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Resultant Amplitude

Two waves, y1...

Question

Two waves, $y_{1} = 2 a cos ω t$ and $y_{2} = 3 a cos (ω t + \frac{π}{2})$ meet at a point. The amplitude of the resultant wave is

A

a

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B

5 a

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C

3.6 a

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D

2.5 a

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Solution

The correct option is C $3.6 a$
Given:
$y_{1} = 2 a cos ω t$
$y_{2} = 3 a cos (ω t + \frac{π}{2})$
So, the amplitudes of wave are,
$A_{1} = 2 a$ and $A_{2} = 3 a$
Also, phase difference,
$α = \frac{π}{2}$
We know that resultant amplitude of superposition of two waves is given by,
$A = \sqrt{A_{1}^{2} + A_{2}^{2} + 2 A_{1} A_{2} cos α}$
$\Rightarrow A = \sqrt{(2 a)^{2} + (3 a)^{2} + 2 \times 2 a \times 3 a \times cos \frac{π}{2}}$
$\Rightarrow A = \sqrt{13 a^{2}} = 3.6 a$

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Resultant Amplitude

Standard XI Physics

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