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Intro to Standing Waves

If the two wa...

Question

If the two waves represented by $y_{1} = 4 s i n ω t$ and $y_{2} = 3 s i n (ω t + π / 3)$ interfere at a point, the amplitude of the resulting wave will be about

A

7

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B

5

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C

6

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D

3.5

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Solution

The correct option is C $6$
$ϕ = π / 3, a_{1} = 4, a_{2} = 3$
So, $A = \sqrt{a_{1}^{2} + a_{2}^{2} + 2 a_{1} . a_{2} cos ϕ} \Rightarrow A \approx 6$

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