Abstract
The three-dimensional wave equation in cartesian coordinates
is solved by plane progressive waves
where \( \overrightarrow n \) is the direction of propagation, \( \vec{n}\cdot \vec{r} = {{n}_{x}}x + {{n}_{y}}y + {{n}_{z}}z \) and
so that the wave equation is satisfied. The quantities n x ,ny, nz can be interpreted as the direction cosines of the angles between the direction of propagation and the x, y, and z axes, respectively:
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Reference
Bernade, A. H.: On the propagation of sound waves in a cylindrical conduit. J.A.S.A. 44 (1968) 616.
Bladel, J. V.: Coupling through a small aperture in a waveguide. J.A.S.A. 47 (1970) 202.
Daniels, F. B.: On the propagation of sound waves in a cylindrical conduit. J.A.S.A. 22 (1950) 563.
Fay, R. D.: Waves in liquid-filled cylinders. J.A.S.A. 24 (1952) 459.
Forristall, G. Z., Ingram, J. D.: Asymmetries in cylindrical waveguides. J.A.S.A. 46 (1969) 164.
Hartig, H. E., Lambert, R. F.: Attentuation in a rectangular slotted tube of (1,0) transverse acoustic waves. J.A.S.A. 22 (1950) 42.
Hoover, R. M., Laird, D. T., Miller, L. N.: Acoustic filter for waterfilled pipes. J.A.S.A. 22 (1950) 38.
Ingard, U., Pridmore-Brown, D.: Propagation of sound in a duct with constrictions. J.A.S.A. 23 (1951) 689.
Jacobi, W. J.: Propagation of sound waves along liquid cylinders. J.A.S.A. 21 (1949) 120.
Junger, M. C.: Sound propagation in a fluid-filled tube with massive wall reactance. J.A.S.A. 28 (1956) 165.
Karal, F. C. Analogous acoustical impedance for discontinuities and constrictions of circular cross section. J.A.S.A. 25 (1953) 327.
Lapin, A. D.: Sound propagation in a waveguide with side branches and volume resonators on the walls. Soy. Phys. Acoust. 7 (1961) 171;
Lapin, A. D.: Sound propagation in inhomogeneous waveguides. Sov. Phys. Acoust. 13 (1967) 198–200;
Lapin, A. D.: Sound propagation in a waveguide of variable cross section. Soy. Phys. Acoust. 14(1968)191–194.
Levine, H.: On the theory of sound reflection in an open-ended cylindrical tube. J.A.S.A. 26 (1954) 200.
Lin, T. C., Morgan, G. W.: Wave propagation through fluid contained in a cylindrical elastic shell. J.A.S.A. 28 (1956) 1165.
Lippert, W. K. R.: The measurement of sound reflection and transmission at right-angled bends in rectangular tubes. Acustica 4 (1954) 313.
Mawardi, O. K.: On the propagation of sound waves in narrow conduits. J.A.S.A. 21 (1949) 482.
Mebkulov, V. V.: Field structure in cylindrical waveguides with a complex cross section. Sov. Phys. Acoust. 5 (1960) 439.
Miles, J. W.: On the change of cross section and bifurcation of a cylindrical tube. J.A.S.A. 22 (1950) 59.
Molloy, C. T.: Lined tube as an element of acoustic circuits. J.A.S.A. 21 (1949) 413.
Shaw, E. A. G.: Acoustic wave guide. I. An apparatus for the measurement of acoustic impedance using plane waves and higher order mode waves in tubes. J.A.S.A. 25 (1953) 224.
Stewart, G. W., Lindsay, R. B.: Acoustics. New York, N. Y.: D. van Nostrand. 1930.
Tanner, R.: Etude expérimentale de divers types de tuyaux sonores bouchés, du point de vue de la pureté de timbre. Acustica 8 (1958) 226.
Wood, J. K., Thurston, G. B.: Acoustic impedance of rectangular tubes. J.A.S.A. 25 (1953) 858.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1971 Springer-Verlag/Wien
About this chapter
Cite this chapter
Skudrzyk, E. (1971). Plane Waves in Three Dimensions. In: The Foundations of Acoustics. Springer, Vienna. https://doi.org/10.1007/978-3-7091-8255-0_17
Download citation
DOI: https://doi.org/10.1007/978-3-7091-8255-0_17
Publisher Name: Springer, Vienna
Print ISBN: 978-3-7091-8257-4
Online ISBN: 978-3-7091-8255-0
eBook Packages: Springer Book Archive