First slide

Interference

Question

Three waves of equal frequencies having amplitudes $10 μm, 4 μm and 7 μm$ arrive of a given point. Phase difference between first and second wave is $\frac{π}{2}$ and that between second and third wave is $\frac{π}{2} .$ .Then amplitude of the resulting wave in $μm$ ,is

Moderate

A

7
B

6
C

5
D

4

Solution

$\begin{array}{l} \vec{A_{R}} = \vec{A_{1}} + \vec{A_{2}} + \vec{A_{3}} \\ ∴ A_{R} = \sqrt{{(A_{1} - A_{3})}^{2} + {A_{2}}^{2}} \\ = \sqrt{{(10 - 7)}^{2} + 4^{2}} μm = 5 μm \end{array}$

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