Explanation

(a) $y = 10^{- 5}\sin\left\lbrack 100t - \frac{x}{10} \right\rbrack$ comparing it with the equation of wave motion $y = r\sin\left\lbrack \frac{2\pi}{T}t - \frac{2\pi}{\lambda}x \right\rbrack$
$\frac{2\pi}{T} = 100,T = \frac{2\pi}{100} = \frac{\pi}{50}s$
$\frac{2\pi}{\lambda} = \frac{1}{10},\lambda = 20\pi$
velocity, $v = \frac{\lambda}{T} = \frac{20\pi}{\pi/50} = 100\ ms^{- 1}$