The previous set of notes ``Reflection and Transmission at a Change in Medium,'' determined the form of scattered, either transmitted and reflected, pulses at a change in medium by working with the general solution to the wave equation. As we shall see below, for the special case of incoming traveling waves of sinusoidal form, the form of transmission and reflection may be determined directly by an appeal to general physical principles. Because all incoming pulse shapes may ultimately be decomposed into a sum of sinusoidal functions by a mathematical procedure called Fourier analysis, by studying scattering of sinusoidal functions one can in fact determine the form of scattering for any pulse shape. Although we shall not study Fourier analysis in this course, it is still useful for us to study scattering amplitudes for sinusoidal pulses at a change in medium because, as we have seen, reflection and transmission amplitudes are independent of the incoming pulse shape. Thus, for any shape pulse, the transmission and reflection scattering amplitudes will be exactly what we compute for sinusoidal pulses.
We also study scattering of sinusoidal pulses at a change in medium because this problem reveals far more general ideas which may be applied to find the solution to the equations of motion for any system driven by an incoming wave of fixed frequency, such as the interference and diffraction setups which we shall study in the next set of notes, ``Interference and Diffraction.''