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Mathematics 309Part I - The elementary geometry of wave motion2. Waves in 1DEven in 1D it is a bit difficult to say what is and isn't a wave, but certain objects are clearly conforming. A simple wave is one which amounts to a graph similar to that of the cosine function that moves regularly in time.
The fundamental relationThe important parameters of a simple wave are amplitude, wave length, velocity, period, and frequency.
The equation of the graphThe equation of a wave at time t=0, amplitude 1, and period 2 is y = cos x. That with amplitude A is y = A cos x. Changing the wave length from 2 to amounts to a horizontal scaling by /2 , and therefore has equation y = A cos 2 x/. Since it is shifted to the right by ct in time t, the equation at time t isy = A cos (2/) (x - ct) = A cos ( 2x/ - t ). Exercises |