Question

The equation of the progressive wave is $y=asin2\pi (nt-\frac{x}{5})$. The ratio of maximum particle velocity to wave velocity is

• A. $\frac{\pi a}{5}$
• B. $\frac{2\pi a}{5}$
• C. $\frac{3\pi a}{5}$
• D. $\frac{4\pi a}{5}$

Answer 1

The correct option is B $\frac{2\pi a}{5}$

The equation for progressive wave, $y=asin2\pi (nt-\frac{x}{5})$

On comparing with, $y=Asin(wt-kx)$,

We get, $A=a$; $k=\frac{2\pi }{5}$; $w=2\pi n$

Maximum particle velocity, $v_m=wA$$⟹v_m=wa$

Wave velocity , $v_w=\frac{w}{k}=\frac{5w}{2\pi }$

$\therefore$ $\frac{v_m}{v_w}=\frac{wa}{\frac{5w}{2\pi }}$ $=\frac{2\pi a}{5}$