Two coherent waves are represented by `y_(1)=a_(1)cos_(omega)` t and `y_(2)=a_(2)sin_(omega)`t. The resultant intensity due to interference will be

Options

A. `(a_(1)+a_(2))`
B. `(a_(1)-a_(2))`
C. `(a_(1)^(2)+a_(2)^(2))`
D. `(a_(1)^(2)-a_(2)^(2))`

Answer

C

Explanation

As, `y_(1)=a_(1)cos omegat=a_(1)sin(omega t+90^(@))and y_(2)=a_(2)sin omegat`
`therefore` Phase difference`=phi=90^(@)`
`R=sqrt(a_(1)^(2)+a_(2)^(2)+2a_(1)a_(2)cos phi)=sqrt(a_(1)^(2)+a_(2)^(2))`
`therefore` Resultant intensity, `I prop R^(2) rArr I prop (a_(1)^(2)+a_(2)^(2))`