Question

A wave equation which gives the displacement along the `Y` direction is given by the equation `y=10^4sin(60t+2x)`, where x and y are in metres and t is time in seconds. This represents a wave
A. travelling with a velocity of `30 m//s` in the negative `X` direction
B. of wavelength `2pi` metre
C. of frequency `60//pi Hz`
D. Of amplitude `10^4` metre travelling along the positive X direction

Answer 1

Correct Answer - A
On comparing the given equation with `y=asin(omegat+kx)`, it is clear that wave is travelling in negative x-direction its amplitude `a=10^4` m and `omega=60,k=2`. Hence frequency `n=(omega)/(2pi)=(60)/(2pi)=(30)/(pi)Hz`
`k=(2pi)/(lamda)=2implieslamda=pim` and `v=(omega)/(k)=(60)/(2)=30m//s`.