The equation of a plane progressive wave is given by $$y = 5 \cos \pi \left(200t - \frac{x}{150}\right)$$ where x and y are in cm and t is in second. The velocity of the wave is __________ m/s.

The standard form of a one-dimensional plane progressive wave travelling in the +x direction is
$$y = A \cos \left(\omega t - kx\right)$$
where $$\omega$$ is the angular frequency and $$k$$ is the angular wave number.

Given equation:
$$y = 5 \cos \pi\left(200t - \frac{x}{150}\right)\qquad (x,y \text{ in cm, } t \text{ in s})$$

Rewrite the argument to identify $$\omega$$ and $$k$$:
$$\pi\left(200t - \frac{x}{150}\right) \;=\; \bigl(\pi \cdot 200\bigr)t \;-\; \bigl(\pi/150\bigr)x$$

Therefore
$$\omega = 200\pi\ \text{rad s}^{-1}, \qquad k = \frac{\pi}{150}\ \text{rad cm}^{-1}$$

Wave speed formula:
$$v = \frac{\omega}{k}$$

Substitute the values:
$$v = \frac{200\pi}{\,\pi/150} = 200 \times 150 = 30000 \text{ cm s}^{-1}$$

Convert to SI units (1 m = 100 cm):
$$v = \frac{30000}{100} = 300 \text{ m s}^{-1}$$

Hence, the velocity of the wave is $$300\ \text{m/s}$$.

Option D which is: $$300$$