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Our sense organs 45

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amplitudes. The pressure exerted by a barely<br />

audible 1,000 Hz tone is 2 x 10 -5 N/m 2 . At the<br />

same frequency the pain threshold is about six<br />

million times greater. The performance of the ear<br />

encompasses several powers of ten (Diagram,<br />

page 23).<br />

A sound at the threshold of audibility causes the<br />

ear drum to vibrate with an amplitude of only<br />

10 -10 cm. We need to use an extraordinary comparison<br />

in order to visualise such a minute displacement.<br />

If our body height were increased by<br />

a factor of 200 million, it would extend from the<br />

earth to the moon. Even at this enormously magnified<br />

scale, the ear drum would only vibrate over<br />

a distance of 2 mm.<br />

The frequency range of the human ear is approximately<br />

10 octaves. One octave comprises the<br />

notes from middle C to C’ (or A to A’, G to G’, etc).<br />

This does not imply absolute values, but indicates<br />

a doubling of the frequency. Two octaves (e. g.<br />

from C to C’’) thus range from a given frequency<br />

f 1 to a frequency f 2 = 4 x f 1 – a fourfold increase.<br />

Similarly three octaves imply an eightfold increase:<br />

f 3 = 2 3 x f 1 . Human hearing ranges over 10 octaves,<br />

from 20 Hz to 20 kHz, involving the factor 2 10 =<br />

1024 = approximately one thousand.<br />

The ability to distinguish between different tones<br />

is astonishingly good. Around a frequency of<br />

1,000 Hz we can detect frequency differences as<br />

small as 3 Hz or 0.3 %.<br />

a)<br />

b)<br />

The zum rim Tunnel of the eingerollte helix is<br />

folded Krempe to der form Helix a tunnel<br />

Sound path 1<br />

Darwinsches Darwin’s<br />

Höckerchen tubercle<br />

Entry to the<br />

Tor tunnel zum<br />

Helixtunnel (flume) of<br />

the helix<br />

Helix<br />

(Schnecke) Helix<br />

Anthelix<br />

Antihelix<br />

(Gegenschnecke)<br />

Concha-Höhle<br />

(Cavum Antihelix conchae)<br />

Wurzel<br />

Crus helicus<br />

der Helix<br />

(Crus helicis)<br />

verdeckte<br />

Partially covered<br />

Öffnung<br />

des<br />

opening<br />

äußeren<br />

of the<br />

Gehörganges<br />

external acoustic<br />

meatus<br />

Ohrdeckel<br />

(Tragus)<br />

Tragus<br />

Antitragus Anti-tragus<br />

Sound path 2<br />

Auricle and sound paths<br />

a) Auricle: Anatomical names of the various parts of<br />

the auricle (outer ear) are shown in the illustration<br />

above left.<br />

b) Possible sound paths: Two possible paths, 1 and 2,<br />

are indicated in the diagram above right:<br />

1 shows the route from the antihelix to the acoustic<br />

meatus (auditory canal), while route 2 follows the<br />

S-shaped curve of the rim of the helix. Route 2 is about<br />

66 mm longer than route 1, so that the time lag is<br />

24<br />

0.2 milliseconds (0.066 m / 330 m/s = 0.0002 seconds).<br />

The result is that the brain has four different sound<br />

inputs from the two ears (it’s as if there were four ears!):<br />

Two of the four are located somewhat higher, and further<br />

out, than the other two. The brain receives the same<br />

signal at four slightly different instants.

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