Two sound waves of equal intensity I produce beats. The maximum intensity of sound produced in beats will be $\mathrm{\sigma }\times \mathrm{I}.$ The value of $\mathrm{\sigma } \mathrm{is} ........$

When two waves of amplitudes a₁ and a₂ superpose to produce beats, the resultant amplitude of the maxima of intensity is 

A = (a₁+ a₂)

Now, intensity $\propto$ (amplitude)². 

Since the two waves have the same intensity, their amplitudes are equal, i.e. a₁ = a₂ = a. Thus, A = 2a.

Therefore, A₂ = 4a² or ${\mathrm{I}}_{\max }=4\mathrm{I}$