Q. The equation of a simple harmonic progressive wave is given by y=A sin (100$\pi t$-3x). find the distance between 2 particles having a phase difference of $\frac{\pi}{3}$.
A) $\frac{\pi}{9}m$
B) $\frac{\pi}{18}m$
C) $\frac{\pi}{6}m$
D) $\frac{\pi}{3}m$
Explanation
(a) Given, y=a sin (100$\ \pi$t-3x)
The general equation,
$k = 3\ and\ k = \frac{2\pi}{\lambda}$
Or
$\lambda = \frac{2\pi}{k}$
$\lambda = \frac{2\pi}{3}$
Phase difference, $\phi = \frac{\pi}{3}$
$\frac{2\pi}{\lambda}.x = \frac{\pi}{3}$
$or\ \ \ \ x = \frac{\pi}{3} \times \frac{\lambda}{2\pi}$
$x = \frac{\pi}{3} \times \frac{2\pi}{3 \times 2\pi}$
Distance,
$x = \frac{\pi}{9}m$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.