Free and Forced Vibrations of Simple Systems

  • Thomas D. Rossing
  • Neville H. Fletcher


Mechanical, acoustical, or electrical vibrations are the sources of sound in musical instruments. Some familiar examples are the vibrations of strings (violin, guitar, piano, etc), bars or rods (xylophone, glockenspiel, chimes, clarinet reed), membranes (drums, banjo), plates or shells (cymbal, gong, bell), air in a tube (organ pipe, brass and woodwind instruments, marimba resonator), and air in an enclosed container (drum, violin, or guitar body).


Sine Compressibility Flange Acoustics 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. Arnold, T.W., and Case, W. (1982). Nonlinear effects in a simple mechanical system. Am. J. Phys. 50, 220.ADSCrossRefGoogle Scholar
  2. Beyer, R.T. (1974). “Nonlinear Acoustics” (Naval Sea Systems Command ), Chapter 2.Google Scholar
  3. Crawford, F.S. Jr. (1965). “Waves.” Berkeley Physics, Vol. 3, Chapter 1. McGraw-Hill, New York.Google Scholar
  4. Fletcher, N.H. (1982). Transient response and the musical characteristics of bowed-string instruments. Proc. Wollongong Coop. Workshop on the Acoustics of Stringed Instruments (A. Segal, ed.). University of Wollongong, Australia.Google Scholar
  5. Kinsler, L.E., Frey, A.R., Coppens, A.B., and Sanders, J.V. (1982). “Fundamentals of Acoustics,” 3rd ed., Chapter 1. Wiley, New York.Google Scholar
  6. Lee, E.W. (1960). Non-linear vibrations. Contemp. Phys. 2, 143.ADSCrossRefGoogle Scholar
  7. Main, I.G. (1978). “Vibrations and Waves in Physics.” Cambridge Univ. Press, London and New York.Google Scholar
  8. Morse, P.M. (1948). “Vibration and Sound,” 2nd ed., Chapter 2. McGraw-Hill New York. Reprinted 1976, Acoustical Soc. Am., Woodbury, New York.Google Scholar
  9. Rossing, T.D. (1982). “The Science of Sound,” Addison-Wesley, Reading, Massachusetts.Google Scholar
  10. Skudrzyk, E. (1968). “Simple and Complex Vibrating Systems,” Chapters 1 and 2. Pennsylvania State University, University Park, Pennsylvania.Google Scholar

Copyright information

© Springer-Verlag New York, Inc. 1995

Authors and Affiliations

  • Thomas D. Rossing
    • 1
  • Neville H. Fletcher
    • 2
  1. 1.Department of PhysicsNorthern Illinois UniversityDe KalbUSA
  2. 2.CSIRO Australia Research School of Physical Sciences and EngineeringAustralian National UniversityCanberraAustralia

Personalised recommendations