Question

The displacement y (in cm) produced by a simple harmonic wave 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

Answer 1

Answer: (C)

$10^{- 3}$sec and 200 m/sec

Answer 2

Comparing with $y = a\sin(\omega t - kx)$ ⇒$a = \frac{10}{\pi},\omega = 200\pi$

$\therefore$ ${v\frac{10}{\pi}\sec}_{\max}$

and $\omega = \frac{2\pi}{T} \Rightarrow 200\pi = \frac{2\pi}{T}$⇒ $T = 10^{- 3}$sec