Question

A progressive wave is represented as A progressive wave is represented as $y=0.2 \cos \pi\left(0.04 t+0.2 x-\frac{\pi}{6}\right)$ where distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of $ \frac{\pi }{2} $ ?

• A. 4 cm
• B. 8 cm
• C. 25 cm
• D. 12.5 cm

Answer 1

Answer: (C)

On comparing the given equation with
$y =a \cos (\omega t+k x-\phi)$
we get, $k =\frac{2 \pi}{\lambda}=0.02$
and $\lambda=100\, cm$
It is given that phase difference between particles,
$\Delta \phi=\frac{\pi}{2}$
So, the path difference between them,
$\Delta p=\frac{\lambda}{2 \pi} \times \Delta \phi$
$=\frac{\lambda}{2 \pi} \times \frac{\pi}{2}=\frac{\lambda}{4}$
$=\frac{100}{4}=25\, cm$