Question

A wave motion is described by $y(x, t) = a \sin (kx - \omega t)$.
Then the ratio of the maximum particle velocity to the wave velocity is

• A. ka
• B. $\frac{\omega}{k}$
• C. $\frac{d \omega}{dk}$
• D. $\frac{x}{l}$

Answer 1

Answer: (A)

Maximum particle velocity $(v_p)_{max} = a \omega$ an wave velocity, $v = \frac{\omega}{k}$
$\therefore \, \, \, Ratio \frac{(v_p)_{max}}{v} = \frac{a \omega k}{\omega} = ka$