The equation of a travelling wave is $y = 60\cos (1800t - 6x)$ where $y$ is in microns, $t$ in seconds and $x$ in metres. The ratio of maximum particle velocity to velocity of wave propagation is
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(c) Maximum particle velocity ${v_{\max }} = \omega a$ and wave velocity $v = \frac{\omega }{k}$
==> $\frac{{{v_{\max }}}}{v} = \frac{{\omega a}}{{\omega /k}} = ka$.
From the given equation $k = {\rm{Co - efficient}}\;{\rm{of}}\,x = 6\,micron$
$\; = 6 \times {10^{ - 6}}m$
==> $\frac{{{v_{\max }}}}{v} = ka = 6 \times {10^{ - 6}} \times 60 = 3.6 \times {10^{ - 4}}$
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