Question

The equations of motion of two waves propagating in the same direction is given by
$y_1=Asin(\omega t-kx)$
and $y_2=Asin(\omega t-kx-\theta )$
The amplitude of the medium particle will be

• A. $\sqrt{2}cos\theta$
• B. $2Acos\theta$
• C. $\sqrt{2}cos\frac{\theta }{2}$
• D. $2Acos\frac{\theta }{2}$

Answer 1

The correct option is D

$2Acos\frac{\theta }{2}$

$y_0=\sqrt{A^2+A^2+2A^2\left(cos\theta \right)}$

$=A\sqrt{2(1+cos\theta )}=2Acos\frac{\theta }{2}$