Question

Equation of a progressive wave is given by $y = 0.2 cos \, \pi \big(0.04 t + 0.02 x - \frac{\pi}{6}\big).$ The 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
• E. None of these

Answer 1

Answer: (C)

Comparing with y = a cos $(\omega t + kx - \phi) $
We get, $ k = \frac{2 \pi}{\lambda} = 0.02 \pi$
$\Rightarrow \lambda = 100 \, km$
Also, it is given that phase difference between particles
$\Delta \phi = \frac{\pi}{2}.$
Hence, path difference between them
$ \Delta x = \frac{\lambda}{2 \pi} \times \Delta \phi$
$ = \frac{\lambda}{2 \pi} \times \frac{\pi}{2}$
$ = \frac{\lambda}{4} = \frac{100}{4}$
$ = 25 \, cm$