Two waves of same amplitude and same intensity interfere at one point. Phase difference between them is θ. Match the following two columns. Column-I Column-IIA)Resultant amplitude for θ=60∘P)2 times the incident waveB)Resultant amplitude for θ=120∘Q)3 times the incident waveC)Resultant intensity for θ=90∘R)4 times the incident waveD)Resultant intensity for θ=0∘S)3 times the incident wave T)None of these

A=2A0cos⁡θ2I=4I0cos2⁡θ2Resultant amplitude for θ=60∘is 3 times Resultant amplitude for θ=120∘is same as individual amplitude. Resultant intensity for θ=90∘is 2 timesResultant intensity for θ=0∘is 4 times the incident wave

Two waves of same amplitude and same intensity interfere at one point. Phase difference between them is θ. Match the following two columns. Column-I Column-IIA)Resultant amplitude for θ=60∘P)2 times the incident waveB)Resultant amplitude for θ=120∘Q)3 times the incident waveC)Resultant intensity for θ=90∘R)4 times the incident waveD)Resultant intensity for θ=0∘S)3 times the incident wave T)None of these

A=2A0cos⁡θ2I=4I0cos2⁡θ2Resultant amplitude for θ=60∘is 3 times Resultant amplitude for θ=120∘is same as individual amplitude. Resultant intensity for θ=90∘is 2 timesResultant intensity for θ=0∘is 4 times the incident wave

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Two waves of same amplitude and same intensity interfere at one point. Phase difference between them is $θ$ . Match the following two columns.
Column-I Column-II
A) Resultant amplitude for $θ = 60^{\circ}$ P) 2 times the incident wave
B) Resultant amplitude for $θ = 120^{\circ}$ Q) 3 times the incident wave
C) Resultant intensity for $θ = 90^{\circ}$ R) 4 times the incident wave
D) Resultant intensity for $θ = 0^{\circ}$ S) $\sqrt{3}$ times the incident wave
T) None of these

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$A \to T; B \to S; C \to R; D \to P$

$A \to S; B \to T; C \to P; D \to R$

$A \to T; B \to S; C \to P; D \to R$

$A \to R; B \to P; C \to S; D \to T$

answer is B.

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Detailed Solution

$\begin{array}{r} A = 2 A_{0} \cos (\frac{θ}{2}) \\ I = 4 I_{0} \cos^{2} (\frac{θ}{2}) \end{array}$

Resultant amplitude for $θ = 60^{\circ}$ is $\sqrt{3}$ times

Resultant amplitude for $θ = 120^{\circ}$ is same as individual amplitude.

Resultant intensity for $θ = 90^{\circ}$ is 2 times

Resultant intensity for $θ = 0^{\circ}$ is 4 times the incident wave

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