Two methods of calculating the effective impedance spectra of acoustically hard, randomly rough, two-dimensional surfaces valid for acoustic wavelengths large compared with the roughness scales have been explored. The first method uses the complex excess attenuation spectrum due to a point source above a rough boundary predicted by a boundary element method (BEM) and solves for effective impedance roots identified by a winding number integral method. The second method is based on an analytical theory in which the contributions from random distributions of surface scatterers are summed to obtain the total scattered field. Effective impedance spectra deduced from measurements of the complex excess attenuation above 2D randomly rough surfaces formed by semicylinders and wedges have been compared to predictions from the two approaches. Although the analytical theory gives relatively poor predictions, BEM-deduced effective impedance spectra agree tolerably well with measured data. Simple polynomials have been found to fit BEM-deduced spectra for surfaces formed by intersecting parabolas corresponding to average roughness heights between 0.25 and 7.5 m and for five incidence angles for each average height. Predicted effects of sea-surface roughness on sonic boom profiles and rise time are comparable to those due to turbulence and molecular relaxation effects.

Topics
Acoustics, Shock waves, Algebraic topology, Integral equations, Boundary element methods
1.
K.
Attenborough
and
S.
Taherzadeh
, “
Propagation from a point source over a rough finite impedance boundary
,”
J. Acoust. Soc. Am.
98
(
3
),
1717
–
1722
(
1995
).
Google Scholar
Crossref
Search ADS
 
2.
P.
Boulanger
,
K.
Attenborough
,
S.
Taherzadeh
,
T.
Waters-Fuller
, and
K. M.
Li
, “
Ground effect over hard rough surfaces
,”
J. Acoust. Soc. Am.
104
,
1474
–
1482
(
1998
).
Google Scholar
Crossref
Search ADS
 
3.
K.
Attenborough
and
T.
Waters-Fuller
, “
Effective impedance of rough porous ground surfaces
,”
J. Acoust. Soc. Am.
108
(
3
),
949
–
956
(
2000
).
Google Scholar
Crossref
Search ADS
PubMed
 
4.
F.
Coulouvrat
, “
Sonic boom in the shadow zone: A geometrical theory of diffraction
,”
J. Acoust. Soc. Am.
111
(
2
),
499
–
508
(
2002
).
Google Scholar
 
5.
R. J.
Lucas
and
V.
Twersky
, “
Coherent response to a point source irradiating a rough plane
,”
J. Acoust. Soc. Am.
76
,
1847
–
1863
(
1984
).
Google Scholar
Crossref
Search ADS
 
6.
S.
Taherzadeh
and
K.
Attenborough
, “
Deduction of ground impedance from measurements of excess attenuation spectra
,”
J. Acoust. Soc. Am.
105
,
2039
–
2042
(
1999
).
Google Scholar
Crossref
Search ADS
 
7.
P. R.
Brazier-Smith
and
J. F. M.
Scott
, “
On the determination of the roots of dispersion equations by use of winding number integrals
,”
J. Sound Vib.
145
,
503
–
510
(
1991
).
Google Scholar
Crossref
Search ADS
 
8.
P.
Boulanger
,
K.
Attenborough
,
T.
Waters-Fuller
, and
K. M.
Li
, “
Models and measurements of sound propagation from a point source over mixed impedance ground
,”
J. Acoust. Soc. Am.
102
,
1432
–
1442
(
1997
).
Google Scholar
Crossref
Search ADS
 
9.
S. N.
Chandler-Wilde
and
D. C.
Hothersall
, “
Efficient calculation of the green function for acoustic propagation above a homogeneous impedance plane
,”
J. Sound Vib.
180
,
705
–
724
(
1995
).
Google Scholar
Crossref
Search ADS
 
10.
S. N.
Chandler-Wilde
and
D. C.
Hothersall
, “
A uniformly valid far-field asymptotic expansion of the Green function for two-dimensional propagation above a homogeneous impedance plane
,”
J. Sound Vib.
182
,
665
–
675
(
1995
).
Google Scholar
Crossref
Search ADS
 
11.
C. F.
Chien
and
W. W.
Soroka
, “
Sound propagation along an impedance plane
,”
J. Sound Vib.
43
(
1
),
9
–
20
(
1975
).
Google Scholar
Crossref
Search ADS
 
