Two small beads are situated at distance a apart on an otherwise uniform taut string. A transverse wave of angular frequency ω is incident from one side, exerting longitudinal forces and respectively, on the beads. The effective “force of attraction” between the beads, is the simplest classical analog to the Casimir effect. We find that can be positive or negative, depending on the values of a and ω. For a broad spectrum of incident “noise,” however, the net “Casimir” force is zero.
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We assume that the ends of the string are so far away that we never have to worry about reflections from them.
6.
Because the boundary conditions are linear, it does not matter whether we state them in terms of y (which is more physical) or in terms of ψ (which is mathematically simpler).
7.
A. P. French, Vibrations and Waves (Norton, New York, 1971), Eq. 7.39.
8.
If an equation of the form (for constants and ) holds for all t, it follows that and
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© 2001 American Association of Physics Teachers.
2001
American Association of Physics Teachers
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