Question

A wave travelling along the $x-axis$ is described by the equation $y_{x,t}=0.005$ sin $(\alpha x-\beta t)$. If the wave length and time period of the wave are $0.08m$ and $2s$ respectively, then $\alpha ,\beta$ in appropriate units are then

• A. $\alpha =25\pi ,\beta =\pi$
• B. $\alpha =\frac{0.08}{\pi },\beta =\frac{2}{\pi }$
• C. $\alpha =\frac{0.04}{\pi },\beta =\frac{1}{\pi }$
• D. $\alpha =12.5\pi ,\beta =\frac{\pi }{2}$

Answer 1

The correct option is A $\alpha =25\pi ,\beta =\pi$

Here, $\lambda =0.08m,T=2s$
$y(x,t)=0.005$sin $(\alpha x-\beta t)$

Compare it with the standard form of equation
$y(x,t)=a$sin $(kx-\omega t)$

we get, $\alpha =k=\frac{2\pi }{\lambda }=\frac{2\pi }{0.08}=25\pi$

$\beta =\omega =\frac{2\pi }{T}=\frac{2\pi }{2}=\pi$