Question

The displacement produced by a simple harmonic wave is $y=\frac{10}{\pi }\sin (2000\pi t-\frac{\pi x}{17})\text{cm}$., where $t,x$ are in SI units. 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 $2000\text{m/s}$
• 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 $200\text{m/s}$

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