Equal loudness curves plot sound level in dB against frequency, linking sounds a listener judges to be equally loud. Free notes and 15 questions answered.
Updated 12 Sept 2026 · Revise Right Team
Equal Loudness Curves & Intensity Perception is part of Physics of the ear (A-level only) in A Level AQA Physics.
8 min
Reading time
34
Lessons in this topic
A Level AQA
Pathway
Reviewed by Revise Right
Content review
What this lesson covers
Equal loudness curves plot sound level in dB against frequency, linking sounds a listener judges to be equally loud. Free notes and 15 questions answered.
Describe the shape and key features of equal loudness curves and explain what they represent
Explain why the human ear does not perceive all frequencies at the same intensity level equally
Justify the need for a logarithmic scale when measuring perceived loudness
Calculate intensity levels in decibels using the logarithmic formula and interpret the results
Key ideas to keep in view
Use this lesson to stay inside Physics of the ear (A-level only) while connecting the detail back to the wider Medical physics (A-level only) topic.
Medical physics (A-level only)
Physics of the ear (A-level only)
A Level AQA Physics
Revision notes
Read the core explanations from Equal Loudness Curves & Intensity Perception before testing yourself from memory.
1. Why Your Ears Lie to You
Play a 100 Hz bass note and a 3000 Hz whistle at exactly the same physical intensity. They will not sound equally loud. Your ears are not flat amplifiers — they are frequency-selective, and the physics behind that selectivity is what this lesson is about.
This matters enormously in medical physics. Audiologists use the patterns of human loudness perception to diagnose hearing loss, calibrate hearing aids, and interpret audiograms. To do any of that, you need two things: equal loudness curves and a logarithmic intensity scale.
2. Intensity and the Logarithmic Scale
Sound carries energy. The intensity $I$ of a sound wave is the power transmitted per unit area, measured in watts per square metre (W m$^{-2}$). The human ear can detect sounds ranging from about $1 \times 10^{-12}$ W m$^{-2}$ (the threshold of hearing) up to around $1$ W m$^{-2}$ (corresponding to approximately 120 dB), approaching the threshold of pain. That is a factor of one trillion — twelve orders of magnitude.
A linear scale is useless here. If you plotted intensity on a ruler from 0 to 1 W m$^{-2}$, the entire range of quiet conversation would be crammed into the first invisible sliver near zero. The ear itself compresses this enormous range into a manageable perception of loudness, and the decibel scale mirrors that compression mathematically.
Notice what the logarithm does: every time the intensity increases by a factor of 10, the intensity level increases by exactly 10 dB. A factor of 100 gives 20 dB; a factor of 1000 gives 30 dB. The enormous physical range of $10^{12}$ maps neatly onto a 0–120 dB scale that the brain can process.
Worked example: Calculating Intensity Level in Decibels
A sound has an intensity of $1 \times 10^{-6}$ W m$^{-2}$. Calculate its intensity level in dB.
$L = 10 \log_{10}\left(\frac{I}{I_0}\right)$ — State the formula first — this earns the method mark [M1].
$L = 10 \log_{10}\left(\frac{1 \times 10^{-6}}{1 \times 10^{-12}}\right)$ — Both values are in W m$^{-2}$, so units cancel cleanly. [M1]
$\frac{1 \times 10^{-6}}{1 \times 10^{-12}} = 10^{-6-(-12)} = 10^{6}$ — Subtracting exponents: $-6 - (-12) = -6 + 12 = 6$. The ratio is $10^6$.
$L = 60 \text{ dB}$ — Always include the unit dB. [A1] This is roughly the level of normal conversation.
Answer: $L = 60$ dB
Here is a useful pattern to memorise: every 10 dB increase corresponds to a tenfold increase in intensity. So 70 dB is ten times more intense than 60 dB, and 80 dB is one hundred times more intense than 60 dB. This relationship comes directly from the definition of the logarithm.
3. Why a Logarithmic Scale Reflects Human Perception
The logarithmic scale is not an arbitrary mathematical convenience — it reflects how the ear actually works. The ear responds to ratios of intensity, not absolute differences. Equal multiplicative increases in intensity produce equal steps in perceived loudness, regardless of the starting level. This is a general principle of sensory physiology known as the Weber-Fechner relationship.
In practical terms, this means that equal steps on the decibel scale correspond to equal steps in perceived loudness — at least approximately. A change from 40 dB to 50 dB feels roughly as significant as a change from 80 dB to 90 dB, even though the second jump involves a far larger absolute increase in physical intensity. The logarithmic scale encodes the ear's compressive response into the measurement system itself.
4. Equal Loudness Curves: What They Show
Now that the decibel scale is established, the next question is: does 60 dB always sound equally loud, regardless of frequency? The answer is no — and equal loudness curves make this visible.
