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 $0.08\, m$ and $2.0\, s$ 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 $\lambda=0.08\, m$ and $T=2.0 \,s$
$\therefore \alpha=\frac{2 \pi}{0.08}=\frac{\pi}{0.04}=\frac{\pi}{4} \times 100.00=25.00 \,\pi$ and $\beta=\frac{2 \pi}{2.0}=\pi$