Question

The displacement produced by a simple harmonic wave is :
$y=\frac{10}{\pi }\sin (2000\pi t-\frac{\pi x}{17})\text{cm}$
The time period and maximum velocity of the particle will be respectively -

• A. ${10}^{-3}$ second and $200\text{m/s}$
• B. ${10}^{-2}$ second and $200\text{m/s}$
• C. ${10}^{-3}$ second and $330\text{m/s}$
• D. ${10}^{-4}$ second and $20\text{m/s}$

Answer 1

The correct option is A ${10}^{-3}$ second and $200\text{m/s}$

$y=\frac{10}{\pi }\sin (200\pi t-\frac{\pi x}{17})$
Comparing with
$y=A\sin (\omega t-kx)$
$\omega =2000\pi =\frac{2\pi }{T}\Rightarrow T={10}^{-3}\text{seconds}$
Maximum velocity $=A\omega$
$\Rightarrow \frac{10}{\pi }\times 2000\pi \times {10}^{-2}=200\text{m/s}$