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

Given:
y = 5 cos [π(200t − x/150)]

Step 1: Compare with standard wave equation
y = A cos(ωt − kx)

So,
ω = 200π
k = π/150

Step 2: Wave velocity formula
v = ω / k

Step 3: Substitute values
\[ v = \frac{200\pi}{\pi/150} = 200 \times 150 = 30000 \text{ cm/s} \]

Step 4: Convert to m/s
\[ 30000 \text{ cm/s} = 300 \text{ m/s} \]

Final Answer: 300 m/s