Two periodic waves with amplitudes A_1 and A_2 travel through a...

The resultant amplitude $A$ of two waves with amplitudes $A_1$ and $A_2$ having a phase difference $\phi$ is given by $A = \sqrt{A_1^2 + A_2^2 + 2A_1A_2\cos\phi}$.

The maximum resultant amplitude occurs when $\cos\phi = 1$, which gives A_\max = A_1 + A_2.

The minimum resultant amplitude occurs when $\cos\phi = -1$, which gives A_\min = |A_1 - A_2|. Since $A_1 > A_2$, A_\min = A_1 - A_2.

The difference between the maximum and minimum resultant amplitudes is A_\max - A_\min = (A_1 + A_2) - (A_1 - A_2) = 2A_2.