Three waves producing displacement in the same direction of same frequency and of amplitudes `10etam, 4etam" and "7eta` m arrive at a point with successive phase difference of `pi//2`. The amplitude of the resultant wave is :--

Options

A. 7 mm
B. 6 mm
C. 5 mm
D. 4 mm

Answer

C

Explanation

First wave and second wave have a phase difference of `pi`
`:.` The resultant amplitude is,
`R_(1) = sqrt(A_(1)^(2) + A_(2)^(2) + 2A_(1)A_(2) cos pi)`
`R_(1) = sqrt((A_(1) - A_(2))^(2))= sqrt((10 - 7)^(2)) = 3`
The resultant wave and second wave have a phase difference of `pi//2`
`:. R = sqrt(A_(2)^(2) + R_(1)^(2)) = sqrt(16 + 9) = sqrt25 = 5mm`