12.2 Interference

Question 1

What does coherence mean?

Answer 1

Waves emitted from two sources having a constant phase difference.

In order for the two waves to be coherent, they must have the same frequency.

Question 2

What are the conditions for constructive interference?

Answer 2

• 0 degrees phase difference between the two waves which interact.
• Path difference is a multiple of the wavelength.

Question 3

What are the conditions for destructive interference?

Answer 3

• 180 degrees phase difference (the waves must be in antiphase)
• Path difference (n + 1/2)λ

Question 4

What do the following terms mean?
- Path difference
- Phase difference
- Maxima
- Minima

Answer 4

Path difference - the difference in distance travelled by two waves from their respective sources to a point.

Phase difference - the difference in phase between two waves, usually measured in radians or degrees.

Maxima - points of constructive interference where the wave amplitudes reinforce.

Minima - points of destructive interference where the waves cancel each other out.

Question 5

What does it first-order mean?

Answer 5

First-order maxima = n = 1
First-order minima = n = 0

Question 6

For destructive interference…

Answer 6

This happens when two waves cancel each other out which only works if they arrive out of phase by π, 3π, 5π.

In terms of path difference that is, 0.5λ, 1.5λ, 2.5λ.

Path difference = (n + 0.5)λ

Hence, first-order minima will be n = 0, which is 0.5λ

Second-order minima will be n = 1, which is 1.5λ

Question 7

For constructive interference…

Answer 7

This happens when two waves produce a resultant displacement which is greater than both individual displacements.

But this only works if they arrive out of phase by 2π, 4π, 6π

In terms of path difference that is, λ, 2λ, 3λ

Path difference = nλ

Hence at central max, n = 0, path difference = 0

First-order maxima, n = 1, path difference = 1λ