$A$ 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$\alpha = 12.5\pi, \beta = \frac{\pi}{2}$
- B$\alpha = 25\pi, \beta = \pi$
- C$\alpha = \frac{0.08}{\pi}, \beta = \frac{2}{\pi}$
- D$\alpha = \frac{0.04}{\pi}, \beta = \frac{1}{\pi}$
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You have learnt that a travelling wave in one dimension is represented by a function $y=f(x, t)$ where $x$ and $t$ must appear in the combination $x-vt$ or $x+vt$,i.e.,$y=f(x \pm vt)$. Is the converse true? Examine if the following functions for $y$ can possibly represent a travelling wave:
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