Correct Answer - Option 3 : 3a
CONCEPT:
Coherent addition of waves:
- The phenomenon in which two or more waves superpose to form a resultant wave of greater, lower, or the same amplitude is called interference.
- The interference is based on the superposition principle according to which at a particular point in the medium, the resultant displacement produced by a number of waves is the vector sum of the displacements produced by each of the waves.
- Let two sources of wave S1 and S2 are coherent.
- Let the intensity of the waves are Io.
For constructive interference:
- If at any point the waves emerging from the source S1 and S2 are in phase then we will have constructive interference and the resultant intensity will be 4Io.
⇒ Path difference = nλ and n = 0,1,2,3,...
For destructive interference:
- If at any point the waves emerging from the source S1 and S2 are in opposite phase then we will have destructive interference and the resultant intensity will be zero.
⇒ Path difference = \(\left ( n+\frac{1}{2} \right )\)λ and n = 0,1,2,3,...
Where λ = wavelength
EXPLANATION:
Given y1 = a.cos(ωt) and y2 = 2a.cos(ωt)
- If the two waves undergo constructive interference, then the resultant displacement is given as,
⇒ y = y1 + y2
⇒ y = a cos(ωt) + 2a cos(ωt)
⇒ y = 3a.cos(ωt) -----(1)
By equation 1, the amplitude 'A' of the resultant wave is given as,
⇒ A = 3a
- Hence, option 3 is correct.
