Question

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. $\frac{\pi }{3}m$

Answer 1

Answer: (A)

Given, $y=A\sin (100\pi t-3x)$
The general equation,
$y=A\sin (\omega t-kx)$
$\therefore k=3$
and $k=\frac{2\pi }{\lambda }$
or $\lambda =\frac{2\pi }{k}=\frac{2\pi }{3}$
Phase difference, $\varphi =\frac{\pi }{3}$
$\frac{2\pi }{\lambda }.x=\frac{\pi }{3}$
or $x=\frac{\pi }{3}\times \frac{\lambda }{2\pi }$
$x=\frac{\pi }{3}\times \frac{2\pi }{3\times 2\pi }=\frac{\pi }{9}m$