Williams, S. A. Department of Physics, Iowa State University, Ames, Iowa.
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The velocity of propagation of a pure sine wave of infinite extent. In one dimension, for example, the form of the disturbance for such a wave is y(x,t) = A sin [2π(x/λ − t/T)]. Here x is the position at which the disturbance y(x,t) exists at time t, λ is the wavelength, T is the period which is related to the wave frequency by T = 1/f, and A is the disturbance amplitude. The argument of the sine function is called the phase. The phase velocity is the speed with which a point of constant phase can be said to move. Thus x/λ − ft = constant, so the phase velocity υp is given by dx/dt = υp = λf. This is the basic relationship connecting phase velocity, wavelength, and frequency. See also: Phase (periodic phenomena); Sine wave; Wave motion
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