Question

Equation of a progressive wave is given by

$y = 0.2\cos\pi\left( 0.04t + .02x - \frac{\pi}{6} \right)$ The distance is expressed in cm and time in second. What will be the minimum distance between two particles having the phase difference of π/2

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

Answer 1

Answer: (C)

25 cm

Answer 2

Comparing with $y = a\cos(\omega t + kx - \varphi)$,

We get $k = \frac{2\pi}{\lambda} = 0.02 \Rightarrow \lambda = 100cm$

Also, it is given that phase difference between particles $\Delta\varphi = \frac{\pi}{2}.$ Hence path difference between them

$\Delta = \frac{\lambda}{2\pi} \times \Delta\varphi = \frac{\lambda}{2\pi} \times \frac{\pi}{2} = \frac{\lambda}{4} = \frac{100}{4} = 25cm$