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).
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).
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).
This content is only available via PDF.
AAPT members receive access to The Physics Teacher and the American Journal of Physics as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.