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Characterizing Sound

Sound, as perceived by our ears, is made of periodic vibrations of air. It can last for a given duration of time. It can feature a specific pitch. It can be more or less intense. This means that to describe a sound, one must use three dimensions: time (in s), frequency (in Hz), and level (in dB).

The representation of level in dB versus frequency in Hz is known as the spectrum.

Sound Level

According to Weber’s law, perception varies like the logarithm of excitation. This has led to a logarithmic expression of the sound level Lp, which is expressed as

Lp = 10 log (p2/p02)

where p is the variation of acoustic pressure, and p0 is the reference corresponding to the smallest perceptible acoustic pressure variation, with

p0 = 2 x 10-5 Pa


The human ear does not perceive all sounds in the same way, depending on their frequency and loudness. This has led to a frequency weighting system standardized over the years by the International Electrotechnical Commission (IEC) [8], based on the Fletcher and Munson equal loudness curves [10]. The A weighting was initially introduced for low-level sounds (up to 40 phons), with higher-level sounds being treated to other weighting curves designated as B, C, and D, the latter being especially devoted to aircraft sound level measurements. Nowadays, both the B and the D curves have disappeared [9], but the C curve, which better takes into account the low-frequency sound levels, is currently used in a few occupational noise regulations. More to the point, it has also found its way into some community noise regulations, for example, in Scandinavian countries [11], where it is used to help define limits for background noise. Here are a few examples of A-weighted sound level values:

  • 18 dB(A): Woodland area without wind (and without birds singing either!)
  • 30 dB(A): Cinema projection room (empty)
  • 45 dB(A): Workstation with the desktop computer’s fan running 70 dB(A): Busy street
  • 90 dB(A): Airport fagade with a plane maneuvering at the pier 140 dB(A): 5 m from a jet engine

Now one has probably noted that due to the weighting curve shape, it is possible to achieve a given weighted value with rather different spectrum shapes. For example, a 100 dB(A) value can be achieved with a 100 dB pure tone at 1000 Hz, but also with 126 dB at 63 Hz. In order to avoid the presence of too sharp a tone or a frequency band in a spectrum, one usually specifies noise limits using simultaneously a global A-weighted sound level value and a frequency contour featuring higher levels in the lower-frequency range than in the higher-frequency range. One can either use the noise rating (NR) contour as defined by standard ISO 1996:1971 [12] or the noise criteria (NC) contour as defined by ANSI S12-2-2008 [13].

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