Question

A wave travelling along the x-axis is described by the equation y(x, t) = 0.005 sin (ax – bt). If the wavelength and time period of the wave are 0.08 m and 2s respectively, the a, b in appropriate units are

• A. $\alpha = 25\pi,\beta = \pi$
• B. $\alpha = \frac{0.08}{\pi},\beta = \frac{2}{\pi}$
• C. $\alpha = \frac{0.04}{\pi},\beta = \frac{1}{\pi}$
• D. $\alpha = 12.5\pi,\beta = \frac{\pi}{2}$

Answer 1

Answer: (A)

$\alpha = 25\pi,\beta = \pi$

Answer 2

Here, $\lambda = 0.08m,T = 2s$

y(x,t) $= 0.005$ $\sin(\alpha x - \beta t)$

Compare it with the standard form of equation

$y(x,t) = a\sin(kx - \omega t)$

We get,

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

$\beta = \omega = \frac{2\pi}{T} = \frac{2\pi}{2} = \pi$