Ratio of Amplitude of Two Interfering Waves

When two waves interfere, the resulting amplitude at any point is the algebraic sum of the amplitudes of the individual waves at that point. Let's consider two interfering waves with amplitudes A1 and A2.

When the waves interfere constructively, the amplitudes add up and we get maximum constructive interference. This occurs when the phase difference between the waves is an integer multiple of 2π (or a whole number of wavelengths). In this case, the resulting amplitude is the sum of the individual amplitudes:

A_max = A1 + A2

On the other hand, when the waves interfere destructively, the amplitudes cancel each other out and we get minimum destructive interference. This occurs when the phase difference between the waves is an odd multiple of π (or a half number of wavelengths). In this case, the resulting amplitude is the difference between the individual amplitudes:

A_min = |A1 - A2|

Ratio of Amplitude of Maxima to Minima

Now, let's consider the given scenario where the ratio of the amplitudes of the two interfering waves is 2:1 (A1:A2 = 2:1). We can substitute these values into the equations for maximum and minimum amplitudes:

A_max = A1 + A2 = 2A2 + A2 = 3A2
A_min = |A1 - A2| = |2A2 - A2| = A2

To find the ratio of the amplitudes of maxima to minima, we divide the maximum amplitude by the minimum amplitude:

Ratio = A_max / A_min = (3A2) / A2 = 3

Therefore, the ratio of the amplitude of maxima to minima is 3:1, which corresponds to option C.