Three waves of equal frequency having amplitudes 10 , , m, 4 , ,m… - Vidyadip

MCQ

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

A
$7$
B
$6$
✓
$5$
D
$4$

✓

Answer

Correct option: C.

$5$

c
(c) The wave $1$ and $3$ reach out of phase. Hence resultant phase difference between them is $\pi $.

$\therefore $ Resultant amplitude of $1$ and $3 = 10 - 7 = 3 \mu m$

This wave has phase difference of $\frac{\pi }{2}$ with $4 \mu m$

$\therefore $ Resultant amplitude = $\sqrt {{3^2} + {4^2}} = 5\,\,\mu m$

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