Wave Motion 4 Question 23
22. Four harmonic waves of equal frequencies and equal intensities $I _0$ have phase angles $0, \frac{\pi}{3}, \frac{2 \pi}{3}$ and $\pi$. When they are superposed, the intensity of the resulting wave is $n I _0$. The value of $n$ is
(2015 Adv.)
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Answer:
Correct Answer: 22. 3
Solution:
- Let individual amplitudes are $A _0$ each. Amplitudes can be added by vector method.
$$ A _1=A _2=A _3=A _4=A _0 $$
Resultant of $A _1$ and $A _4$ is zero. Resultant of $A _2$ and $A _3$ is
$$ A=\sqrt{A _0^{2}+A _0^{2}+2 A _0 A _0 \cos 60^{\circ}}=\sqrt{3} A _0 $$
This is also the net resultant.
Now, $\quad I \propto A^{2}$
$\therefore$ Net intensity will become $3 I _0$.
$\therefore$ Answer is 3 .
