Beats

When two waves of slightly different frequency overlap a phenomenon known as beats results. In sound the resulting effect is a kind of throbbing sensation.
The final displacement (y):
y = y₁ + y₂ = a (2pf₁t + sin 2pf₂t) = 2a cos 2p([f₁ – f₂]t/2 x sin 2p([f₁ + f₂]t/2)

(a) amplitude varies with time with a frequency [f₁ – f₂]/2
(b) The ear is sensitive to the intensity and not the amplitude of a vibration:

Beat frequency (f) = 2 x amplitude frequency = [f₁ – f₂]