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Hearing threshold (auditory threshold) is the minimum amount of sound
energy that a person perceives as sound. The hearing threshold is Iо = 10 –12 W/m .
2
2
Sound pressure corresponding to this value is equal to Ро = 2 · 10 N/m .
–5
Pain threshold is sound energy at which the sound already causes painful
2
2
sensations. It corresponds to the strength of I = 10 W/m , and a sound pressure P =
2
20 N/m .
Bel (B) is the logarithm of the ratio of the actual sound parameter to accepted
limit value in acoustics.

I
L I  lg act , (10.1)
I lim
where LI – sound intensity level;
Iact – the actual value of sound intensity;
Ilim – the limited value of sound intensity.
The whole range from auditory to pain threshold is concluded in the 14 B or
140 dB.
Sound is usually measured with microphones responding proportionally to the
sound pressure. The power in a sound wave goes as the square of the pressure.
(Similarly, electrical power goes as the square of the voltage.) The log of the square
of x is just 2 log x, so this introduces a factor of 2 when we convert to decibels for
pressures.

Sound pressure levels in decibels are caused by some common sources (Table
10.1, Figure 10.1).

Table 10.1 - Situation examples of the sound pressure levels
Example Sound pressure level, dB
The explosion of the atomic bomb (fatal 200
threshold)
Loud music 110
The turning machine 100
Normal working conditions for our 60
classrooms
Quiet conversation 30
The clock process 30

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