When Do Two Waves Create a Heterodyne Wave?

It is well known that when two waves are added they produce beats. These beats are the amplitude modulation of the initial waves and occur periodically at a rate equal to the frequency difference of the two waves. Acoustical beats arise from sound waves of nearly equal frequencies. Optical beats arise from the interference of two light waves of nearly equal frequencies. Despite these examples, adding two waves does not always create a new wave at the beat frequency—a heterodyne wave. A heterodyne wave is, however, created only when the wave amplitudes combine nonlinearly. The resulting heterodyne wave can be identified because it is an additive term at a new frequency in the output waveform. An electrical circuit provides a unique opportunity to understand the responses of linear and nonlinear devices (resistors and diodes) to the sum of two sinusoidal waves. Using the resistor, the output frequencies are the same while the diode creates new (heterodyne) frequencies. A speaker in the circuit provides an audio demonstration of the difference between the devices.