Question

The equation of two progressive waves is given b
y1= Asin(kx - wt) and y2 = Asin(kx - wt + 0)
then amplitude of medium particle will be
(1) 2Acoso
(2) 2Acos0/2
(3) 2Asino
(4) 2Asino/2​

Answer 1

Answer:

The amplitude of medium particle will be

$R = 2Acos(\frac{\theta}{2})$

Explanation:

As we know that the given wave equations are

$y_1 = A sin(kx - wt)$

$y_2 = A sin(kx - wt + \theta)$

now we know that the above two waves are coherent waves and due to superposition of above two waves we will have interference phenomenon

So we will have resultant amplitude given as

$R = \sqrt{A_1^2 + A_2^2 + 2A_1A_2cos\theta}$

now we have

$R = \sqrt{A^2 + A^2 + 2A^2cos\theta}$

$R = \sqrt2 A\sqrt{1 + cos\theta}$

$R = 2Acos(\frac{\theta}{2})$

#Learn

Topic : Interference

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