Picture a graph with frequency on the horizontal axis (ranging from about 20 Hz to 20 kHz, plotted on a logarithmic frequency scale) and sound pressure level in dB SPL on the vertical axis. Each curve on this graph connects all the frequency-intensity combinations that a listener judges to be equally loud. These are the equal loudness curves, originally determined experimentally by Fletcher and Munson in 1933 and later refined into the ISO 226 standard.
Each curve is labelled in phons. A sound has a loudness of $N$ phons if it sounds equally loud as a 1 kHz pure tone at $N$ dB SPL. The 1 kHz reference point is where every equal loudness curve crosses its phon value — so the 40-phon curve passes through 40 dB at 1 kHz, the 70-phon curve passes through 70 dB at 1 kHz, and so on.
The shape of the curves reveals the ear's frequency sensitivity directly. At low frequencies (below about 200 Hz), the curves rise steeply — meaning you need a much higher physical intensity to achieve the same perceived loudness as at 1 kHz. At around 3–4 kHz, the curves dip to a minimum, showing that the ear is most sensitive in this region. This dip corresponds to the resonant frequency of the ear canal, which naturally amplifies sounds in this range.
5. Reading and Interpreting Equal Loudness Curves
Being able to extract information from equal loudness curves is a core exam skill. There are three types of reading you need to practise: finding the dB SPL required at a given frequency for a given phon level, comparing the sensitivity of the ear at different frequencies, and explaining what the overall shape of the curves tells us about perception.
The curves are not flat — a flat curve would mean equal sensitivity at all frequencies, which is not the case for the human ear.
At low frequencies (below ~200 Hz), the curves rise steeply, indicating reduced sensitivity: more intensity is needed to achieve the same perceived loudness.
Near 3–4 kHz, the curves dip to their lowest point, indicating peak sensitivity: less intensity is needed here than at 1 kHz for the same perceived loudness.
At very high frequencies (above ~10 kHz), sensitivity falls again and the curves rise.
As loudness level increases (higher phon values), the curves become flatter — the ear's frequency response becomes more uniform at high intensities.
That last point is particularly important and often tested. At low phon levels (quiet sounds), the low-frequency region of the curve is very high — the ear barely detects bass frequencies at low volumes. At high phon levels (loud sounds), the curve flattens out, meaning bass frequencies are perceived much more proportionally. This is why music played quietly sounds 'thin' and lacking in bass compared to the same music played loudly at the same frequency balance.
6. Worked Interpretation: Using the Curves in Context
Exam questions on equal loudness curves often ask you to read off values and then explain what those values mean physically. The step-by-step below models the reasoning chain you should use.
Worked example: Interpreting Equal Loudness Curve Data
From an equal loudness curve diagram, a student reads that a 100 Hz tone requires 70 dB SPL to lie on the 40-phon curve, while a 1 kHz tone requires 40 dB SPL to lie on the same curve. Explain what this tells us about the ear's sensitivity at these two frequencies, and calculate the ratio of intensities of the two tones.
Both tones lie on the 40-phon curve, so a normal listener judges them to be equally loud. — The phon value defines perceived loudness. Same phon = same perceived loudness, regardless of frequency.
100 Hz tone: 70 dB SPL. 1 kHz tone: 40 dB SPL. Difference = 70 - 40 = 30 dB. — The 100 Hz tone needs 30 dB more intensity level to sound equally loud. This means the ear is less sensitive at 100 Hz than at 1 kHz. [B1]
$\Delta L = 10 \log_{10}\left(\frac{I_{100}}{I_{1k}}\right) = 30 \text{ dB}$ — A difference in intensity level corresponds to a ratio of intensities. Rearrange to find the ratio.
$\log_{10}\left(\frac{I_{100}}{I_{1k}}\right) = \frac{30}{10} = 3$ — Divide both sides by 10.
$\frac{I_{100}}{I_{1k}} = 10^{3} = 1000$ — The 100 Hz tone has 1000 times the physical intensity of the 1 kHz tone, yet both sound equally loud. [A1] This powerfully illustrates the ear's non-uniform frequency response.
Answer: The ear is less sensitive at 100 Hz than at 1 kHz. The 100 Hz tone must have 1000 times the physical intensity of the 1 kHz tone to sound equally loud.
That factor of 1000 in intensity for the same perceived loudness is striking. It underlines why a linear intensity scale would be completely inadequate for describing human hearing — and why both the decibel scale and the phon scale are necessary tools.
7. Exam Technique and Common Mistakes
Questions on this topic tend to fall into three categories: calculation of intensity level in dB, description or explanation of what equal loudness curves show, and evaluation of why a logarithmic scale is necessary. Each requires a slightly different approach.
For calculation questions, the most common error is forgetting that $I_0 = 1 \times 10^{-12}$ W m$^{-2}$ and substituting a different reference value, or failing to include the factor of 10 in front of the logarithm. Always write the formula in full before substituting — this secures the method mark even if arithmetic slips occur later.
