Question

The equation of a wave travelling on a string is $ y=4\,\sin \left[ \frac{\pi }{2}\left( 8t-\frac{x}{8} \right) \right], $ where x, y are in cm and t in second. The velocity of the wave is

• A. 64 cm/s, in - x direction
• B. 32 cm/s, in - x direction
• C. 32 cm/s, in + x direction
• D. 64 cm/s, in + x direction

Answer 1

Answer: (D)

$ Y=4\,\sin \,\left( 4\pi t-\frac{\pi \,x}{16} \right) $ where, $ \omega =4\pi $ and $ k=\frac{2\pi }{\lambda }=\frac{\pi }{16} $ $ \Rightarrow $ $ v=\frac{\omega }{k}= $ 64 cm/s along + x direction.