Four harmonic waves of equal freuencies and equal intensity `I_(0)` have phase angles `0, (pi)/(3), (2pi)/(3)` and `pi`. When they are superposed, the intensity of the resulting wave is `nI_(0)`. The value of `n` is

Options

A. 1
B. 2
C. 3
D. 4

Answer

C

Explanation

Since all the waves are of equal intenties , so their amplitudes are equal i.e., `I_(0)=A_(0)^(2)`
Phasor diagram of given waves is shown in figure . This diagram is identical to fig.
Resultant intensity is
`I=I_(1)+I_(2)+2sqrt(I_(1)I_(2)) cos theta`
`=I_(0)+I_(0)+2sqrt(I_(0)I_(0))cospi//3`
`=3I_(0)=nI_(0) (`Given `), `So `n=3`