If two waves represented by `y_(1)=4 sin omega t` and `y_(2)=3sin (omega t+(pi)/(3))`interfere at a point, the amplitude of the resulting wave will be about

Options

A. 7
B. 6
C. 5
D. `3.5`

Answer

B

Explanation

`A = sqrt(a_(1)^(2) + a_(2)^(2) + 2a_(1) a_(2) cos phi)`
`A = sqrt(16 + 9 + 2 xx 4 xx 3 xx cos pi//3)`
`therefore A = sqrt(25 + 24 xx (1)/(2))`
`= sqrt(25 + 12) = sqrt(37) = 6.082`
`A ~~ 6`