Standing Waves

  • Fritz K. Kneubühl


A standard example of a one-dimensional standing wave [Alonso & Finn 1967 B, 1970 B, 1992 B, Courant & Hilbert 1968 B, Halliday et al. 1993 B, Hazen & Pidd 1965 B, Kneubühl 1994 B] is the motion of a string in a guitar, harp, violin or piano that is stretched between two clamps separated by a fixed distance. Such a string is somehow made to oscillate. The driving force does not need to have a particular frequency of its own. The string selects automatically a frequency such that an integer number of half wavelengths fits into the distance between the two fixed supports. This phenomenon is called resonance. The lowest resonant frequency usually predominates, while higher resonant frequencies called overtones contribute various amounts. In the case of a string it is obvious that the overtones are integral multiples of the lowest frequency and are therefore named harmonics.


Standing Wave Helmholtz Equation Resonant Mode Circular Membrane Inhomogeneous Boundary Condition 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1997

Authors and Affiliations

  • Fritz K. Kneubühl
    • 1
  1. 1.Institute of Quantum Electronics, Physics DepartmentSwiss Federal Institute of Technology (ETH)ZürichSwitzerland

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