Interference happens when two waves overlap. Where they add, you get a bright fringe or a loud sound; where they cancel, you get a dark fringe or a quiet spot.
This lesson is part of SPM Physics waves. It builds on explaining reflection, refraction and diffraction.
How do I decide whether a point is bright or dark?
Compare the distances from the two sources to the point. The difference is the path difference.
| Path difference | Type of interference | Result |
|---|---|---|
| 0, λ, 2λ, 3λ | Constructive | Bright fringe or loud sound |
| ½λ, 1½λ, 2½λ | Destructive | Dark fringe or quiet sound |
Worked example: two loudspeakers
An original setup has two speakers playing one note, wavelength 1.0 m. A listener stands where one speaker is 6.0 m away and the other is 7.5 m away.
The path difference is 7.5 − 6.0 = 1.5 m, which is 1½λ. That is an odd number of half wavelengths, so the interference is destructive and the sound is quiet.
Moving so that the distances become 6.0 m and 8.0 m gives a path difference of 2.0 m = 2λ, which is constructive and loud.
How do I use λ = ax/D for a double slit?
Light passes through two narrow slits, separated by a, and lands on a screen at distance D. Bright fringes are evenly spaced, and x is the distance from one bright fringe to the next.
An original experiment has a = 0.50 mm and D = 2.0 m. The span from the centre of the first bright fringe to the centre of the sixth bright fringe is 12.0 mm.
Five gaps lie between six fringes, so x = 12.0 ÷ 5 = 2.4 mm. Then λ = ax ÷ D = (0.50 × 10⁻³ × 2.4 × 10⁻³) ÷ 2.0 = 6.0 × 10⁻⁷ m, which is 600 nm.
The mistake that costs marks
The slip is to use the whole span as x. Dividing by the number of fringes, not the number of gaps, is a second version of the same error.
| Step | Wrong | Right |
|---|---|---|
| x from 6 fringes spanning 12.0 mm | 12.0 mm | 12.0 ÷ 5 = 2.4 mm |
| λ | 2.4 × 10⁻⁶ m (five times too large) | 6.0 × 10⁻⁷ m |
The number of gaps is always one less than the number of fringes counted. Write that subtraction in your working.
What changes if I change the setup?
Since x = λD ÷ a, three changes are useful to predict.
- Longer wavelength (red instead of blue light): fringes spread further apart.
- Larger D (screen further away): fringes spread further apart.
- Larger a (slits further apart): fringes move closer together.
Check yourself
Light of wavelength 5.0 × 10⁻⁷ m passes through slits 0.40 mm apart onto a screen 1.6 m away. Find the fringe separation x.
Answer
x = λD ÷ a = (5.0 × 10⁻⁷ × 1.6) ÷ (0.40 × 10⁻³) = 8.0 × 10⁻⁷ ÷ 4.0 × 10⁻⁴ = 2.0 × 10⁻³ m, which is 2.0 mm.
What to study next
Interference is one property shared by sound and light. Continue with comparing sound and electromagnetic waves, then test yourself in the waves practice set.
If you want a teacher to check your fringe-counting method, see online one-to-one Physics tuition.