Question

The equation of a progressive wave is $Y=a\sin (\omega t-kx)$, then the velocity of the wave is

• A. $k\omega$
• B. $k/\omega$
• C. $\omega /k$
• D. $a\omega$

Answer 1

The correct option is C $\omega /k$

given equation of wave is $y=a\sin (\omega t-kx)$
$\frac{dy}{dt}=a\omega \cos (\omega t-kx)$
$\frac{dy}{dx}=-ak\cos (\omega t-kx)$
velocity of wave $v=\frac{dx}{dt}=\frac{\left(\frac{dy}{dt}\right)}{\left(\frac{dy}{dx}\right)}=\frac{a\omega }{ak}=\frac{\omega }{k}$