Playing with thisthe manipulate below might help:. It's based on the the acoustics of beats.
Manipulate[Plot[
{Cos[a*t] + Cos[b*t], 2*Cos[(b - a) t/2], -2*Cos[(b - a) t/2]}, {t, 0, 10},
PlotStyle -> {
Directive[Opacity[0.7]],
Directive[Black, Thick],
Directive[Black, Thick]}],
{{a, 20}, 1, 50}, {{b, 21}, 1, 50}]