Question

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 seconds. Find the wave velocity :

Answer 1

Step 1: Identify $\omega$ and $k$ from the wave equation $y = A \cos(\omega t - kx)$.
Given: $y = 5 \cos(200\pi t - \frac{\pi x}{150})$.
$\omega = 200\pi \text{ rad/s}$.
$k = \frac{\pi}{150} \text{ cm}^{-1}$.

Step 2: Calculate wave velocity $v = \frac{\omega}{k}$.
$v = \frac{200\pi}{\pi/150} = 200 \times 150 = 30,000 \text{ cm/s}$.

Step 3: Convert to meters per second.
$v = \frac{30,000}{100} = 300 \text{ m/s}$.

Final Answer: 300 m/s.