AQA A-Level Physics Paper 1, November 2020: Question 3

✅ Correct Answer

• Sources must have the same frequency and a constant phase difference.
• This is achieved by connecting both loudspeakers to the same signal generator.

💡 Key Knowledge

Coherence is a fundamental prerequisite for observing stable interference patterns with any type of wave (sound, light, or microwaves).

✅ Correct Answer

• At point A, the sound waves from both speakers superpose and are in phase (zero phase difference), producing a maximum (constructive interference).
• As the student moves away from A, a path difference is introduced, causing waves to go out of phase, so amplitude decreases (destructive interference).
• Moving further towards B, the waves move back into phase, increasing the amplitude again.

❌ Common Errors

Do not use the word "interfere" when describing superposition—examiners strictly penalize this loose phrasing. Avoid relying on diagrams in your written explanation.

📐 Step-by-Step Calculation

1. Identify geometry: Distance OA = 2.25 m, loudspeaker separation = 0.30 m (so half-separation = 0.15 m). Distance AB = 0.95 m.
2. Calculate distance PB:
   PB = √((2.25)² + (0.95 - 0.15)²) = √(5.0625 + 0.64) = √(5.7025) = 2.39 m.
3. Calculate distance QB:
   QB = √((2.25)² + (0.95 + 0.15)²) = √(5.0625 + 1.21) = √(6.2725) = 2.50 m.
4. Find path difference:
   QB - PB = 2.50 m - 2.39 m = 0.11 m (accept 0.11 m to 0.12 m).

🧠 Exam Technique

Always show explicit evidence of using Pythagoras' theorem. State your intermediate values (PB and QB) clearly so the examiner can award partial credit even if a minor arithmetic slip occurs.

📐 Calculation & Answer

Since point B is the first point of minimum/maximum past A (or based on path difference equalling roughly one wavelength depending on setup context), use c = f λ :

speed = 2960 Hz × 0.12 m = 355.2 m s&sup{-1}

Using the strict mark scheme path difference values (~0.12 m or 0.11 m) with f = 2960 Hz gives around 330 m s&sup{-1} to 360 m s&sup{-1}.

💡 Key Knowledge

Ensure consistent unit handling. Working must explicitly link frequency and wavelength to wave speed.

✅ Correct Answer

• Decreasing the frequency causes the wavelength to gradually increase ( λ = c / f ).
• As wavelength increases, the path difference at point C gets closer to one wavelength (or maxima spacing increases).
• Consequently, the sound amplitude at point C will get larger/louder as the waves move closer to being in phase.

🧠 Top-Level Responses

To secure full marks, top responses explicitly connect f to λ first, then explain how changing λ shifts the interference fringe pattern relative to the fixed position of point C.