Home Engineering Building Acoustics

# NOTIONS OF LEVELS

## 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

## Weightings

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].

Found a mistake? Please highlight the word and press Shift + Enter
 Related topics