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U. Glaeser

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used [32,44]<br />

© 2002 by CRC Press LLC<br />

TABLE 27.1 Critical Bandwidth and Equivalent Rectangular Bandwidth<br />

(ERB) as Functions of the Respective Center Frequency<br />

Center Frequency f c (Hz) Critical Bandwidth ∆f c (Hz) ERB (Hz) ∆f c/ERB<br />

50 100 33 3.0<br />

100 100 38 2.7<br />

200 100 47 2.2<br />

500 120 77 1.5<br />

1000 160 128 1.3<br />

2000 300 240 1.3<br />

5000 900 651 1.4<br />

10,000 2300 1585 1.5<br />

[dB]<br />

SPL , Lp<br />

120<br />

100<br />

FIGURE 27.6 Equal-loudness contours for pure tones.<br />

80<br />

60<br />

40<br />

20<br />

0<br />

10 -2<br />

10 -1<br />

Frequency, f<br />

120 phones<br />

110<br />

100<br />

90<br />

80<br />

70<br />

60<br />

50<br />

40<br />

30<br />

20<br />

10<br />

(27.14b)<br />

Chosen values of ∆f c and ERB are listed in Table 27.1. Critical bandwidth is greater than ERB even three<br />

times for low frequencies but for higher frequencies, starting with ca. 500 Hz, it is 1.3–1.5 times larger only.<br />

Approximately 24 nonoverlapping critical bands cover the whole audible frequency range, but it does<br />

not mean that there exist 24 peripheral auditory filters only. In fact, they occur as continuously distributed<br />

filters along the frequency axis and any audible tone creates an individual peripheral auditory filter centered<br />

on it.<br />

The ear canal acts as a resonator and increases the sound pressure at the tympanic membrane in the<br />

frequency range of 1.5–5 kHz, with a maximum at 3.5 kHz by about 10–15 dB. The sensitivity of the ear<br />

varies strongly with the frequency and reaches the maximum exactly in this band. In Fig. 27.6 equalloudness<br />

contours for pure tones are plotted. They are labeled in units of loudness called phones. By<br />

definition, the loudness in phones is numerically equal to SPL in decibels at the frequency f = 1000 Hz.<br />

The lowest curve in Fig. 27.6 represents the threshold of audibility (in quiet). This curve can be approximated<br />

with expression [47] in decibels<br />

L ptp<br />

=<br />

10 0<br />

[kHz]<br />

ERB = 24.7( 4.37f + 1)<br />

3.64f 0.8 –<br />

– 6.5e<br />

0.6 f 3.3 – – ( )2<br />

+<br />

10 3 – f 4<br />

10 1<br />

(27.15)

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