Question

A wave representing by the equation `y = a cos(kx - omegat)` is suerposed with another wave to form a stationary wave such that point `x = 0` is a node. The equation for the other wave is
A. `y=asin(kx+omegat)`
B. `y=-acos(kx+omegat)`
C. `y=-acos(kx-omegat)`
D. `y=-asin(kx-omegat)`

Answer 1

Correct Answer - B
Since the point `x=0` is a node and reflection is taking place from point `x=0`. This means that reflection must be taking place from the fixed end and hence the reflected ray must suffer an additional phase change of `pi` or a path change of `(lamda)/(2)`
So, if `y_("incident")=acos(kx-omegat)`
`rArr y_("refl ected")=acos(-kx-omegat+pi)=-acos(omegat+kx)`