A plane progressive wave is given by `x=(40 cm) cos(50pit-0.02piy)` where `y` is in cm and `t` in `s`. The particle velocity at `y=25m` in time `t=(1)/(100)s` will be `10pisqrt(n) m//s`. What is the value of `n`.

Explanation

To solve the problem, we need to find the particle velocity of the wave given by the equation:

\[ x = (40 \, \text{cm}) \cos(50\pi t - 0.02\pi y) \]

at \( y = 25 \, \text{m} \) and \( t = \frac{1}{100} \, \text{s} \).

### Step 1: Convert Units
First, we need to convert \( y \) from meters to centimeters since the wave equation is given in centimeters.
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