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Q.

The equation of a simple harmonic wave is given by $y = 3 \sin \frac{π}{2} (50 t - x)$ where x and y are in meters and t is in seconds. The ratio of maximum particle velocity to the wave velocity is

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a

$\frac{2}{3} π$

b

$3 π$

c

$\frac{3}{2} π$

d

$2 π$

answer is A.

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Detailed Solution

$y = 3 \sin \frac{π}{2} (50 t - x) Particle velocity = \frac{\partial y}{\partial t} = 3 (\frac{π}{2} \times 50) \cos \frac{π}{2} (50 t - x) Maximum particle velocity = 75 π m / s Wave velocity v = \frac{ω}{k} = \frac{50}{1} = 50 m / s & Required ratio = \frac{75 π}{50} = \frac{3}{2} π$

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