Explanation

(a) The standard equation of wave is given by
Y=a sin (kx-ωt) …….(i)
Where a is amplitude, k the wave constant and ω the angular velocity.
Given wave equation is
$y = 0.07\sin(12\pi x - 3000\pi t)$……(ii)
Comparing Eqs. (i) with (ii), we get
A=0.07, k=12π
$\therefore\ \ k = \frac{2\pi}{\lambda} = 12\pi\ \ \ $
$\Longrightarrow \ \ \ \lambda = \frac{1}{6}m$
Also, ω=3000π=2πv
∴ v=1500
Hence, velocity (v)=frequency(v)×wavelength ($\ \lambda$)
$v = 1500 \times \frac{1}{6} = 250\ ms^{- 1}$