Question

What is the relation between particle velocity (v), the wave velocity (c) and the slope (s) of the wave?

• A. $ v=-cs $
• B. $ c=-vs $
• C. $ {{v}^{2}}={{c}^{2}}s $
• D. $ {{c}^{2}}={{v}^{2}}s $

Answer 1

Answer: (A)

Let the wave equation
$ y=A\sin (\omega t-kx) $
then $ v=\frac{dy}{dt}A\omega \cos (\omega t-kx) $
and $ s=\frac{dy}{dx}Ak\cos (\omega t-kx) $
$ =\frac{-kv}{\omega }=-\frac{v}{c} $
$ v=-cs $