Question

Two waves have their amplitudes in the ratio 1 : 9 . The maximum and minimum intensities when they interfere are in the ratio

Answer 1

Answer:

Let the intensities of the two waves be I

1

​

and I

2

​

.

Given : I

1

​

:I

2

​

=9:1

Ratio of maximum and minimum intensities $$\dfrac{I_{max}}{I_{min}} = \bigg(\dfrac{\sqrt{I_1} +\sqrt{I_2}}{\sqrt{I_1} - \sqrt{I_2}}\bigg)^2$$

Or $$\dfrac{I_{max}}{I_{min}} = \bigg(\dfrac{\sqrt{\frac{I_1}{I_2}} +1}{\sqrt{\frac{I_1}{I_2}} - 1}\bigg)^2$$

Or $$\dfrac{I_{max}}{I_{min}} = \bigg(\dfrac{\sqrt{9} +1}{\sqrt{9} - 1}\bigg)^2 = \bigg(\dfrac{3+1}{3-1}\bigg)^2$$

$$\implies \ $$

I

min

​

I

max

​

​

=

4

16

​

=

1

4

​

Explanation: