Q. 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) $18^{0}$
B) $54^{0}$
C) $36^{0}$
D) $72^{0}$
Explanation
(d) $y = 8\sin{2\pi(0.1x - 2t)}$
Compare it with the equation of wave motion
$y = r{sin2\pi}\left( \frac{x}{\lambda} - \frac{t}{T} \right)$
$\frac{1}{\lambda} = 0.1,\lambda = 10\ cm$
From $\phi = \frac{2\pi}{\lambda}x = \frac{2\pi}{10} \times 2 = 0.4 \times 180{^\circ} = 72{^\circ}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.