Calculating intensity levels

Applying the Weber-Fechner law we can write:

The minimum intensity audible to the human ear, I0, is about 10-12 Wm-2, and corresponds to 0 dB.

An intensity 10 times as large corresponds to 10 dB, 100 times as large to 20 dB, and so on.

sensation S

sensation S

1o stimulus 1

Figure 7.10 Sensation and stimulus.

1o stimulus 1

Figure 7.10 Sensation and stimulus.

In Figure 7.10, a graphical representation of the Weber-Fechner law, sensation S is plotted against stimulus I and A S represents a just-noticeable increase in sensation. The figure shows that as the stimulus increases it takes a much larger change in stimulus to produce a just-noticeable increase in sensation.

The 'threshold of hearing' corresponds to an intensity level of 0 dB and the 'threshold of pain' corresponds to an intensity level of 120 dB. Prolonged exposure to intensity levels in excess of 100 dB can permanently damage hearing, and at around 150 dB the eardrum may rupture.

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| live rock music 120 dB, I = 10 Io | | motorcycle 100 dB, I = 1010 Io | | average factory 80 dB, I = 108 Io ] background music 60 dB, I = 106 Io | | library 40 dB, I = 104 Io rustling leaves 20 dB, I = 102 Io Decibel levels of some commonly encountered sounds

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