Question

A wave has the equation $y=0.1\sin [100\pi t-kx]$ and wave velocity $100m/s$ , its wave number is equal to

Answer 1

The general equation of the wave in sinusoidal form is

$y=A\sin \left(kx-\omega t+\varphi \right)$

As per the given question we have $A=0.1m,\omega =100\pi \frac{rad}{sec}$

$f=\frac{\omega }{2\pi }$

Hence, by substituting the given values in above equation we get

$f=50Hz$

We have the value of wave velocity $100\frac{m}{sec}$ and we know that,

$v=f\lambda$

So by substituting the values we get,

$\lambda =\frac{v}{f}=\frac{100}{50}m$

$=2m$

So by using all the values found and substituting in the equation

$k=\frac{2\pi }{\lambda }$, we get

Wave number$\left(k\right)$is equal to$\pi m^{-1}$