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Two plane monochromatic waves propagati...

Two plane monochromatic waves propagating in the same direction with amplitudes `A and 2 A` and differing un phase by `pi//3` superimpose. Calculate the amplitude of the resulting wave.

Text Solution

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Given, amplitude of first wave= `A_1 = A`
Amplitude of secod wave = `A_2 = 2A_1 = 2A`
Phase difference , `phi = pi/3`
Amplitude of resultant wave is given by
`A_R = sqrt(A_1^2 + A_2^2 + 2A_1A_2 cos phi)`
`= sqrt(A^2 + (2A)^2 + 2A xx 2A (cos) pi/3)`
`sqrt(5A^2 + 4A^2 xx 1/2) = sqrt(7A^2) = sqrt(7)A`.
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