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Equation of motion of two waves in the same direction is given by $y_{1} = A \sin (ωt - kx)$ , $y_{2} = A \sin (ωt - kx - θ)$ . The amplitude of the particle of the medium will be

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$2 A \cos \frac{θ}{2}$

2A cos $θ$

$\sqrt{2} Acos \frac{θ}{2}$

$1.2 f, 1.2 λ$

answer is A.

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Detailed Solution

The resultant amplitude is given by

$A_{R} = \sqrt{A^{2} + A^{2} + 2 AA \cos θ} = \sqrt{2 A^{2} (1 + \cos θ)}$

= $2 Acos \frac{θ}{2}$

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