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This shows a superposition (in black) of two waves of frequecies f1 (red) and f2 (green).

Try these experiments:

Some math:

Let the wave at your ear be a superposition of two simple waves

          y    =    sin k1 t   +   sin k2 t  

where k1 and k2 are two different frequencies.

Using the well-known identity, we can express this as

          y    =    2 cos dt   sin kt  
          d   =   ( k1 -- k2 ) / 2       (half the difference between the frequencies)
          k   =   ( k1 + k2 ) / 2      (average frequency)

For instance, values k1 = 30 and k2 = 32 give

          y  =   2 cos t   sin 31 t  

i.e., a sound of 31 Herz (average frqn'cy), the volume of which varies as cos t, giving 2 beats per second.