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)

$\frac{\pi}{9}m$

Answer 2

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