Two coherent waves are y₁ = a cos(ωt) and y2 = 2a cos(ωt). If the two waves undergo constructive interference, then the resultant amplitude will be:

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 = 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.