Equations of a stationery and a travelling waves are `y_(1)=a sin kx cos omegat and y_(2)=a sin (omegat-kx)` The phase differences between two between `x_(1)=(pi)/(3k)` and `x_(2)=(3pi)/(2k) are phi_(1) and phi_(2)` respectvely for the two waves. The ratio `(phi_(1))/(phi_(2))`is

Options

A. `1`
B. `5//6`
C. `3//4`
D. `6//7`

Answer

D

Explanation

At `x_(1) = (pi)/(3K)` and `x_(2) = (3pi)/(2K)`
Nodes are not formed bacause neither `x_(1)` nor `x_(2)` gives `sin kx = 0`
`:. Deltax = x_(2) - x_(1) = (7pi)/(6K)`
As this `Deltax` between `lambda` and `(lambda)/(2) :. phi = pi`
and `phi_(2) = KDeltax = (7pi)/(6) :. (phi_(1))/(phi_(2)) = (6)/(7)`