The purpose of this article is to provide an analytical solution for the acoustic field in a duct with sinusoidal area variation along the length. The equation describing the acoustic field in a variable area duct is a second-order partial differential equation. It is converted into a second-order ordinary linear differential equation, whose solution is dependent on the choice of area variation. The solution for the differential equation is obtained in terms of the area and is obtained neglecting the mean flow. Therefore, it is applicable in the absence of mean flow or in cases where the effects of mean flow are insignificant.

References

References
1.
Kumar
,
B. M.
, and
Sujith
,
R. I.
,
1998
, “
Exact Solution for One-Dimensional Acoustic Fields in Ducts With Polynomial Mean Temperature Profiles
,”
ASME J. Vibr. Acoust.
,
120
, pp.
965
969
.10.1115/1.2893927
2.
Sujith
,
R. I.
,
Waldherr
,
G. A.
, and
Zinn
,
B. T.
,
1995
, “
An Exact Solution for One-Dimensional Acoustic Fields in Ducts With an Axial Temperature Gradient
,”
J. Sound Vib.
,
184
, pp.
389
402
.10.1006/jsvi.1995.0323
3.
Munjal
,
M. L.
, and
Prasad
,
M. G.
,
1986
, “
On Plane-Wave Propagation in a Uniform Pipe in the Presence of a Mean Flow and a Temperature Gradient
,”
J. Acoust. Soc. Am.
,
80
, pp.
1501
1506
.10.1121/1.394406
4.
Peat
,
K. S.
,
1988
, “
The Transfer Matrix of a Uniform Duct With a Linear Temperature Gradient
,”
J. Sound Vib.
,
123
, pp.
43
53
.10.1016/S0022-460X(88)80076-2
5.
Kapur
,
A.
,
Cummings
,
A.
, and
Mungur
,
P.
,
1972
, “
Sound Propagation in a Combustion Can With Axial Temperature and Density Gradients
,”
J. Sound Vib.
,
25
, pp.
129
138
.10.1016/0022-460X(72)90601-3
6.
Cummings
,
A.
,
1977
, “
Ducts With Axial Temperature Gradients: An Approximate Solution for Sound Transmission and Generation
,”
J. Sound Vib.
,
51
, pp.
55
67
.10.1016/S0022-460X(77)80112-0
7.
Dokumaci
,
E.
,
1998
, “
An Approximate Analytical Solution for Plane Sound Wave Transmission in Inhomogeneous Ducts
,”
J. Sound Vib.
,
217
, pp.
853
867
.10.1006/jsvi.1998.1785
8.
Eisenberg
,
N.
, and
Kao
,
K.
,
1969
, “
Propagation of Sound Through a Variable Area Duct With a Steady Compressible Flow
,”
J. Acoust. Soc. Am.
,
49
, pp.
169
175
.10.1121/1.1912314
9.
Simmons
,
G. F.
,
1972
,
Differential Equations With Applications and Historical Notes
,
Tata-McGraw-Hill
,
New York
.
10.
Riley
,
K. F.
,
Hobson
,
M. P.
, and
Bence
,
S. J.
,
2006
,
Mathematical Methods for Physics and Engineering
,
Cambridge University
,
Cambridge, UK
.
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