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(C) The given equation of the travelling wave is $y = a \sin 2 \pi (p t - \frac{x}{5})$.Comparing this with the standard wave equation $y = a \sin (\o

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$\frac{2 \pi a}{5}$

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(C) The given equation of the travelling wave is $y = a \sin 2 \pi (p t - \frac{x}{5})$.Comparing this with the standard wave equation $y = a \sin (\omega t - kx)$,we have $\omega = 2 \pi p$ and $k = \frac{2 \pi}{5}$.The maximum particle velocity is given by $v_{max} = a \omega = a (2 \pi p) = 2 \pi a p$.The wave velocity is given by $v = \frac{\omega}{k} = \frac{2 \pi p}{2 \pi / 5} = 5 p$.The ratio of the maximum particle velocity to the wave velocity is $\frac{v_{max}}{v} = \frac{2 \pi a p}{5 p} = \frac{2 \pi a}{5}$.

The equation of a travelling wave is $y = a \sin 2 \pi (p t - \frac{x}{5})$. Then the ratio of the maximum particle velocity to the wave velocity is ...........

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