Equal Loudness Curves
- The normal human ear can detect sounds of frequencies from about 20 Hz to 20 000 Hz
- Different people may perceive sound differently due to a range of factors
- For example, hearing loss can occur due to ageing or exposure to excessive noise
- Equal loudness curves can be produced to gain an understanding of an individual's hearing abilities
- All sounds on a given curve are perceived as equally loud
- An equal loudness curve is a plot of intensity level, in dB, against frequency, in Hz
- Both axes use a logarithmic scale to match the large range of intensities and frequencies the human ear can detect
Equal Loudness Curve for a Normal Ear
Equal loudness curves for a normal ear show the sound intensity level required to produce the same sensation of loudness at different frequencies
- The loudness of a sound, for a given person, can be measured by comparing it with a standard source of sound at 1 kHz
- The process for generating an equal loudness curve is as follows:
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- A reference signal is played through a pair of earphones - this is a sound of frequency 1 kHz at a fixed intensity level (volume)
- A sound of a different frequency is played through the earphones
- The intensity level (volume) of the sound is adjusted until both sounds seem to have the same loudness - the intensity level of this point is recorded
- The process is repeated at different frequencies, then a curve can be plotted on a graph of intensity level against frequency - this is the equal loudness curve
Worked example
On the axes below, sketch an equal loudness curve showing the normal response of a healthy ear.
Annotate the frequency axis with an appropriate scale.
Answer:
Step 1: Recall the frequency range of human hearing
- For a normal ear, the range of human hearing is 20 to 20,000 Hz
Step 2: Recall how to plot a logarithmic scale
- On a logarithmic scale, each large division on the scale represents an increase by the base of the log (usually 10) to a power that increases linearly (i.e. 101, 102, 103)
- Then for each small division, instead of progressing linearly (e.g. 0, 1, 2, 3, 4...), a logarithmic scale progresses nonlinearly, but still in equal increments (e.g. 10, 20, 30, 40...)
Step 3: Label the frequency axis with a logarithmic scale
- There are 3 large divisions on the axes provided, so we should plot the frequencies between 100, 1000 and 10 000 Hz, as this range is where the ear is most sensitive
- 10, 100 and 1000 Hz would be too low of a range
- 1000, 10 000 and 100 000 Hz would be too large of a range
- Between the large divisions, there are 9 small divisions - there is no 'zero' on a logarithmic scale, so each small division represents increments of 100 and 1000 respectively
- The scale should start at 100 Hz, then 1000 Hz at the midpoint, and end at 10 000 Hz
- Between 100 Hz and 1000 Hz, each division on the scale represents 100 Hz
- Between 1000 Hz and 10 000 Hz, each division on the scale represents 1000 Hz
- Therefore, the locations of 300 Hz and 3000 Hz are two divisions from 100 Hz and 1000 Hz respectively
Step 4: Draw a U-shaped curve with the lowest point at 3000 Hz
- The equal loudness curve for a normal ear has a U-shape
- The frequency a normal ear is most sensitive to is about 3000 Hz
- Therefore, this corresponds to the quietest sound or lowest intensity level on the decibel scale
Worked example
The diagram shows the equal loudness curve obtained when a patient has a hearing test at a level above the threshold of hearing.
Answer:
(a) Hearing test to generate the equal loudness curve:
- The patient listens to a reference sound at 1 kHz and intensity level 10 dB
- Then they listen to a sound at a different frequency and loudness
- They switch between the sound at 1 kHz and the sound at the new frequency and the loudness is adjusted until the same loudness is perceived - the value of loudness is recorded
- The process is repeated for frequencies between 20 Hz and 20 kHz
(b) Equal loudness curve for 100 dB at 1000 Hz:
- The general shape should be flatter and must pass through point 100 dB at 1000 Hz
- Both curves are most sensitive at about 3000 Hz, so they both have a minimum intensity level here
Examiner Tip
An understanding of the unit 'phon' is not required in this specification but you may come across it in your revision of equal loudness curves, so it is included here to aid your understanding
The loudness of a sound in phons is defined as the intensity level in decibels of a sound at 1000 Hz that has the same loudness as the sound, i.e. a 40 dB sound at 1000 Hz has a loudness of 40 phons. From the same curve, a 100 dB sound at 10 000 Hz also has a loudness of 40 phons.
