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

Wave is represented as $y=0.1\sin (100\pi t-kx)$
On comparing with general equation

$\omega =100\pi$

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

We know,

Wave number

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

Putting the values in the equation and after solving we get wave number is $\pi m^{-1}$