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

Different Forms of Equations

Four harmonic...

Question

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

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Solution

Let the amplitude of each wave is A.
The ones having phases of 0 and $π$ will cancel each other.

Resultant of other two is having angle $\frac{π}{3}$ between them is $2 A cos \frac{π}{6} = \sqrt{3} A$
Intensity $I \propto A^{2}$
$\Rightarrow I_{0} = K A^{2}$
And,
$I = K (\sqrt{3} A)^{2} = 3 K A^{2}$
So,
$I = 3 I_{0}$
$\Rightarrow n = 3$

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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

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