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Two waves of equal amplitude when superp...

Two waves of equal amplitude when superposed, give a resultant wave having an amplitude equal to that of either wave. The phase difference between the two waves is

A

`(pi)/(2)` radian

B

`(2pi)/(3)` radian

C

`(3pi)/(4)` radian

D

`(pi)/(6)` radian

Text Solution

Verified by Experts

The correct Answer is:
B
`A = a_(1) = a_(2)`
`:. A = sqrt(a_(1)^(2) + a_(2)^(2)+ 2a_(1) a_(2) cos theta)`
`A^(2) = A^(2) + A^(2) + 2A^(2) cos theta " " :. A^(2) = 2A^(2) [1 + cos]`
`:. (1)/(2) = 1 + cos theta :. cos theta = - (1)/(2) :. theta = 120^(@) or (2pi)/(3)`
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