Q. The displacement y of a particle in a medium can be expressed as $y = 10^{- 6}\sin\left( 100t + 20x + \frac{\pi}{4} \right)$m, where t is in second and x in metre. The speed of the wave is
A) $2000\ ms^{- 1}$
B) $5\ ms^{- 1}$
C) $20\ ms^{- 1}$
D) $5\pi\ ms^{- 1}$
Explanation
(b) As given,
$y = 10^{- 6}\sin{\left( 100t + 20x + \frac{\pi}{4} \right)\ \ }\ldots(i)$
Comparing it with
$y = a\sin(\omega t + kx + \phi)\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ldots(ii)$
We find,
$\omega = 100\ rads^{- 1},k = 20/m$
$\therefore\ \ \ v = \frac{\omega}{k} = \frac{100}{20} = 5ms^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.