Question

The intensity of the two coherent waves is I_o. If the two waves undergo constructive interference then the resultant intensity will be:
1. I_o
2. 2Io
3. 4Io
4. None of these

Answer 1

Correct Answer - Option 3 : 4Io

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:

• 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. Hence, option 3 is correct.