The One-Dimensional Wave Equation and Its Solutions

  • Eugen Skudrzyk


At a sufficiently great distance from the sound source, the wave fronts become plane. The solutions of the wave equation then depend only on the coordinate x in the direction of propagation, \( \left( \frac{\partial \Phi }{\partial y}=\frac{\partial \Phi }{\partial z}=0 \right) \) and the wave equation reduces to
$$ \frac{{{\partial }^{2}}\Phi }{\partial {{x}^{2}}}=\frac{1}{{{c}^{2}}}\frac{{{\partial }^{2}}\Phi }{\partial {{t}^{2}}} $$


Wave Equation Particle Velocity Sound Pressure Order Quantity Natural Vibration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Andreev, N. N.: Concerning second order quantities in acoustics. Soy. Phys. Acoust. 1 (1955) 1–11.Google Scholar
  2. Arons, A. B., Yennie, D. R.: Phase distortion of acoustic pulses obliquely reflected from a medium of higher sound velocity J.A.S.A. 22 (1950) 231.Google Scholar
  3. Beranek, L. L.: Acoustics. New York, N. Y.: McGraw-Hill. 1954.Google Scholar
  4. Chernov, L. A.: Wave propagation in a random medium. New York, N. Y.: McGraw-Hill. 1960.Google Scholar
  5. Heymann, O.: Die Differentialgleichungen des Schallfeldes. Akust. Z. 2 (1937) 193–202.MATHGoogle Scholar
  6. Hunter, J. L.: Acoustics. Englewood Cliffs, N. J.: Prentice-Hall. 1957.Google Scholar
  7. Karnovskii, M. I.: Interaction acoustical impedance of spherical radiators and resonators. Comptes Rendus (Doklady) de l’Academie des Sciences de l’URSS,Vol. XXXII, No. 1, 1941.Google Scholar
  8. Kinsler, L. E., Frey, R.: Fundamentals of acoustics. New York, N. Y.: Wiley. 1962.Google Scholar
  9. Kuml, W., Oberst, H., Skudrzyk, E. Impulsverfahren zur Messung der Reflexion von Wasserschallabsorbern in Rohren. Acustica 3 (1953) 421–433.Google Scholar
  10. Lamb, H.: Dynamical theory of sound, 2. Aufl., S. 122–125. London: Arnold. 1925; Hydrodynamics. Cambridge 1906, 1932.Google Scholar
  11. Mclachlan, N. W.: Loudspeakers. Oxford: Clarendon Press. 1934.Google Scholar
  12. Miller, N. B.: Reflections from gradual transition sound absorbers 30 (1958) 967.Google Scholar
  13. Morse, P. M.: Vibration and sound. New York, Toronto, London: McGraw-Hill. 1948.Google Scholar
  14. Morse, P. M., Ingard, U.: Linear acoustic theory, p. 1 127 in Handbook d. Physik,Vol. XI/7. Berlin—Göttingen—Heidelberg: Springer. 1962;Google Scholar
  15. Morse, P. M., Theoretical acoustics.New York, N. Y.: McGraw-Hill 1968.Google Scholar
  16. Rayleigh, Lord: The theory of sound, Vol. I. London: Macmillan. 1894.MATHGoogle Scholar
  17. Samuels, J. C.: Reflection and refraction of elastic waves at the interface of two moving semi-infinite plane media. J.A.S.A. 31 (1959) 1076.Google Scholar
  18. Schmidt, H.: Einführung in die Theorie der Wellengleichung. Leipzig: J. A. Barth. 1931.Google Scholar
  19. Skudrzyk, E. J.: The natural frequencies of rooms with rough walls and the diffuse sound reflections. Akust. Z. 4 (1939) 172–186;Google Scholar
  20. Skudrzyk, E. J.: Die Grundlagen der Akustik. Wien: Springer. 1954.Google Scholar
  21. Stephens, R. W. B., Bate, A. E.: Wave motion and sound. London: Arnold. 1950.Google Scholar
  22. Stewart, G. W., Lindsay, R. B.: Acoustics. New York, N. Y.: D. van Nostrand. 1930.Google Scholar
  23. Tatarski, V. I.: Wave propagation in a turbulent medium. New York, N. Y.: McGraw-Hill. 1961.Google Scholar
  24. Waterhouse, R.: Sampling statistcis for an acoustic mode. J.A.S.A. 47 (1970) 961.Google Scholar
  25. Weinstein, M. S.: On the failure of plane wave theory to predict the reflection of a narrow ultrasonic beam. J.A.S.A. 24 (1952) 284.Google Scholar
  26. Wien-Harms: Handbuch der Experimentalphysik, Bd. XVII, 1. Teil, MARTIN, H.: Schwingungen kontinuierlicher Systeme und Wellenvorgänge, Bd. XVII, 2. Teil, Technische Akustik I, Bd. XVII, 3. Teil, Technische Akustik II. Leipzig: Akadem. Verlagsges. 1934.Google Scholar
  27. Wood, A. B.: A textbook of sound. London: Bell. 1930.Google Scholar

Copyright information

© Springer-Verlag/Wien 1971

Authors and Affiliations

  • Eugen Skudrzyk
    • 1
  1. 1.Ordnance Research Laboratory and Physics DepartmentThe Pennsylvania State UniversityUniversity ParkUSA

Personalised recommendations