Q. A wave travelling along the x-axis is described by the equation y(x, t) =0.005 cos (αx-βt). If the wavelength and the time period of the wave are 0.08m and 2.0s, respectively, than α and β in appropriate unit are
A) a=25.00π, β π
B) $\alpha = \frac{0.08}{\pi},\ \beta = \frac{2.0}{\pi}$
C) $\alpha = \frac{0.04}{\pi},\beta = \frac{1.0}{\pi}$
D) $\alpha = 12.5\pi,\ \beta = \frac{\pi}{2.0}$
Explanation
(a) Given, y(x,t)=0.005 cos (ax-βt)
$\frac{2\pi}{\lambda} = a\ \ \ \ \ and\frac{2\pi}{T} = \beta$
So,
$a = \frac{2\pi}{0.08} = 25\pi\ \ \ and\ \beta = \frac{2\pi}{2} = \pi$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.