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=asin(omegat+kx+(pi)/(3))`
B. `y_2=acos(omegat+kx+(pi)/(3))`
C. `y_2=acos(omegat+kx+(2pi)/(3))`
D. `y_2=acos(omegat+kx+(4pi)/(3))`

Answer

D

Explanation

At `x=0` the phase difference should be `pi`
Thus, the correct option is (d) .
Aleternate solution:
`y_2=acos(omegat+kx+phi+_0)`
`:. y=y_1+y_2=acos(omegat-kx+(pi)/(3))`
`+acos(omegat+kx+phi_0)`
`=2acos[omegat+((pi)/(3)+phi_0)/(2)]xxcos[kx+(phi_0-(pi)/(3))/(2)]`
`y=0` at `x+0` for any `timplieskx+(phi_0-(pi)/(3))/(2)=(pi)/(2)` at `x=0`
`:. phi_0=(4pi)/(3)`. Hence `y_2=acos(omegat+kx+(4pi)/(3))`