Question

The equation of a simple harmonic progressive wave is given by $y = A \sin (100 \pi t - 3 x).$ 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, $y = A \sin (100 \pi t - 3 x)$
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, $\phi = \frac{\pi}{3}$
$\frac{2 \pi}{\lambda}.x = \frac{\pi}{3}$
or $x = \frac{\pi}{3} \times \frac{\lambda}{2 \pi}$
$x =\frac{\pi}{3} \times \frac{2 \pi}{3 \times 2 \pi} = \frac{\pi}{9} m$