The wave described by `y=0.25sin(10pix-2pit)`. Where x and y are in metre and t is second, is a wave travelling along the

Options

A. `-ve` x direction with frequency `1 Hz`
B. `+ve` x direction with frequenc `pi Hz` and wavelength `lamda=0.2m`
C. `+ve` x direction with frequency `1 Hz` and wavelength `lamda=0.2m`
D. `-ve` x direction with amplitude `0.25 m` and wavelength `lamda=0.2m`

Answer

C

Explanation

The given wave equation.
`y=0.25sin(10pix-2pit)`
The minus (`-`) between `(10pit)` and `(2pit)` implies that the wave is travelling along positive x direction. Now comparing Eq. (i) with standard wave equation `y=asin(kx-omegat)` ..(ii)
We have
`a=0.25m,omega=2pi,k=10pim`
:. `(2pi)/(T)=2piimpliesf=1Hz`
also, `lamda=(2pi)/(k)=(2pi)/(10pi)=0.2m`
Therefore the wave is travelling along `+ve` x-direction with frequency 1 Hz and wavelength 0.2m.