I want to discuss a few other phenomena that occur when listening to sounds. Keep in mind that if these exist with sound waves, then really they exist all over nature in other waves as well. [br][br]The tuning forks pictured above are used to tune instruments, but how it works will only make sense if you understand beats. Beats have their name because of the rhythmic way in which intensity will change for a wave that is made of two sinusoidal waves of very similar but not identical frequencies. Below is both a graphical form of the waves and also audio to hear the effect.

The ear does not pick up on two pitches played together in this fashion. There is only one tone heard, but the intensity (or loudness) of the tone varies. The single tone that is heard is the average of the two tones played, or just [math]f_{pitch}=\frac{f_1+f_{2_{ }}}{2}[/math]. On the other hand, the frequency of the intensity fluctuation is given by the absolute value of the difference of the frequencies. It's the absolute value because there is no way of knowing which one should be subtracted from the other. The frequency of the intensity fluctuation is called the [b]beat frequency, [/b]and is [math]f_{beat}=\left|f_1-f_2\right|[/math].[br][br]You will notice beats sometimes when two cars with loud exhausts drive near one another at similar engine speeds - perhaps while taking off from a stoplight. More commonly, beats are used for the tuning of musical instruments. If a tuning fork is used to tune a string on a guitar, for instance, the idea is to eliminate the beats that you hear when the tuning fork and string are sounding at the same time. That's because, as you can test in the graphic above, when the two frequencies are the same, the beats disappear. So really tuning means listening for beats and trying to eliminate them.