As A.P.French in Vibrations and Waves writes,
The beating effect is most easily analyzed if we consider the addition of two SHM's of equal amplitude: $$ \mathbf{x_1} = \mathrm{A} \cos{\omega_1 .t} \& \mathbf{x_2} = \mathrm{A} \cos{\omega_2 .t}$$ . . . Clearly their addition,as a purely mathematical result,can be carried out for any values of $\omega_1$ & $\omega_2$. But its description as a beat phenomenon is physically meaningful only if $|{\omega_2 - \omega_1}| \ll \omega_1 + \omega_2.$
Why is it so? What does the author want to say??
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