Thank you for the very satisfying response.
Wow, i never though of it in term of Fourier series.
I admit that I have a poor understanding on the definition of geometry back then.
Yup, definitely got confused by the trigonometry identity.
At first, I was skeptical that two periodic waves which are close in wavelength regardless of their shape will generate a beat frequency given only proof of the cosine-cosine case. Later, I toyed with MATLAB and plotted sine-sine, cosine-cosine & sine-squarewave graph which showed beat...
It is easily derived from trigonometric identities that
cos(2*pi*f1*t)+cos(2*pi*f2*t)=2cos(2*pi*(f2+f1)*t)*cos(2*pi*(abs(f2-f1)*t))
which proves that superposition of two cosine wave will generate a beat frequency, but what about about a universal proof that applies to any kind of...