A-Level · Physics · AQA · Mark scheme decoded
AQA A-Level Physics: Equal Loudness Curves and Sound Intensity Levels — mark scheme explained
The short answer
In the realm of medical physics, understanding how humans perceive sound is crucial. This involves the production and interpretation of equal loudness curves, the human perception of relative intensity levels, and the need for a logarithmic scale to reflect this.
The question
A sound has an intensity of 1.0 × 10 -6 W/m 2 . Calculate its intensity level in decibels.
[Paraphrased for study — not reproduced from any exam paper.]
Mark scheme, decoded
How the examiner actually awards the marks on this topic.
Gradora's own decode of the marking approach — not the exam board's published mark scheme.
How marks are awarded
For calculation questions, marks are typically awarded for correct substitution of values into the formula, correct use of logarithms, and the final answer. For explanation and interpretation questions, marks are given for clear reasoning, accurate definitions, and relevant context.
What the command words demand
- Calculate
- Perform a numerical calculation using the given formula and values.
- Explain
- Provide a clear and concise explanation, including reasoning and context.
- Interpret
- Analyze and explain the meaning of data or graphs, such as equal loudness curves.
- Compare
- Identify similarities and differences between two or more concepts or quantities.
Model answer
A full-mark response to the question above, worked through step by step.
Timing: Allocate about 5-7 minutes for each question on this topic to ensure you have enough time to carefully read the question, perform calculations, and provide detailed explanations.
- Use the formula for intensity level: L I = 10 log 10 (I / I 0 ).1 mark
- Substitute the given values: I = 1.0 × 10 -6 W/m 2 and I 0 = 1.0 × 10 -12 W/m 2 .1 mark
- L I = 10 log 10 (1.0 × 10 -6 / 1.0 × 10 -12 ).0 marks
- Simplify the expression inside the logarithm: L I = 10 log 10 (10 6 ).1 mark
- Calculate the logarithm: log 10 (10 6 ) = 6.0 marks
- Multiply by 10: L I = 10 × 6 = 60 dB.1 mark
Final answer: 60 dB
Work through every step correctly and you earn all 4 marks.
Another worked example
A sound has an intensity level of 80 dB. Calculate its intensity in W/m 2 .
- Use the formula for intensity level: L I = 10 log 10 (I / I 0 ).1 mark
- Substitute the given values: L I = 80 dB and I 0 = 1.0 × 10 -12 W/m 2 .1 mark
- Rearrange the formula to solve for I: 80 = 10 log 10 (I / 1.0 × 10 -12 ).0 marks
- Divide both sides by 10: 8 = log 10 (I / 1.0 × 10 -12 ).1 mark
- Convert the logarithmic equation to an exponential equation: I / 1.0 × 10 -12 = 10 8 .1 mark
- Multiply both sides by 1.0 × 10 -12 : I = 10 8 × 1.0 × 10 -12 = 1.0 × 10 -4 W/m 2 .1 mark
Final answer: 1.0 × 10 -4 W/m 2
Work through every step correctly and you earn all 5 marks.
Common mistakes
Confusing intensity (I) with intensity level (L I ).
Why it happens: Students often mix up the units and concepts of intensity and intensity level. Intensity is measured in W/m 2 , while intensity level is measured in dB.
Fix: Always check the units and use the correct formula for each quantity. Intensity (I) = P / A, and intensity level (L I ) = 10 log 10 (I / I 0 ).
Using the wrong reference intensity (I 0 ).
Why it happens: The threshold of hearing is a crucial value in the formula for intensity level. Using an incorrect reference intensity can lead to significant errors.
Fix: Always use I 0 = 1.0 × 10 -12 W/m 2 as the reference intensity when calculating intensity levels in dB.
Forgetting to apply A-weighting for low-frequency sounds.
Why it happens: The dBA scale is designed to account for the frequency response of the human ear. Forgetting this can lead to incorrect measurements and interpretations.
Fix: When working with the dBA scale, remember it applies a frequency-dependent correction read from the standardised A-weighting curve — attenuating low and very high frequencies while slightly boosting frequencies near 2-4 kHz. Never assume a single fixed correction value applied to the intensity level.
Misinterpreting equal loudness curves.
Why it happens: Equal loudness curves show how different frequencies need to be adjusted to be perceived as equally loud. Misinterpreting these curves can lead to incorrect conclusions about human perception of sound.
Fix: Study the shape and characteristics of equal loudness curves carefully. Understand that humans are more sensitive to mid-range frequencies than to very low or high frequencies.
Using a linear scale instead of a logarithmic scale for intensity levels.
Why it happens: The human ear perceives sound intensity logarithmically, not linearly. Using a linear scale can lead to significant errors in calculations and interpretations.
Fix: Always use the logarithmic formula L I = 10 log 10 (I / I 0 ) when calculating intensity levels in dB.
Confusing decibels (dB) with A-weighted decibels (dBA).
Why it happens: The dBA scale is specifically designed to account for the frequency response of the human ear, while the dB scale does not. Confusing these can lead to incorrect measurements and interpretations.
Fix: Understand the difference between dB and dBA scales. Use the dBA scale when dealing with environmental noise measurements or any situation where the frequency response of the human ear is relevant.
Where the marks go
The question types you’ll meet on this topic and the marks each one carries — so you know what to expect and where to focus.
| Question type | What you’re asked to do | Marks |
|---|---|---|
| Calculate Intensity Level | Find the sound intensity level in decibels using the logarithmic intensity formula. | 4 |
| Calculate Intensity | Rearrange the decibel formula to find sound intensity from a given intensity level. | 5 |
| Calculate Intensity Level | Use the decibel formula with logarithms to convert a sound intensity into an intensity level. | 5 |
| Calculate Sound Intensity | Rearrange the decibel formula and use logarithms to find intensity from an intensity level. | 6 |
| Total across these question types | 20 | |
Question types and mark tariffs are Gradora’s guidance based on how this topic is typically examined — not the board’s official paper structure.