Question

A wave travelling along the x -axis is described by the equation $y(x,t)=0.005\cos (\alpha x-\beta t).$ If the wavelength and the time period of the wave are $0.08m$ and $2.0s$ respectively, then $\alpha$ and $\beta$ in appropriate units are

• A. $\alpha =12.50\pi ,\beta =\frac{\pi }{2.0}$
• B. $\alpha =25.00\pi ,\beta =\pi$
• C. $\alpha =\frac{0.08}{\pi },\beta =\frac{2.0}{\pi }$
• D. $\alpha =\frac{0.04}{\pi },\beta =\frac{1.0}{\pi }$

Answer 1

Answer: (B)

The wave travelling along the $x$ -axis is given by
$y(x,t)=0.005\cos (\alpha x-\beta t)$
$\therefore \alpha =k=\frac{2\pi }{\lambda }$ and $\beta =\omega =\frac{2\pi }{T}$
As $\lambda =0.08m$ and $T=2.0s$
$\therefore \alpha =\frac{2\pi }{0.08}=\frac{\pi }{0.04}=\frac{\pi }{4}\times 100.00=25.00\pi$ and $\beta =\frac{2\pi }{2.0}=\pi$