Two periodic waves of intensities I1 and I2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

Question

Two periodic waves of intensities I1 and I2 pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is (A)  I1 +I2  (B)  (√I1+√I2)2  (C)  (√I1-√I2)2  (D)  2(I1+I2)

Tardigrade Admin · Accepted Answer

Resultant intensity of two periodic wave is given by

I = I_{1} + I_{2} + 2 I_{1} I_{2} cos δ

where

δ

is the phase difference between the waves.
For maximum intensity,

δ = 2 nπ

n = 0, 1, 2,

... etc.
Therefore, for zero order maxima, cos

δ

= 1

I_{ma x} = I_{1} + I_{2} + 2 I_{1} I_{2} = (I_{1} + I_{2})^{2}

For minimum intensity,

δ = (2 n - 1) π,

n = 1, 2

, ... etc.
Therefore, for 1st order minima,

cos δ

= - 1

I_{min} = I_{1} + I_{2} - 2 I_{1} I_{2}

= (I_{1} - I_{2})^{2}

Therefore,

I_{ma x} + I_{min} = (I_{1} + I_{2})^{2} + (I_{1} - I_{2})^{2}

= 2 (I_{1} + I_{2})

Q. Two periodic waves of intensities $I_{1}$ and $I_{2}$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

$I_{1} + I_{2}$

$(I_{1} + I_{2})^{2}$

$(I_{1} - I_{2})^{2}$

$2 (I_{1} + I_{2})$

Q. Two periodic waves of intensities I1​ and I2​ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

I1​+I2​

(I1​​+I2​​)2

(I1​​−I2​​)2

2(I1​+I2​)

Q. Two periodic waves of intensities $I_{1}$ and $I_{2}$ pass through a region at the same time in the same direction. The sum of the maximum and minimum intensities is

$I_{1} + I_{2}$

$(I_{1} + I_{2})^{2}$

$(I_{1} - I_{2})^{2}$

$2 (I_{1} + I_{2})$