Physics 9702 · Paper 2

Coherence

Point two ordinary lamps at a wall. You get no bright-and-dark pattern at all, just an even glow.
The reason: each lamp keeps jumping to a new phase at random, so the two never stay in step. For a steady pattern the two sources must hold a constant phase difference and never drift. That is what being means.

Coherent sources

Here is the exam definition, word for word: two sources are coherent if they have a constant phase difference (and so the same frequency).
A constant phase difference needs the same frequency. Say the two sources have different frequencies. Then one wave keeps getting ahead of the other. So their phase difference keeps changing.
Once the phase difference keeps changing, each point keeps switching between loud and quiet. The bright and dark bands never stay in one place. So the wall just looks the same everywhere.
A laser is coherent, so it gives a clear pattern. Two separate lamps are not. Their light comes in short random bursts, so no steady pattern forms.

Coherent means the phase gap never changes (top). Different frequencies make the gap grow, so the waves slide out of step — not coherent (bottom).

Coherent means a constant phase difference, and so the same frequency. No constant phase difference means no steady pattern.

Your turn— tap to reveal the worked answer (9702/12/F/M/24 Q30)

What is the meaning of coherence for two wave sources?

Answer: the two sources have a constant phase difference. That is the definition of coherence. (9702/12/F/M/24 Q30)

Coherent sources do not need equal amplitude (equal-size waves). Equal amplitude only makes the dark bands go fully black. With unequal amplitude the dark bands are just dim, not fully black. The pattern is still there.
The one rule that matters is a constant phase difference. Equal amplitude is not needed.

Your turn— tap to reveal the worked answer (9702/11/O/N/24 Q27)

For two sources to be coherent, must they have the same frequency, the same amplitude, or both?

Answer: they must have the same frequency and a constant phase difference. They do not need the same amplitude. (9702/11/O/N/24 Q27)