First slide

Superposition of waves

Question

Three waves of equal frequency having amplitudes 10 $μ$ m, 4 $μ$ m and 7 $μ$ m arrive at a given point with successive phase difference of $\frac{π}{2}$ . The amplitude of the resulting wave in $μ$ m is given by

Moderate

A

7
B

6
C

5
D

4

Solution

The wave 1 and 3 reach out of phase. Hence resultant phase difference between them is $π$ .
$∴$ Resultant amplitude of 1 and 3 = $10 - 7 = 3 μm$
This wave has phase difference of $\frac{π}{2}$ with $4 μm$
$∴$ Resultant amplitude = $\sqrt{3^{2} + 4^{2}} = 5 μm$

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