In molecular spectroscopy, an anharmonic oscillator has a nonparabolic potential which results in a nonharmonic absorption spectrum, but the same oscillator treated classically has a precisely harmonic vibrational spectrum. To avoid confusion, it is suggested that such an oscillator should simply be called nonlinear. The term “inharmonic” is suggested as an appropriate descriptor for classical oscillators, such as metal bars, that have nonharmonic vibrational spectra even in the linear limit of small vibrations.
REFERENCES
1.
2.
F. V. Hunt, Origins in Acoustics (1978) (reprinted by Acoustical Society of America, Woodbury, NY, 1992), Chap. 1.
3.
N. H.
Fletcher
, “The nonlinear physics of musical instruments
,” Rep. Prog. Phys.
62
, 723
–764
(1999
).4.
P. M. Morse, Vibration and Sound (1948), 2nd ed. (reprinted by Acoustical Society of America, Woodbury, NY, 1981), pp. 85, 161–162.
5.
J. Goodisman, Diatomic Interaction Potential Theory (Academic, New York, 1973), Vol. 1, pp. 72–86.
6.
Universality in Chaos, edited by P. Cvitanovic (Adam Hilger, Bristol, 1984).
7.
G. L. Baker and J. P. Gollub, Chaotic Dynamics: An Introduction (Cambridge U.P., Cambridge, 1996).
8.
H. L. F. Helmholtz, On the Sensations of Tone (1877), 4th ed., translated by A. J. Ellis (Dover, New York, 1954).
9.
G. Herzberg, Molecular Spectra and Molecular Structure (Van Nostrand, New York, 1950), pp. 90–92.
10.
M. D. Harmony, “Molecular spectra and structure,” in A Physicist’s Desk Reference, edited by H. L. Anderson (American Institute of Physics, New York, 1989), p. 242.
11.
W. A. Sethares, Tuning, Timbre, Spectrum, Scale (Springer, London, 1998).
12.
A. B. Pippard, The Physics of Vibration (Cambridge U.P., Cambridge, 1978), Vol. 1, pp. 12–21.
13.
In music theory an enharmonic change is one in which the naming of a note changes, for example, from G♯ to A♭. In modern equal-tempered tuning, as for example on the piano, there is no pitch change involved, but in older and more subtle tuning systems, such as meantone (Ref. 14) there is a pitch change of a small fraction of a semitone.
14.
J. Backus, The Acoustical Foundations of Music (W. W. Norton, New York, 1969), Chap. 8.
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© 2002 American Association of Physics Teachers.
2002
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