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A plane progressive wave is given by $x = (40 c m) \cos (50 π t - 0.02 π y)$ where y is in cm and t in s. The particle velocity at y = 25 cm in time t = 1/100s will be $10 π \sqrt{n} m / s .$ What is the value of n.

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Detailed Solution

Given that: $x = 40 \cos (50 π t - 0.02 π y)$
Particle velocity $v_{P} = \frac{d x}{d t} = (40 \times 50 π) (- \sin (50 π t - 0.02 π y))$
Putting y=25 cm and $t = \frac{1}{100} s$
$v_{P} = 0$

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