What is a wave equation? What is a traveling-wave solution?
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◆The wave equation is an important second-order linear partial differential equation for the description of waves—as they occur in classical physics—such as mechanical waves (e.g. water waves, sound waves and seismic waves) or light waves.
◆A function u(x,t) is called a traveling wave if it has the form u(x,t)=f(x−at), for some function f, called the waveform, and some number a, called the wave speed.
a.) Show that if a traveling wave solves the wave equation, and the waveform is not a line, then a=±c.
b.) Show that for the diffusion equation, there are traveling wave solutions with any speed. What is the general form of the waveform for a given speed a?
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