Question

A simple harmonic progressive wave is represented by the equation y = 8 sin 2$\pi$ (0.1x – 2t) where x and y are in cm and t is in seconds. At any instant the Phase difference between two particles separated by 2.0 cm in the x-direction is

• A. 18⁰
• B. 36⁰
• C. 54⁰
• D. 72⁰

Answer 1

Answer: (D)

72⁰

Answer 2

y = 8 sin 2$\pi\left( \frac{x}{10} - 2t \right)$given by comparing with standard equation y = a sin 2$\pi\left( \frac{t}{T} - \frac{x}{\lambda} \right)$

$\lambda = 10cm$

So Phase Difference = $\frac{2\pi}{\lambda}$× path difference =$\frac{2\pi}{10} \times 2 = \frac{2}{5} \times 180{^\circ}$= 72⁰