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

Answer 1

Answer: (A)

$\alpha =25.00\pi ,\beta =\pi$

wavelength $\lambda =0.08m$
Time period $T=2s$
$\therefore \alpha =K=\frac{2\pi }{\lambda }=\frac{2\pi }{0.08}=\frac{200\pi }{8}=25\pi$
$\beta =w=\frac{2\pi }{T}=\frac{2\pi }{2}=\pi$