The application of technical directives, standards and official ordinances on noise abatement requires a basic knowledge that goes beyond the principles given in sections 2.1 and 2.2. What still has to be treated is especially the measure for noise, its mathematical and metrological handling and its assessment.
 

2.4.1     Sound scale

The ear's range of perception

The human ear is able to perceive sound vibrations with a frequency ranging from about 16 to 20,000 oscillations per second (hertz). Figure 2/3 differentiates this frequency range, that lies between very high and very deep tones, according to speech, music and other noises. By clicking on figure 2/4 , you can select different audio examples of particular frequencies.

Figure 2/3 further illustrates that the audible range has a lower limit as for sound pressure, which is called threshold of hearing. The sound pressure (more exactly a change in the sound pressure) corresponds to the pressure fluctuations of sound waves and is relevant for the perception of loudness, because the higher the pressure fluctuations, the more energy is transmitted by the sound waves. Above the threshold of pain, the auditory event is associated with sensations of pain.
 

The decibel scale

The values of the sound pressures given in figure 2/3 for the audible range cover a scale from 0.00002 to 200 pascals (Pa), i.e. a range of seven decimal powers, illustrating the astonishing power of perception of our sense organ, the ear. This also shows that a linear sound scale based on the absolute sound pressure values would be unsuitable due to the wide range of values.

A logarithmic scale was therefore defined for the sound scale as a means of presenting a manageable range of values and of better corresponding to the non-linear perception of loudness. The scale used at the right margin of figure 2/3 is based on the sound (pressure) level and indicated in decibel (dB = 1/10 bel). A sound pressure of 2x10-5 Pa is assigned to the threshold of hearing (at 2,000 Hz), which is equal to the sound level value 0 dB on the decibel scale. The threshold of pain forms the top of the scale with a sound level value of 140 dB and a sound pressure of 200 Pa. If the A-weighted sound level is used, the threshold of pain is at 120 dB(A).
 

The decibel and the definition of sound pressure level

The unit "bel" is named after the American scientist Alexander Graham Bell (1847-1922) and it represents no physical unit but only a dimensionless measure, just like the term "per cent". It expresses the ratio of a physical quantity (usually power or intensity) and another value of this quantity as a decadic logarithm relative to a specified reference level. The result is called "level".

As the sound power is proportional to the squared sound pressure, we can deduce that:

1 bel = 10 dB : tenfold power or tenfold pressure relative to 0 bel
2 bels = 20 dB : hundredfold power or hundredfold pressure relative to 0 bel

This explanation leads to the following definition of sound pressure level:
 

Explanation of the abbreviations:

Lp = sound pressure level
p = sound pressure (at this level value)
p0 = reference sound pressure
(standardized threshold of hearing = 2x10-5 Pa)
  

Properties of the sound level scale

The absolute sound pressure increases tenfold each time the sound level increases by 20 dB. A sound level difference of 6 dB corresponds to a sound pressure ratio of 1:2.

The sound power (in watt) and the sound intensity (in W/m2) increase tenfold in steps of 10 dB each. A sound level difference of 3 dB corresponds to a sound power ratio of 1:2. 

In the context of noise protection, it is also important to know that the human perception of loudness follows a power function as well, i.e. that a tenfold increase in the sound power or an increase in the sound level by 10 dB is perceived as a doubling of the loudness. "Loudness" is defined as a measure of subjective loudness assessment (in sone).
  

A-weighting

The perception of tones of identical sound pressure by the human ear varies according to their frequency (tone pitch). This can be seen in figure 2/3 , in which the curve of the threshold of hearing depends on the frequency. High tones are perceived comparatively louder than deep tones. In order to ensure a metrological registration of noises that is true to human perception, the fact that the perception of loudness depends on the frequency is taken into account by using filters which muffle frequencies of the measured noises to different extents within the sound level meter (see section 2.4.4).

The present context only requires the internationally used "A-filter" or the A-weighting curve given in figure 2/5. This is why we will only use the A-weighted sound level with the unit dB(A) in the following.

Figure 2/6 gives an outline of the sound levels of everyday noises with the measurement being carried out according to the procedure mentioned above.