Question

The equation of a wave motion is given by, $y=7\sin (7\pi t-0.4\pi x+\frac{\pi }{3})$. The ratio of wave velocity to the maximum particle velocity equal is
(Assume SI units)

• A. $44:7$
• B. $22:7$
• C. $22:5$
• D. $5:44$

Answer 1

The correct option is D $5:44$

Given $y=7\sin (7\pi t-0.4\pi x+\frac{\pi }{3})$
on comparing with $y=7\sin (\omega t-kx+\varphi )$
$A=7\text{m};k=0.4\pi$

Ratio of wave velocity to maximum particle velocity is $\frac{V_{\text{wave}}}{V_{\text{max par}}}=\frac{V}{A\omega }=\frac{1}{Ak};[\because V=\frac{\omega }{k}]$

$\frac{V_{\text{wave}}}{V_{\text{max par}}}=\frac{1}{7\times 0.4\times \pi }=\frac{7}{7\times 0.4\times 22}$
$\frac{V_{\text{wave}}}{V_{\text{max par}}}=\frac{10}{88}$
$\frac{V_{\text{wave}}}{V_{\text{max par}}}=5:44$