Question

A wave is represented by $y=0.1\sin (100\pi t-kx),$ where $y,t,x$ are in SI units. If wave velocity is $100\text{m/s},$ its wave number is

• A. $1{\text{m}}^{-1}$
• B. $2{\text{m}}^{-1}$
• C. $\pi {\text{m}}^{-1}$
• D. $2\pi {\text{m}}^{-1}$

Answer 1

The correct option is C $\pi {\text{m}}^{-1}$

Given $y=0.1\sin (100\pi t-kx)$
on comparing with general equation
$\omega =100\pi$

Given wave velocity is $v=100{\text{ms}}^{-1}$

Wave number is
$k=\frac{\omega }{v}=\pi {\text{m}}^{-1}$