For 'explain' questions about the logarithmic scale, the mark scheme typically requires two linked ideas: first, that the range of intensities detectable by the ear spans many orders of magnitude (state the range, e.g. $10^{-12}$ to $1$ W m$^{-2}$); second, that the ear responds to ratios of intensity rather than absolute differences, so a logarithmic scale reflects perceived loudness more accurately than a linear one.
Taken together, the logarithmic decibel scale and the equal loudness curves form the quantitative foundation for understanding human hearing — and both spec requirements are directly examined through calculation, description, and explanation questions at A level.
Sources and content standards
Published by Revise Right. Use the official specification reference to check the requirements for your course. Content updated: 2026-09-12.
Human hearing covers roughly 20 Hz to 20 kHz, the range shown on equal loudness curves. Sensitivity is far from even across it: the ear is least sensitive at low frequencies and over 10 kHz, and most sensitive at around 3–4 kHz.
What are equal loudness curves?
Equal loudness curves plot sound pressure level in dB against frequency, each curve connecting all the frequency-intensity combinations a listener judges to be equally loud. They are labelled in phons, dip to a minimum around 3–4 kHz, where the ear is most sensitive, and rise steeply at low frequencies, under about 200 Hz, and again at very high frequencies.
What is a phon?
The phon is the unit of loudness level. A sound of any frequency has a loudness level of N phons if a normal listener judges it to be equally loud as a 1 kHz tone at N dB SPL. So every equal loudness curve crosses its phon value at 1 kHz: the 40-phon curve passes through 40 dB at 1 kHz.
What is the threshold of hearing?
The threshold of hearing is I₀ = 1 × 10⁻¹² W m⁻², the reference intensity at 1 kHz. A sound at this intensity has an intensity level of 0 dB, and the ear can detect sounds up to about 1 W m⁻², around 120 dB.
Why is a logarithmic scale used for loudness?
A logarithmic scale is used because the ear detects intensities from about 1 × 10⁻¹² W m⁻² to around 1 W m⁻², twelve orders of magnitude, and responds to ratios of intensity rather than absolute differences. Equal multiplicative increases in intensity produce roughly equal steps in perceived loudness, so the decibel scale reflects perception far better than a linear one.
Why is the ear most sensitive at around 3–4 kHz?
The ear is most sensitive at around 3–4 kHz because this is the resonant frequency of the ear canal, which naturally amplifies sounds in that range. That is why the equal loudness curves dip to their lowest point there: less intensity is needed than at 1 kHz for the same perceived loudness.
Why does quiet music sound thin and lacking in bass?
At low loudness levels the equal loudness curves rise very steeply at low frequencies, so the ear barely detects bass at low volumes. At higher phon levels the curves become flatter and bass is perceived more proportionally, so the same music played quietly sounds thin compared with when it is played loudly.
How much more intense is 80 dB than 60 dB?
A sound at 80 dB is one hundred times more intense than a sound at 60 dB, because every 10 dB increase corresponds to a tenfold increase in intensity. In the same way, 70 dB is ten times more intense than 60 dB.
What is the Weber-Fechner relationship?
The Weber-Fechner relationship is the principle that sensory physiology responds to ratios, not absolute differences. For hearing, equal multiplicative increases in intensity produce roughly equal steps in perceived loudness, which is why a change from 40 dB to 50 dB feels about as significant as one from 80 dB to 90 dB.
Who discovered equal loudness curves?
Equal loudness curves were first determined experimentally by Fletcher and Munson in 1933 and were later refined into the ISO 226 standard. Each curve connects all the frequency and intensity combinations that a listener judges to be equally loud.
What range of sound intensities can the ear detect?
The ear detects intensities from about 1 × 10⁻¹² W m⁻², the threshold of hearing, up to around 1 W m⁻², approaching the threshold of pain. That is a factor of one trillion, twelve orders of magnitude, which maps onto a 0–120 dB scale.
How sensitive is the ear to low frequencies?
The ear is much less sensitive at low frequencies: under about 200 Hz the equal loudness curves rise steeply, so far more intensity is needed for the same perceived loudness. On the 40-phon curve, a 100 Hz tone needs 70 dB SPL while a 1 kHz tone needs only 40 dB SPL.
How much more intense must a 100 Hz tone be to sound as loud as a 1 kHz tone?
On the 40-phon curve, a 100 Hz tone needs 70 dB SPL and a 1 kHz tone needs 40 dB SPL. The 30 dB difference means log₁₀ of the intensity ratio is 3, so the 100 Hz tone must be 10³ = 1000 times more intense to sound equally loud.
Why do equal loudness curves get flatter at higher loudness?
Equal loudness curves become flatter at higher phon values because the ear's frequency response becomes more uniform at high intensities. At low phon levels the bass region of the curve is very high, but at high phon levels bass frequencies are perceived much more proportionally.
What does a reading of 40 phons mean?
A sound at 40 phons is judged by a normal listener to be equally loud as a 1 kHz pure tone at 40 dB SPL. Every equal loudness curve crosses its phon value at 1 kHz, so the 40-phon curve passes through 40 dB there.