If resultant wave of two waves, each of amplitude A is also A then, phase difference between those two waves is

Options

A. `60^(@)`
B. `90^(@)`
C. `120^(@)`
D. `180^(@)`

Answer

C

Explanation

If amplitude of rresultant wave due to supeerpositon of two waves with amplitudes `A _(1) and A_(2)` with phase difference `del,` is A. then we have
`A .= sqrt (A _(1) ^(2) + A _(2) ^(2) + 2 A _(1) A _(2) cos delta)`
` therefore A^(.2) = A _(1) ^(2) + A _(2) ^(2) + 2 A_(1) A _(2) cos delta `
But here, ` A_(1) = A _(2) =A. =A` (suppose) and so: `A ^(2) = 2A ^(2) + 2 A ^(2)cos delta `
`therefore A ^(2) =2A ^(2) (1 + cos delta )`
`therefore 1/2 =1 + cos delta `
`therefore cos delta =-1/2`
`therefore delta = 120^(@) (becausecos 120 ^(@) =-(1)/(2))`