Two longitudinal waves propagating in the X and Y directions superimpose. The wave equations are as below `Phi_(1)=A(omegat-kx)` and `Phi_(2)=Acos(omegat-ky)`. Trajectory of the motion of a particle lying on the line `y=x((2n+1)lamda)/(2)` will be

Options

A. straight line
B. circle
C. ellipse
D. none of these

Answer

A

Explanation

`Phi_(1)=Acos(omegat-kx)` …(i)
`Phi_(2)=Acos(omegat-ky)` …(ii)
Put `y=x+((2n+1))/(2)lamda` in (ii)
`Phi_(2)=Acos[omegat-k(x+(2n+1)(lamda)/(2))]`
`thereforePhi=Acos(omegat-kx-(2n+1)pi)`
`Phi_(2)=-Acos(omegat-kx)=-Phi_(1)`
`therefore` Shape of path is straight line.