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. $ 1{{m}^{-1}} $
• B. $ 2{{m}^{-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}} $