38.3 Frequency and Loudness Response

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The threshold of hearing, defined for binaural listening, is that sound pressure in the free field which one

can just still hear as the signal is decreased. The threshold of hearing, for what is considered normal

hearing, is shown in Figure 38.2. As seen from the curve, human hearing is most sensitive in the range of

2000 to 5000 Hz; furthermore, we note that the response in this range is very close to 0 dB, or

20 £ 1026 Pa. At the other end of the scale, there is the threshold of pain, which is usually taken as about

135 to 140 dB. Thus, there is a dynamic range of normal hearing of approximately 140 dB.

FIGURE 38.1 (a) Main components of the human ear; (b) functional diagram of the ear.

38-2 Vibration and Shock Handbook

© 2005 by Taylor & Francis Group, LLC

One also readily notes from the curve of Figure 38.2 that the threshold of hearing is a function of

frequency. For example, with normal hearing, one would just be able to hear a 2000-Hz tone at a 0-dB

level. However, one would require a pressure level of about 15 dB to be able to barely hear a 200-Hz tone.

Thus, in describing the subjective loudness of sound, it is necessary to consider the characteristics of the

human ear. This concept of loudness is quantized by the loudness level.

The loudness level of a particular sound is determined by the subjective comparison of the loudness of

the sound to that of a 1000-Hz pure tone. The level, measured in phons, is equal numerically to the sound

pressure level, in dB, of the 1000-Hz tone, which was regarded to be of equal loudness. A set of

internationally standardized equal loudness contours is plotted in Figure 38.2. In keeping with the

definition of loudness level, note that at 1000-Hz, all the equal loudness contours are equal in phons to

the sound pressure level in dB.

Example 38.1

Determine the sound pressure level of a 100-Hz tone with a loudness level of 30 phon.

Solution

From Figure 38.2, we find the sound pressure level to be 44 dB.

30

−20

−10

0

10

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30

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140

40 50 80 100 200 300 500 800

Frequency [Hz]

1k 2 k 3 k 5 k 8 k 10k 20 k

Phon

20

30

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100

110

120

130

Phon

Sound pressure level (dB)

Normal binaural

threshold of hearing

10

FIGURE 38.2 Equal-loudness contour for free-field binaural listening.

Hearing and Psychological Effects 38-3

© 2005 by Taylor & Francis Group, LLC

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