Q. Equation of motion in the same direction are given by $y_{1} = 2a\sin{(\omega t - kx)}$ and $y_{2} = 2a\sin{(\omega t - kx - \theta)}$ The amplitude of the medium particle will be
A) $2a\cos\theta$
B) $\sqrt{2}a\cos\theta$
C) $4a\cos{\theta/2}$
D) $\sqrt{2}a\cos{\theta/2}$
Explanation
(c) Resultant amplitude
$A_{R} = 2A\cos{\left( \frac{\theta}{2} \right) = 2 \times (2a)\cos{\left( \frac{\theta}{2} \right) = 4a\cos\left( \frac{\theta}{2} \right)}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.