P.
Nikolaou
, “An extension to the directive line source model for diffraction by half planes and wedges
,” Acust. Acta united Acust.
102
(2
), 307
–321
(2016
).27.
P.
Menounou
and P.
Nikolaou
, “Analytical model for predicting edge diffraction in the time domain
,” J. Acoust. Soc. Am.
142
(6
), 3580
–3592
(2017
).28.
P.
Nikolaou
and P.
Menounou
, “Analytical and numerical methods for efficient calculation of edge diffraction by an arbitrary incident signal
,” J. Acoust. Soc. Am.
146
(5
), 3577
–3589
(2019
).29.
F.
Oberhettinger
, “Diffraction of waves by a wedge
,” Commun. Pure Appl. Math.
7
(3
), 551
–563
(1954
).30.
F.
Oberhettinger
, “On asymptotic series for functions occurring in the theory of diffraction of waves by wedges
,” J. Math. Phys.
34
(1-4
), 245
–255
(1955
).31.
F.
Oberhettinger
, “On the diffraction and reflection of waves and pulses by wedges and corners
,” J. Res. Natl. Bur. Stand.
61
(5
), 343
–365
(1958
).32.
U. P.
Svensson
, R. I.
Fred
, and J.
Vanderkooy
, “An analytic secondary source model of edge diffraction impulse responses
,” J. Acoust. Soc. Am.
106
, 2331
–2344
(1999
).33.
D.
Chu
, T. K.
Stanton
, and A. D.
Pierce
, “Higher-order acoustic diffraction by edges of finite thickness
,” J. Acoust. Soc. Am.
122
, 3177
–3193
(2007
).© 2023 Acoustical Society of America.
2023
Acoustical Society of America
You do not currently have access to this content.
