Question

The equation of a wave is represented by $ y={{10}^{-4}}\sin \left( 100t-\frac{x}{10} \right)m, $ the velocity of the wave will be

• A. $ 0.1\text{ }m{{s}^{-1}} $
• B. $ 10\text{ }m{{s}^{-1}} $
• C. $ 100\text{ }m{{s}^{-1}} $
• D. $ 1000\text{ }m{{s}^{-1}} $

Answer 1

Answer: (D)

The given equation comparing with standard equation
$ y=A\sin \frac{2\pi }{\lambda }(vt-x) $
$ \therefore $ $ \frac{2\pi }{\lambda }v=100 $
and $ \frac{2\pi }{\lambda }=\frac{1}{10} $
$ \Rightarrow $ $ v=1000\text{ }m{{s}^{-1}} $