Question

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

The correct option is A $\alpha =25.00\pi ,\beta =\pi$

Given : $\lambda =0.08$ $m$ $T=2.0s$

The given equation is: $y(x,t)=0.005cos(\alpha x-\beta t)$

On comparing with standard equation: $y(x,t)=Acos(kx-wt)$

$\therefore$ $\alpha =k=\frac{2\pi }{\lambda }$

$⟹$ $\alpha =\frac{2\pi }{0.08}=25\pi$

Also, $\beta =w=\frac{2\pi }{T}$

$⟹$ $\beta =\frac{2\pi }{2}=\pi$