Waves on Stretched Strings

  • Stephen Nettel

Abstract

The string under tension, when only lightly disturbed, is the simplest example of a distributed system undergoing linear wave motion. This chapter begins with a derivation of the wave equation governing the vibrations of the string. As in Chap. 2 we divide the analysis into natural and driven motion. The natural motion is shown to consist of an infinite number of independent contributions, each contribution a so-called normal mode. Associated with each mode is a harmonic oscillator, with a natural frequency characteristic of the mode. The spatial dependences of the modes together form a complete orthonormal basis over the interval occupied by the string. This last fact facilitates the solution of the initial value problem. Analysis of the driven motion reveals that the oscillator characterizing each mode displays a resonance response just as did the single oscillator in the previous chapter.

Keywords

Sine Dinate Crest Acoustics Verse 

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Further Reading

  1. W.C. Elmore, M.A. Heald: Physics of Waves (Dover, New York 1985)Google Scholar
  2. P.R. Wallace: Mathematical Analysis of Physical Problems (Dover, New York 1984)MATHGoogle Scholar
  3. P.M. Morse, K.V. Ingard: Theoretical Acoustics (McGraw-Hill, New York 1968)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Stephen Nettel
    • 1
  1. 1.Department of PhysicsRensselaer Polytechnic InstituteTroyUSA

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