Four harmonic waves of equal frequencies and equal intensities I 0 have phase angles 0- -3- 2 -3 and - When they are superposed- the intensity of the resulting wave is nI 0- The value of n is

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Standard XII

Physics

Solar Cell

Four harmonic...

Question

Four harmonic waves of equal frequencies and equal intensities $I_{0}$ have phase angles $0, \frac{π}{3}, \frac{2 π}{3} a n d π$ . When they are superposed, the intensity of the resulting wave is $n I_{0}$ . The value of n is ___

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Solution

Suppose amplitude of individual harmonic wave be A and intensity be $l_{0}$ .
When they are super imposed such that first and fourth wave produce destructive interference, while $2^{n d}$ and $3^{r d}$ form constructive interference only as shown in phaser method.

So, resultant amplitude,
$A_{r}^{2} = A^{2} + A^{2} + 2. A . A . c o s 60^{\circ}$
$A_{r}^{2} = 3 A^{2}$
$∴$ Intensity of the resulting wave, $I_{r} = 3 l_{0}$
[ $∴$ Intensity of a wave, $l = A^{2}$ ]

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Four harmonic waves of equal frequencies and equal intensities I0 have phase angles 0,π3,2π3 and π. When they are superposed, the intensity of the resulting wave is nI0. The value of n is ___

Four harmonic waves of equal frequencies and equal intensities $I_{0}$ have phase angles $0, \frac{π}{3}, \frac{2 π}{3} a n d π$ . When they are superposed, the intensity of the resulting wave is $n I_{0}$ . The value of n is ___