Two waves represented by `y=asin(omegat-kx)` and `y=acos(omegat-kx)` are superposed. The resultant wave will have an amplitude.

Options

A. a
B. `sqrt(2)a`
C. `2a`
D. zero

Answer

B

Explanation

Given that, two waves
`y=a sin (omega t-kx)` and `y=a cos (omega t-kx)`
Here, the phase difference between the two waves is `pi/2`.
So, the resultant amplitude, `A=sqrt(a_(1)^(2)+a_(2)^(2)+2a_(1)a_(2) cos phi)`
`["Here, "a_(1)=a, a_(2)=a and phi=pi/2]`
`:. A=sqrt(a^(2)+a^(2)+2a^(2)"cos"pi/2)`
or `A=sqrt(a^(2)+a^(2)+0)implies A=sqrt(2)a`