Superposition of two waves trains of same amplitudes and nearly same frequencies, moving in the same direction, results in the formation of beats. The maximum loudness heard at the waxing is n times the loudness of each of the component wave trains. The value of n is:

Correct option is C

​$$\text{When two sound waves of nearly the same frequency interfere, they produce a phenomenon known as} \\\text{beats. The loudness of the sound alternates between a maximum and a minimum at the frequency of the beat.} \\\text{The maximum loudness occurs when the sound waves are in phase (waxing), and the minimum loudness occurs when they are out of phase (waning).} \\\bullet \text{ Maximum loudness at waxing is given by:} \\I_{\text{max, waxing}} = (a_1 + a_2)^2 = (a + a)^2 = 4a^2 \\\text{where } a_1 \text{ and } a_2 \text{ are the amplitudes of the two waves, and } a \text{ is their individual amplitude.} \\\bullet \text{ Loudness of each component wave train is:} \\I_1 = a_1^2 = a^2, \quad I_2 = a_2^2 = a^2 \\\text{Thus, the maximum loudness is 4 times the loudness of one wave train.} \\I_{\text{max, waxing}} = 4a^2 \quad \text{and} \quad I_{\text{each component}} = a^2 \\\text{The maximum loudness is 4 times the loudness of each component wave train. Therefore, the value of } n \text{ is 4.}$$​​