We have 2 sound waves of same amplitude
#y_1 = A sin 2 pi f_1 t#
#y_2 = A sin 2 pi f_2 t#
The resultant wave is
And by the sum to product identity:
The red cosine term is the beat frequency we can perceive, ie
The amplitude of the resultant beat can therefore be seen to be
And that is what is perceived when, say, 2 musical notes that are very close in pitch are plucked on a guitar: in the model proposed above, a sinusoid pattern to its amplitude.