Answer:
Option C
Explanation:
Given wave equation , y= a sin 2 $\pi$ (bt-cx)
Compairing the above equation with the general equation of the progressive wave which is given as
$y=A_{0} \sin 2 \pi (ft-\frac{x}{\lambda})$
We get, frequency , f=b, wavelength, $\lambda=\frac{1}{c}$ and amplitude of the wave , A0=a
As, we know , that the maximum velocity of the particle,
$V_{max}=A_{0}\omega= a\times 2\pi b$ ......(i)
Wave velocity, $V_{wave}=f\lambda$
$\Rightarrow$ $ V_{wave}=\frac{b}{c}$ .......(ii)
it is given that,
$ V_{max}=2V_{wave}$
So, by substituting the values from
Eqs. (i) and (ii) in the above realation , we get
$a2\pi b=2\frac{b}{c}$
$\therefore$ $c=\frac{1}{a\pi}$