Waves in Infinite Media

  • Ari Ben-Menahem
  • Sarva Jit Singh


A wave is a disturbance, usually periodic, that travels with finite velocity through a medium. Sound waves, water waves, and electromagnetic waves are some examples. All wave motions have two important characteristics in common: First, energy is propagated to distant points and, second, the disturbance travels through the medium without giving the medium as a whole any permanent displacement. Each successive particle of the medium performs a motion similar to its predecessor’s but later in time, and returns to its origin. Whatever the nature of the medium that transmits the waves, be it air, a stretched string, a liquid, or an electrical cable, these two properties enable us to relate all wave motions together. Indeed, many types of waves are governed by a second-. order linear partial differential equation
$${\nabla ^2}\Psi = {1 \over {{c^2}}}{{{\partial ^2}\Psi } \over {\partial {t^2}}},$$
where Ψ(r, t) represents the disturbance traveling with the velocity c. Equation (2.1) is known as the wave equation.


Plane Wave Helmholtz Equation Spherical Wave Infinite Medium Spherical Bessel Function 
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Copyright information

© Springer-Verlag New York Inc. 1981

Authors and Affiliations

  • Ari Ben-Menahem
    • 1
  • Sarva Jit Singh
    • 2
  1. 1.Weizmann Institute of ScienceRehovotIsrael
  2. 2.Maharshi Dayanand UniversityRohtakIndia

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