AQA A-Level Physics Paper 3 (3BB), June 2025: Question 3

✅ Mark Scheme Requirements

• Mark 1: The minimum intensity (or minimum power per unit area / power per m²) that a normal ear can detect / hear. [1]
• Mark 2: At a frequency of 1 kHz (or 1000 Hz). [1]

💡 Key Knowledge

The standard reference threshold intensity is taken as:

I ₀ = 1.0 × 10⁻¹² W m⁻² at 1 kHz

By international convention, 1 kHz is chosen as the standard reference tone because it sits in the middle of human conversational sensitivity and represents 0 dB on the threshold curve.

🧠 Exam Technique

Whenever defining a threshold or base measurement in medical physics, ask yourself: "Under what standard condition is this tested?" Two-mark definitions almost always reserve the second mark for specifying the standard test condition: at 1 kHz.

❌ Common Errors

• Writing "minimum sound intensity level" instead of "intensity" (Intensity level is measured in dB, whereas threshold is fundamentally an intensity in W m⁻²).
• Simply stating the numerical value 1.0 × 10⁻¹² W m⁻² without giving the word definition requested by the prompt.
• Forgetting to state at 1 kHz entirely, losing 50% of the marks.

❌ Common Calculation Traps

• Unit conversion error: Converting 60 mm² by dividing by 1000 instead of 1000² (i.e. multiplying by 10⁻³ instead of 10⁻⁶). Remember: 1 mm² = 10⁻⁶ m².
• Logarithm inversion error: Using eⁿ instead of 10ⁿ , or forgetting to divide the decibel value by 10 before taking the antilog.
• Conflating dB with intensity: Multiplying 78 directly by the area. Decibels are logarithmic units, not power per unit area!

🧠 Exam Technique

Show every rearrangement step clearly! The mark scheme allows a maximum of 2 marks from intermediate steps if an arithmetic error occurs:

• Mark 1: Reading 78 ± 1 dB from Figure 4
• Mark 2: Correctly substituting into and rearranging the intensity level formula
• Mark 3: Evaluating P = I × A giving 3.8 × 10⁻⁹ W

✅ Mark Scheme Criteria

• Mark 1: For frequencies f < 1 kHz, curve must:
  • Pass through exactly (1000 Hz, 100 dB).
  • Have a decreasing gradient (flattening out as frequency increases).
  • Meet the top boundary of the grid without crossing/touching the existing 40-phon curve (it is much flatter than the given curve).
• Mark 2: For frequencies f > 1 kHz, curve must:
  • Show a single dip below 100 dB located around 3 kHz (acceptable between 2 kHz and 4 kHz).
  • Rise after the dip such that the line reaches the right-hand edge at an intensity level > 100 dB.

💡 What Your Sketch Must Look Like

Equal loudness curves represent lines of constant perceived loudness (measured in phons). As loudness increases to high levels (e.g. 100 phon):

• The ear's frequency response becomes flatter (less curved at low frequencies).
• The auditory canal resonance dip (around 3 kHz to 3.5 kHz) remains present because it is a physical acoustic property of the outer ear canal.
• Curves of different phon values never cross each other.

🧠 How to Draw the Line Accurately

1. First, put a distinct dot at (1000 Hz, 100 dB).
2. To the left ( f < 1000 Hz), draw a smooth line rising towards the top-left, curving upwards more gently than the original curve (reaching ~115–120 dB at 20–30 Hz).
3. To the right ( f > 1000 Hz), dip slightly below 100 dB (down to around 95–98 dB) with the minimum turning point centred at 3 kHz.
4. Curve back upwards sharply towards the right-hand edge (10 kHz), terminating above 105 dB.

❌ Common Sketching Errors

• Drawing a parallel curve: Simply copying the shape of the lower curve shifted upwards. At higher intensities, curves are significantly flatter at low frequencies.
• Missing the reference point: The curve must pass precisely through 100 dB at 1 kHz.
• Placing the dip incorrectly: Placing the resonance dip at 1 kHz or 5 kHz rather than between 2 kHz and 4 kHz.
• Crossing curves: Letting the sketched line touch or intersect the existing lower curve.