Question

Three harmonic waves having equal frequency v and same intensity $I_0$, have phase angles $0, \frac{\pi}{4}$ and $-\frac{\pi}{4}$ When they are superimposed the intensity of the resultant wave is close to :

• A. $0.2\, I_0$
• B. $I_0$
• C. $3\, I_0$
• D. $5.8 \,I_0$

Answer 1

Answer: (D)

$=A\,sin\,\omega t+A\,sin\left(\omega t-\frac{\pi}{4}\right)+A\,sin\left(\omega t+\frac{\pi }{4}\right)$
$=A\,sin\,\omega t+\sqrt{2}\,=A\,sin\,\omega t$
$=\left(\sqrt{2}+1\right)=A\,sin\,\omega t$
Resultant wave amplitude $=\left(\sqrt{2}+1\right)A
as I\,\propto\,A^{2}$
so $\frac{I}{I_{0}}=\left(\sqrt{2}+1\right)^{2}$
$I=5.8\,I_{0}$