Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120°. The resultant amplitude will be
(a) A
(b) 2A
(c) 4A
(d) $\sqrt{2} A$ .

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Solution

(a) A

We know the resultant amplitude is given by
$R_{net} = \sqrt{A^{2} + A^{2} + 2 A^{2} \cos 120 º} (ϕ = 120 °) = \sqrt{2 A^{2} - A^{2}} [∵ \cos 120 º = \frac{- 1}{2}] = A$

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Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120°. The resultant amplitude will be (a) A (b) 2A (c) 4A (d) 2A.

(a) A We know the resultant amplitude is given by Rnet=A2+A2+2A2 cos 120º (ϕ=120°)=2A2-A2 ∵ cos 120º=-12=A

Two sine waves travel in the same direction in a medium. The amplitude of each wave is A and the phase difference between the two waves is 120°. The resultant amplitude will be
(a) A
(b) 2A
(c) 4A
(d) $\sqrt{2} A$ .

(a) A

We know the resultant amplitude is given by
$R_{net} = \sqrt{A^{2} + A^{2} + 2 A^{2} \cos 120 º} (ϕ = 120 °) = \sqrt{2 A^{2} - A^{2}} [∵ \cos 120 º = \frac{- 1}{2}] = A$