A standing wave pattern is formed on a string One of the waves if given by equation `y_1=acos(omegat-kx+(pi)/(3))` then the equation of the other wave such that at `x=0` a node is formed.

Options

A. `y_(2)=a sin (omegat+kx+(pi)/3)`
B. `y_(2)=a cos(omegat+kx+(pi)/3)`
C. `y_(2)=a cos(omegat+kx+(2pi)/3)`
D. `y_(2)=a cos (omegat+kx+(4pi)/3)`

Answer

D

Explanation

At x=0 the phase difference should be `pi`
`:.` the correct option is D
Alternate solution
`y_(2)=a cos(omegat+kx+phi_(0))`
`:. Y=y_(1)+y_(2)=a cos (omegat-kx+(pi)/3)+a cos(omega t +kx+phi_(0))`
`=2acos[omegat +((pi)/3+phi_(0))/2]xx cos [kx+(phi_(0)-(pi)/3)/2]`
`:' y=0` at x=0 for any `trArr kx+(phi_(0)-(pi)/3)/2=(pi)/2` at x=0
`:. phi_(0)=(4pi)/3` hence `y_(2)=a cos(omegat+kx+(4pi)/3)`