Exact solutions for one-dimensional, transient acoustic wave propagation in curvilinear geometries with mean temperature variations are presented in this paper. These solutions are obtained by using a transformation of the spatial and acoustic variables in a manner suggested by the WKB approximation. The analysis is performed for spherical and cylindrical co-ordinate systems. Temperature profiles admitting exact traveling wave type solutions are derived. Although these solutions resemble the approximate, “high frequency,” WKB form of solution of the wave equation, they have the interesting property that they are exact, regardless of the scale of the acoustic disturbance relative to that of the inhomogeneity. Calculations showing the propagation of waves in cylindrical and spherical geometries are presented.

1.
Kinsler, L., Frey, A., Coppens, A., and Sanders, J., 1982, Fundamentals of Acoustics, John Wiley and Sons, New York.
2.
Eisenberg
,
N.
, and
Kao
,
T.
,
1969
, “
Propagation of Sound through a Variable Area Duct with a Steady Compressible Flow
,”
J. Acoust. Soc. Am.
,
49
, pp.
169
175
.
3.
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
.
4.
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
.
5.
Karthik
,
B.
,
Manoj Kumar
,
B.
, and
Sujith
,
R. I.
,
2000
, “
Exact Solutions to One-Dimensional Acoustic Fields with Temperature Gradient and Mean Flow
,”
J. Acoust. Soc. Am.
,
108
, pp.
38
43
.
6.
Karthik
,
B.
,
Mohanraj
,
R.
,
Ramakrishnan
,
R.
, and
Sujith
,
R. I.
,
1999
, “
Exact Solution for Sound Propagation in Ducts with an Axial Mean Temperature Gradient and Particulate Damping
,”
J. Acoust. Soc. Am.
,
106
, pp.
2391
2395
.
7.
Lighthill, J., 1978, Waves in Fluids, pp. 120–128, Cambridge University Press, U.K.
8.
Dokumaci
,
E.
,
1998
, “
An Approximate Analytical Solution for Plane Sound Wave Transmission in Inhomogeneous Ducts
,”
J. Sound Vib.
,
217
, pp.
853
867
.
9.
Cummings
,
A.
,
1977
, “
Ducts with Axial Temperature Gradients: An Approximate Solution for Sound Transmission and Generation
,”
J. Sound Vib.
,
51
, pp.
55
67
.
10.
Crighton, D. G., Dowling, A. P., Ffowcs Williams, J. E., Heckl, M., and Leppington, F. G., 1992, Modern Methods in Analytical Acoustics, Springer Verlag: London.
11.
Subrahmanyam
,
P.
,
Sujith
,
R. I.
, and
Lieuwen
,
T.
,
2001
, “
A Family of Exact Transient Solutions for Acoustic Wave Propagation in Inhomogeneous, Non-Uniform Area Ducts
,”
J. Sound Vib.
,
240
(
4
), pp.
705
715
.
12.
Thompson, P. E., 1972, Compressible Fluid Dynamics, pp. 198–201, McGraw-Hill, Inc.
You do not currently have access to this content.
{"ft_lang_label":"__label__en","ft_lang_prob":0.81470704,"math_prob":0.8677875,"size":3767,"snap":"2022-40-2023-06","text_gpt3_token_len":921,"char_repetition_ratio":0.09859155,"word_repetition_ratio":0.18461539,"special_character_ratio":0.22644013,"punctuation_ratio":0.1858006,"nsfw_num_words":0,"has_unicode_error":false,"math_prob_llama3":0.9594091,"pos_list":[0],"im_url_duplicate_count":[null],"WARC_HEADER":"{\"WARC-Type\":\"response\",\"WARC-Date\":\"2022-10-03T08:22:10Z\",\"WARC-Record-ID\":\"<urn:uuid:56fbe757-fb55-478a-9996-777b73899edd>\",\"Content-Length\":\"122739\",\"Content-Type\":\"application/http; msgtype=response\",\"WARC-Warcinfo-ID\":\"<urn:uuid:256aea97-86f7-4431-ba8b-7053af9c646f>\",\"WARC-Concurrent-To\":\"<urn:uuid:fb7f6f67-06e6-4414-a4ff-dead24e3755e>\",\"WARC-IP-Address\":\"52.179.114.94\",\"WARC-Target-URI\":\"https://asmedigitalcollection.asme.org/vibrationacoustics/article-abstract/125/2/133/469366/Propagation-of-Sound-in-Inhomogeneous-Media-Exact?redirectedFrom=PDF\",\"WARC-Payload-Digest\":\"sha1:GFPL6TDEJLNLFY6XHWCJ76O7JXDQVCYS\",\"WARC-Block-Digest\":\"sha1:RXH5XFZS47DDO3KUEROZZIY7VRHRR3JC\",\"WARC-Identified-Payload-Type\":\"text/html\",\"warc_filename\":\"/cc_download/warc_2022/CC-MAIN-2022-40/CC-MAIN-2022-40_segments_1664030337404.30_warc_CC-MAIN-20221003070342-20221003100342-00438.warc.gz\"}"}