Interference of Waves:
When two waves of same frequency and amplitude travel in opposite directions and meet at a point, they superpose to produce a resultant wave. This phenomenon is called interference of waves.

Intensity of Waves:
The intensity of a wave is defined as the power per unit area carried by the wave. It is given by the formula:

I = P/A

where I is the intensity, P is the power and A is the area.

Ratio of Intensities:
If two waves of intensities I1 and I2 interfere to produce a resultant wave of intensity I, then the ratio of intensities is given by:

I1/I2 = (I ± 2√(I1I2))/(I - 2√(I1I2))

where the plus sign is used when the waves are in phase and the minus sign is used when the waves are out of phase.

Ratio of Maximum and Minimum Intensities:
When two waves interfere, they produce a resultant wave whose intensity varies between the maximum and minimum values. The ratio of maximum and minimum intensities is given by:

Imax/Imin = (I1 + I2 ± 2√(I1I2))/(I1 + I2 - 2√(I1I2))

where the plus sign is used when the waves are in phase and the minus sign is used when the waves are out of phase.

Solution:
Given, the ratio of intensities of two waves causing interference is 9:4.

Let the intensities of the two waves be 9x and 4x.

Using the formula for ratio of intensities, we get:

9x/4x = (I + 2√(81x^2))/ (I - 2√(81x^2))

Simplifying this equation, we get:

I = 25x^2/9

Using the formula for ratio of maximum and minimum intensities, we get:

Imax/Imin = (9x + 4x + 2√(9x*4x))/(9x + 4x - 2√(9x*4x))

Simplifying this equation, we get:

Imax/Imin = 25:1

Therefore, the ratio of maximum and minimum intensities is 25:1. Hence, the correct answer is option D.