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An Introductory Physics Course with Peter Eyland
Lecture 6 (Hearing)

In this lecture the following are introduced:
•The human ear's structure and function
•Intensity and Loudness
•Intensity level
•Hearing loss
•The Fletcher-Munson curves

The Human Ear

The ear is an amazing sound detection unit.
It is sensitive to a wide range of intensities and frequencies (20Hz - 16kHz).
It has good direction and orientation location.
It requires only low maintenance.
Early researchers were von Helmholtz and von Békésy (Nobel Prize for medicine in 1961)



1. Auditory canal
(diameter 7mm, length 27mm)

6. Round window
a safety valve at the end of cochlea

2. Tympanic membrane (Ear drum)
(area 70mm2, thickness 0.1mm)

7. Oval window
the start of the pressure wave through cochlea (area 3mm2)

Ossicles (Hammer, Anvil & stirrups)


3. Malleus (Hammer bone)

8. Semicircular canals
(for balance)

4. Incus (Anvil bone)

9. Cochlea

5. Stapes (Stirrup bone)

10. Eustachian tube
(pressure adjustment)

The external shapes are used for direction finding. The auditory (or ear) canal resonates at ~ 3200 Hz and this doubles the pressure at the ear drum. The ossicles form a lever system, which connects the ear drum to the oval window. This also increases the pressure by about 2.


The coupling between these bones and the oval window is controlled by muscles, which loosen reflexively as the sound level increases. This protective mechanism operates slowly, so sudden loud noises are quite dangerous. "Stun grenades" make a very loud sound, which blow out the ear drums and dazes the unprotected person for a few seconds. Also, continuous exposure to loud noise will cause the ossicles to wear and the muscles to be permanently weak.
The ratio of the area of the ear drum to the area of the round window is 70/3 and this gives a pressure gain of >20. The overall amplification from ear canal to cochlea is about 100.
The cochlea sends the auditory sensation to the brain. It is a tapering tube, with two chambers, that is wound up like a snail shell. It is about 35mm long with an average diameter 1.5mm which uncoiled looks like this:


Pressure waves from the oval window vibrate the hairs on the basilar membrane in the upper chamber. When they get to the end they return along the lower chamber. The different frequencies affect the hairs at different places. A 5mm change in distance along most of the basilar membrane corresponds to a doubling in frequency. Thus the cochlea produces a frequency spectrum for the sound.


Intensity and Loudness

The intensity of sound is given by power/area. This is an objective measurement and has the unit of Watt.m-2.
Loudness is a subjective perception.
For a long time it was thought that the ear responded logarithmically to sound intensity, i.e. that an increase of 100x in intensity (W.m-2) would be perceived as a loudness increase of 20x. Accordingly, the Intensity Level was defined to represent loudness. It is logarithmic and has the unit of Bel (after Alexander Graham Bell, not the Babylonian deity).
The deciBel (β) is commonly used as the smallest difference in loudness that can be detected.


The reference intensity (10-12 W.m-2is the (alleged) quietest sound that can be heard. Only about 10% of people can hear this 0 dB sound and that only in the frequency range of 2kHz to 4kHz. About 50% of people can hear 20dB at 1kHz. (The frequency response will be looked at later.)

Approximate Intensity Levels

Type of sound

Intensity level at ear (dB)

Threshold of hearing


Rustle of leaves


Very quiet room


Average room




Busy street


Loud radio


Train through station




Threshold of discomfort


threshold of pain


damage to ear drum


The average intensity level for each of two radios is set to 45dB. They are tuned to different radio stations. Find the average intensity level when they are both turned on.

    worked example

Here the Intensity doubles but the Intensity Level goes up by only 0.3dB.

Other Units

There are other ways of representing the human response, some of these are:
    loudness (which puts the threshold of hearing at 4dB),
    loudness where 1 Sone = 40dB at 1kHz.

Degrees Of Hearing Loss

Jamie Berke is hearing impaired, one of the "Rubella Bulge" of babies born deaf in the 1960s when their mothers contracted rubella during pregnancy. She was raised orally, and learned sign language in her teens. Jamie gives some information at

A person can have up to 25 dB hearing level (HL) and still have "normal" hearing. Those with a mild hearing loss (26-45 dB HL) may have difficulty hearing and understanding someone who is speaking from a distance or who has a soft voice. They will generally hear one-on-one conversations if they can see the speaker's face and are close to the speaker. Understanding conversations in noisy backgrounds may be difficult.

Those with moderate hearing loss (46-65 dB HL) have difficulty understanding conversational levels of speech, even in quiet backgrounds. Trying to hear in noisy backgrounds is extremely difficult. Those with severe hearing loss (66-85 dB HL) have difficulty hearing in all situations. Speech may be heard only if the speaker is talking loudly or at close range. Those with profound hearing loss (greater than 85 dB HL) may not hear even loud speech or environmental sounds. They may not use hearing as a primary method of communicating.

Fletcher-Munson Curves

Fletcher and Munson were researchers who first accurately measured and published a set of curves showing the human ear's frequency sensitivity versus loudness. The lines show averaged perceived equal loudnesses at different frequencies. The lines show the ear to be most sensitive to sounds in the 3 kHz to 4 kHz area, a range that corresponds to ear canal resonances.

The lines give a unit called the phon.
100Hz at 71dB has the same apparent loudness as 60dB at 1kHz and hence it is 60 phons.
The important range for speech is 300Hz - 3000Hz.
Loud noise and age cause the high frequency response to decline.

D.W. Robinson and R.S. Dadson, re-did the auditory response curves in 1956 in an article titled:
'A re-determination of the equal-loudness relations for pure tones', British Journal of Applied Physics, 7, 1956, 166-181. These data are generally regarded as being more accurate than those of Fletcher and Munson. Both sources apply only to pure tones in otherwise silent free-field conditions, with a frontal plane wave etc.

Find out which tone is louder, 80dB at 100Hz or 80dB at 3kHz.

80dB at 100Hz is about 75 phon, whereas 80dB at 3kHz is about 85 phon. So the 3kHz tone appears louder.


Frequency is an objective physical quantity. The subjective sensation of this is called the pitch of the note. The ear is not linear with frequency (Hertz). There is a "S" shaped curve between frequency and pitch.
The ear is reasonably linear in the range 400Hz to 2kHz, but outside this range, the perception of pitch and frequency is non-linear. For example: 400Hz is perceived as 500Hz, 2000Hz as 1500Hz, but 10kHz is perceived to be 3kHz. The subjective determination of frequency has a unit called the mel, and is thought to be due to the variable elastic properties of the basilar membrane.

Some interesting sounds


The ear has an automatic gain control but it is relatively slow.
The overall amplification from ear canal to cochlea is about 100x.
The cochlea sends an auditory sensation to the brain with a frequency spectrum.
Sound Intensity is Power per unit Area and measured in W.m-2.
Sound Intensity Level is a logarithmic scale of Intensity and is measured in deciBels.
The Fletcher-Munson curves show lines which are an averaged perception of equal loudness (in phons).
Frequency is measured in Hertz and the perceived frequency (or Pitch) is measured in Mels.

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