In the usual treatment of waves in introductory courses, one begins with traveling waves and the frequency/wavelength relationship
fλ = v,
where v is the wave velocity. One then makes the point about superposition and shows that two waves traveling in opposite directions can add up to a standing wave; Eq. (1) still applies. This approach is problematic in two ways: (1) The motion being described, standing waves, has no apparent “velocity,” and so it seems unnecessarily complex—perhaps unreasonably complex—to construct it out of moving waves; (2) It is not easy to derive the formula for the velocity of waves, especially for an audience without calculus or without multi-variate calculus (the wave equation).
Topics
Mechanical waves, Standing waves, Partial differential equations
1.
Henry Semat, Fundamentals of Physics, 4th ed. (Holt, Rinehart and Winston, Austin, TX, 1966); David Halliday and Robert Resnick, Physics, 3rd ed. (Wiley, New York, 1978); Francis W. Sears, Mark W. Zemansky, and Hugh D. Young, College Physics, 6th ed. (Addison-Wesley, Reading, MA, 1985).
2.
Douglas C. Giancoli, Physics (Prentice-Hall, Upper Saddle River, NJ, 1980); Edwin R. Jones and Richard L. Childers, Physics (Addison-Wesley, Reading, MA, 1990); Raymond A. Serway and Jerry S. Faughn, College Physics (Saunders, 1985).
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© 2007 American Association of Physics Teachers.
2007
American Association of Physics Teachers
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