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.