Question

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

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

Answer 1

Answer: (C)

The standard equation of wave is $y=a\sin (\omega t-kx)$ .. (i)
where $a$ is amplitude, $\omega$ the angular velocity and $x$ the displacement at instant $t$ .
Given equation is $y=0.1\sin (100\pi t-kx)$ .. (ii)
Comparing Eq. (i) with Eq. (ii), we get
$\omega =100\pi$
$\therefore$ Wave number
$=\frac{\omega }{v}=\frac{100\pi }{100}=\pi m^{-1}$