When tones are played simultaneously, their harmonics can interact in a variety of ways in our auditory system. One potential interaction is beating. It can occur when two of the harmonics of the constituent sounds fall within about 15 Hz of each other. Beating is a periodic pulsation of the loudness of a sound at a rate equal to the frequency difference between the nearly-coincident harmonics. It is not always easy to predict what combinations of tones will cause beating. Whether or not beating is heard depends upon the amplitude of the harmonics in question and a variety of other factors whose discussion is beyond the scope of this work. For our purposes it is enough to know that beating happens in many musical situations.
It is important to realize that beating is a perceptual, not a physical phenomenon. In other words, it is psycho-acoustic, not acoustic, in nature. Many authors explain beating by showing a graph of two superposed sinusoids whose frequencies are close. Indeed it is easy for our visual system to extract a convincingly pulsating shape from such graphs. This approach takes advantage of visual shape detection as an analog of auditory loudness perception. The problem with this approach is that it tends to give the impression that beating is a physical, not a perceptual phenomenon. Since we can both see and hear beating, it is tempting to assume that beating ``exists'' in some absolute sense. This is of course false. It is only by virtue of a system capable of some nonlinear processing (such as our auditory system) that two sinusoids can produce something that fluctuates at their difference frequency. In the air (a largely linear system), nothing beats.