Beats are produced by two progressive waves. Maximum loudness at the waxing is x times the loudness of each wave. The value of x is

 Let a be the amplitude of each wave. At maximum, resultant amplitude
$$\begin{gathered} =\mathrm{a}+\mathrm{a}=2\mathrm{a} \\ \mathrm{Intensity} \mathrm{of} \mathrm{each} \mathrm{wave} = {\mathrm{a}}^2 \\ \mathrm{Maximum} \mathrm{loudness} = \mathrm{xx} \mathrm{loudness} \mathrm{of} \mathrm{each} \\ \mathrm{or} 4{\mathrm{a}}^2=\mathrm{x}\times {\mathrm{a}}^2 \\ \mathrm{X}=4 \end{gathered}$$