12.
IMSL Math Library User’s Manual, Version 3.0, Visual Numerics, Inc., Houston, TX (1994).
13.
P. Boulanger and K. Attenborough, “Effective Impedance of Rough Sea Surfaces,” D8 SOBER Report, Project No. GRD1-2000-25189 University of Hull (2002).
14.
M.
Rousseau
and
F.
Coulouvrat
, “
Scattering of a high frequency acoustic wave by a sinusoidal swell: Asymptotic formulation, numerical simulation and fluid motion influence
,”
Acustica
86
,
821
–
829
(
2000
).
Google Scholar
 
15.
J. P.
Chambers
,
J. M.
Sabatier
, and
R.
Raspet
, “
Grazing incidence propagation over a soft rough surface
,”
J. Acoust. Soc. Am.
102
,
55
–
59
(
1997
).
Google Scholar
Crossref
Search ADS
 
16.
J. F.
Allard
,
L.
Kelders
, and
W.
Lauriks
, “
Ultrasonic surface waves above a doubly periodic grating
,”
J. Acoust. Soc. Am.
105
,
2528
–
2531
(
1999
).
Google Scholar
Crossref
Search ADS
 
17.
K.
Attenborough
, “
Acoustical impedance models for outdoor ground surfaces
,”
J. Sound Vib.
99
(
4
),
521
–
544
(
1985
).
Google Scholar
Crossref
Search ADS
 
18.
K.
 
Attenborough
, “
Ground parameter information for propagation modeling
,”
J. Acoust. Soc. Am.
 
92
,
418
–
427
(
1992
);
Google Scholar
Crossref
Search ADS
 
see also
R.
Raspet
and
K.
Attenborough
, “
Erratum: ‘Ground parameter information for propagation modeling
,”
J. Acoust. Soc. Am.
92
,
3007
(
1992
).
Google Scholar
Crossref
Search ADS
 
19.
R.
Raspet
and
J. M.
Sabatier
, “
The surface impedance of grounds with exponential porosity profiles
,”
J. Acoust. Soc. Am.
99
(
1
),
147
–
152
(
1996
).
Google Scholar
Crossref
Search ADS
 
20.
P. Boulanger and K. Attenborough, “Effective impedance of rough sea surfaces for varying incidence angle and roughness scale,” Task3.4 SOBER Report, EC FP5 Project No. GRD1-2000-25189 University of Hull (2002).
21.
H.
Medwin
and
G.
D’Spain
, “
Near-grazing, low-frequency propagation over randomly rough, rigid surfaces
,”
J. Acoust. Soc. Am.
79
(
3
),
657
–
665
(
1986
).
Google Scholar
Crossref
Search ADS
 
22.
I.
Tolstoy
, “
Smooth boundary conditions, coherent low-frequency scatter, and boundary modes
,”
J. Acoust. Soc. Am.
75
(
1
),
1
–
22
(
1984
).
Google Scholar
Crossref
Search ADS
 
23.
H.
Medwin
,
G. L.
D’Spain
,
E.
Childs
, and
S. J.
Hollis
, “
Low frequency grazing propagation over periodic steep-sloped rigid roughness elements
,”
J. Acoust. Soc. Am.
76
(
6
),
1774
–
1790
(
1984
).
Google Scholar
Crossref
Search ADS
 
24.
H.
Medwin
,
J.
Baillie
,
J.
Bremhorst
,
B. J.
Savage
, and
I.
Tolstoy
, “
The scattered acoustic boundary wave generated by grazing incidence at a slightly rough rigid surface
,”
J. Acoust. Soc. Am.
66
(
4
),
1131
–
1134
(
1979
).
Google Scholar
Crossref
Search ADS
 
25.
D. J. James and G. Kerry, “The Propagation of Blast Noise Across Acoustically Hard Surfaces,” Proceedings of Internoise 2000.
26.
Airbus France SA (AM-B), Final Technical Report on Project No. GRD1-2000-25189 SOBER (2004).
27.
F. Coulouvrat and T. Auger, “Influence of molecular relaxation on the rise time of sonic booms,” Proceedings of the 7th International Symposium on Long Range Sound Propagation, Ecole Centrale de Lyon, 25–26 July (1996), 177–191.
28.
P.
Boulanger
,
R.
Raspet
, and
H.
Bass
, “
Sonic boom propagation through a realistic turbulent atmosphere
,”
J. Acoust. Soc. Am.
98
,
3412
–
3417
(
1995
).
Google Scholar
Crossref
Search ADS
 
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