Question

Three waves from three coherent sources meet at some point. Resultant amplitude of each is A_0. Intensity corresponding to A_0 is I_0. Phase difference between first wave and second wave is 60^@. Path difference between first wave and third wave is lambda/3. The first wave lags behind in phase angle from second and third wave. Find resultant intensity at this point.

Answer 1

Hence the resultant intensity is I = 4Io

Explanation:

By using the relation I∝ A^2, we can also find the resulting intensity.

Further, a path difference of λ3 is equivalent to phase difference of 120∘

Now, resultant of first and third acting at 120∘ is also A0 (as A = 2A0 (cos) ϕ2 and ϕ = 120∘)

since the first and third are equal, so this resultant A0 passes through the bisector line of these two or in the direction of second amplitude vector. Therefore, the resultant amplitude is

A=A0 + A0 = 2A0

and the resultant intensity is

I = 4I0 (as I ∝ A^2)

Hence the resultant intensity is I = 4Io