A wave `y = a sin (omegat - kx)` on a string meets with another wave producing a node at `x = 0`. Then the equation of the unknown wave is

Options

A. `+acos(kx-omegat)`
B. `-acos(kx+omegat)`
C. `-acos(kx-omegat)`
D. `+acos(omegat-kx)`

Answer

C

Explanation

`y_(1)=acos(kx+omegat)` . . i.e., wave travelling towards -ve x-axis to form a standing wave, 2nd wave must be travelling towards +ve x-axis.
To form node, `y_(1)+y_(2)=0` for all instants at x=0
`y_(1)+y_(2)=acos(wt)+y_(2)=0`
`implies y_(2)=-acos(wt)implies y_(2)` can only be `-acos(kx-wt)`