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)

$v=-cs$

Answer 2

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