Question

The equation of a transverse wave is $y=a\sin 2\pi [t-(x/5\left)\right]$, then the ratio of maximum particle velocity and wave velocity is :

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

Answer 1

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

$Y=a\sin (2\pi t-\frac{2\pi }{5}x)$
$K=\frac{2\pi }{5}$
$w=2\pi$ ; $K=\frac{w}{V}$
$\frac{2\pi }{V}=\frac{2\pi }{5}$
$V_{p_2}=a\times 2\pi Cor(2\pi \gamma -\frac{2\pi }{5}x)$
$V_p\times ma=2\pi a$

$\frac{V_{p}ma}{V}=\frac{2\pi a}{5}$