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superposition of waves of different frequencies

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In some media, waves of different frequencies travel at different speeds. Such a medium is called a dispersive medium because waves that are not sinusoidal will change shape or disperse over time.

For example, a superposition of two such waves of different frequencies is described by the equation:

y(x,t) = cos(k1x - w1t) + cos(k2x - w2t)

Substitute into the equation above the following expressions for k1, k2, w1 and w2

And show that: (see attachment for equation)

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Solution Summary

The superposition of waves of different frequencies was investigated. The solution shows the work in detail.