Final answer:
The ratio of the amplitudes of two waves when the intensity ratio of their interference pattern is 36:1 is the square root of the intensity ratio, which gives us an amplitude ratio of 6:1.
Step-by-step explanation:
To determine the ratio of the amplitudes of the two waves when the maximum and minimum intensities are in a ratio of 36:1, we use the principle of superposition of waves and the relationship between intensity and amplitude.
When two waves interfere, the resulting intensity I at a point is given by the square of the resultant amplitude (A). For constructive interference (maximum intensity), the amplitudes add up, while for destructive interference (minimum intensity), the amplitudes subtract. If Imax represents the maximum intensity and A1 and A2 are the amplitudes of the two waves, we can say:
Imax ≈ (A1 + A2)2
And for minimum intensity, Imin:
Imin ≈ (A1 - A2)2
We are given that the ratio Imax/Imin = 36/1. From this ratio and the equations above, we need to find the ratio A1:A2. By solving these equations, we can see that when the ratio of intensities is 36:1, the amplitude ratio is the square root of the intensity ratio, which is 6:1.
This means that if A1 is the amplitude of one wave and A2 is the amplitude of the other wave, then A1:A2 = 6:1.