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
What each mark is really for — in plain English — and the wording trap that loses it.
- S1
Use the formula for intensity level: L I = 10 log 10 (I / I 0 ).
- S2
Substitute the given values: I = 1.0 × 10 -6 W/m 2 and I 0 = 1.0 × 10 -12 W/m 2 .
- S3
L I = 10 log 10 (1.0 × 10 -6 / 1.0 × 10 -12 ).
- S4
Simplify the expression inside the logarithm: L I = 10 log 10 (10 6 ).
- S5
Calculate the logarithm: log 10 (10 6 ) = 6.
- S6
Multiply by 10: L I = 10 × 6 = 60 dB.
Model answer
Worked through, with each step tagged to the mark it earns.
- S1
Use the formula for intensity level: L I = 10 log 10 (I / I 0 ).
- S2
Substitute the given values: I = 1.0 × 10 -6 W/m 2 and I 0 = 1.0 × 10 -12 W/m 2 .
- S3
L I = 10 log 10 (1.0 × 10 -6 / 1.0 × 10 -12 ).
- S4
Simplify the expression inside the logarithm: L I = 10 log 10 (10 6 ).
- S5
Calculate the logarithm: log 10 (10 6 ) = 6.
- S6
Multiply by 10: L I = 10 × 6 = 60 dB.
Final answer: 60 dB
Common mistakes
- Confusing intensity (I) with intensity level (L I ). — 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 ). — 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. — 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. — 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. — 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). — 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
- Full worked solution (all marking points)4 marks