A wave is travelling along X-axit. The disturbance at x=0 and t=0 is `A//2` and is increasing. Where A is amplitute of the wave. If `y=A sin(kx-omegat+emptyset)`, deetemine the initial phase `empyset`.

Explanation

At `x=0` and `t=0`, the disturbance is `A//2`. Hence
`A/2=Asin phi rArr sin phi=(1)/(2)`
which gives `pi/(6),(5pi)/(6)`
one of these two values is to be accepted. The basis for this is that `phi` should also satisfy the value of `(dely)/(delt)` given in question.
The rate of increment of `y` is given by
`(deltay)/(deltat)=omegaA cos (kx-omegat+phi)`
At `x=0` and `t=0`,
`(deltay)/(deltat)=omegaA cos phi`
if `y` increase, `(deltay)/(deltat)` is positive. since `(deltay)/(deltat)` is positive, `phi=(5pi)/(6)` will be suitable initial phase:
`(deltay)/(deltat)=-omegaA co s (5pi)/(6)`
`(deltay)/(deltat)=omegaA(-sqrt((3)/(2)))`
`(deltay)/(deltat)=sqrt(3)/(2) omegaA gt 0`
Thus, the initial phase is `phi=5pi//6`.