First slide

Superposition of waves

Question

The displacement of a particle is given by
$x = 3 \sin (5 π t) + 4 \cos (5 π t)$
The amplitude of the particle is

Easy

A

3
B

4
C

5
D

7

Solution

For the given super imposing waves
$a_{1} = 3, a_{2} = 4$ and phase difference $φ = \frac{π}{2}$
$\Rightarrow A = \sqrt{a_{1}^{2} + a_{2}^{2} + 2 a_{1} a_{2} cosπ / 2} = \sqrt{{(3)}^{2} + {(4)}^{2}} = 5$

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