Two waves with same amplitude and frequency s | vedclass

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(B) Let the amplitude of each wave be $A$. The intensity $I$ is proportional to the square of the amplitude,so $I \propto A^2$. Let $I_0 = kA^2$ be th

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$2: 1$

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(B) Let the amplitude of each wave be $A$. The intensity $I$ is proportional to the square of the amplitude,so $I \propto A^2$. Let $I_0 = kA^2$ be the intensity of each wave.Case $1$: When the waves arrive in phase,the phase difference $\phi = 0$. The resultant amplitude is $A_R = A + A = 2A$. The resultant intensity is $I_1 = k(2A)^2 = 4kA^2 = 4I_0$.Case $2$: When the waves arrive $90^{\circ}$ ($\pi/2$ radians) out of phase,the resultant amplitude is $A_R = \sqrt{A^2 + A^2 + 2AA \cos(90^{\circ})} = \sqrt{2A^2} = A\sqrt{2}$. The resultant intensity is $I_2 = k(A\sqrt{2})^2 = 2kA^2 = 2I_0$.The ratio of the resultant intensities is $\frac{I_1}{I_2} = \frac{4I_0}{2I_0} = \frac{2}{1}$.

Two waves with same amplitude and frequency superpose at a point. The ratio of resultant intensities when they arrive in phase to that when they arrive $90^{\circ}$ out of phase is $\left[\cos \frac{\pi}{2}=0\right]$

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