Q. The displacement $y(in\ cm)$ produced by a simple harmonic waves is $y = \frac{10}{\pi}\sin{\left( 2000\pi t - \frac{\pi x}{17} \right).}$ The periodic time and maximum velocity of the particles in the medium will respectively be
A) $10^{- 3}\sec$ and $330\ m/sec$
B) $10^{- 4}\sec$ and $20\ m/sec$
C) $10^{- 3}\sec$ and $200\ m/sec$
D) $10^{- 2}\sec$ and $2000\ m/sec$
Explanation
(c) Comparing with $y = a\sin{(\omega t - kx)} \Rightarrow a = \frac{10}{\pi},\omega = 2000\pi$
$\therefore v_{\max} = a\omega = \frac{10}{\pi} \times 2000\pi = 2000m/sec$
and $\omega = \frac{2\pi}{T} \Rightarrow 200\pi = \frac{2\pi}{T} \Rightarrow T = 10^{- 3}\sec$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.