THE SUPERPOSITION OF WAVES IN NON-DISPERSIVE MEDIA

The travelling wave ψ = Acos(kx − ωt) is described as monochromatic because it has a single frequency ω and a single wavelength λ (= 2π/k). Moreover, it extends to ± infinity along the x-axis. (In practice this is unrealistic and a real wave has a beginning and an end, although its length may be considerable. For example, researchers have used lasers to produce monochromatic light waves many kilometres long.) A monochromatic wave cannot carry any information since its amplitude and frequency do not vary. To send information we need to modulate the wave in some way as is done, for example, in the transmission of Morse code. A modulated wave consists of the superposition of a group of waves of different frequencies. We have already met the superposition of waves in, for example, the formation of standing waves. There the waves travelled in opposite directions. Here we consider the superposition of waves travelling in the same direction. We shall consider the phenomenon of beats and also the amplitude modulation of radio waves where it is clearly the intention to transmit information.