Question

If $\vec{u}$ is instantaneous velocity of particle and $\vec{v}$ is velocity of wave, then

• A. $\vec{u}$ is perpendicular to $\vec{v}$
• B. $\vec{u}$ is parallel to $\vec{v}$
• C. $|\vec{u}|$ is equal to $|\vec{v}|$
• D. $|\vec{u}|=$ (slope of wave form) $|\vec{v}|$.

Answer 1

Answer: (D)

$\vec{u}$ may be perpendicular or parallel to $\bar{v}$ depending on whether it is a transverse or longitudinal wave.
$y=A \sin k x-\omega t $
$\frac{d y}{d t}=A \omega \cos k x-\omega t$
$\frac{d y}{d t}=v $
$u=-A \omega \cos k x-\omega t $
$|v|=\frac{\omega}{k}$
Slope of $y=A \sin k x-\omega t$
$\frac{d y}{d x}=A k \cos k x-\omega t$
$\left|\frac{d y}{d x}\right|=|v|\left|\frac{d y}{d x}\right|$
$u=|v|$ (Slope of waveform)