Echoes, Interference, and Beats

Two or more sound waves from different sources tend either to increase or to decrease the sound intensity at different points, depending on whether the waves are related so as to add or to subtract at the point under consideration. Thus, if a steady tone of single frequency is sounded in a room, the waves directly from the source and those coming indirectly from reflecting surfaces such as walls will reinforce each other at certain points and will tend to neutralize each other at other points. At certain locations in the room, depending on the configuration of the room and the frequency of the sound, the sound will be intense, while at other points the sound will be weak.

When two sounds of different frequencies are simultaneously produced, the two waves combine instantaneously as in Fig. 2. It is often loosely stated that this phenomenon gives rise to a beat note. Such a beat note is created, but by the mechanism of hearing, and not in the air. The ear is a non-linear device, and such a device creates within itself new frequencies (in this instance the beat note) when two different frequencies are simultaneously impressed on it (cf. Analysis of an Amplitude-Modulated Wave).

Figure 2. Two pure tones of the same amplitude but of different frequencies combine as shown. The beat note which the ear "hears" is, however, created by the hearing mechanism itself.

This can be proved in the following manner: Connect two good loud speakers to separate oscillators of good wave form. Set one oscillator on, for instance, 1500 cycles, and the other on 2000 cycles. The ear should then "hear" a 500-cycle tone. Next, pick up the resultant sound with a microphone and analyze the output with a wave analyzer. This device will show that only a 1500-cycle tone and a 2000-cycle tone are present. If this is true, the 500-cycle "sound" must have been produced by the ear and brain, and not by the mere mixture or "beating together" of the two waves in the air.

These statements are not exactly correct for very intense sounds (reference 6, also, Fig. 23) but they do hold for the ordinarily observed phenomenon of beat notes.