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Equation of a progressive wave is $y = 2 \sin π (\frac{x}{18} - \frac{t}{10})$ , where x and y are in cm. Then ratio of maximum particle velocity to the velocity of propagation is

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$π : 4$

$π : 6$

$π : 9$

$π : 3$

answer is B.

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Detailed Solution

Maximum particle velocity, $u_{\max} = ω . A$

Velocity of propagation, $V = \frac{ω}{K}$

$∴ \frac{u_{\max}}{V} = \frac{ω A}{\frac{ω}{K}} = K A = \frac{π}{18} \times 2 = \frac{π}{9}$

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