Addition of sound level contributions can be performed as a logarithmic addition. Let’s add two contributions, L_{p1} and L_{p2}; the resulting sound pressure level L_{ptot} will be

Should one find logarithms unmanageable, all is not lost: it is possible to use a simple table of additions (Table 2.1). Starting with the highest of the two sound level values to be added (which is noted X in Table 2.1), one looks up the difference to the value to be added. A couple of examples are given in Section 2.3.6.2.

By the way, one can derive an important consequence for noise control purposes: Adding a noise source whose contribution is no greater than the original sound level minus 15 dB will not affect the overall sound level value.

Eq uivalent Sound Levels and Statistical Sound Levels

How does one describe a temporally fluctuating noise? A simple way is to make reference to its energetic value and use the equivalent sound level, given the symbol L_{eq}, which represents a nonfluctuating signal containing as much acoustic energy as the signal under study over the period of time considered. Incidentally, the A-weighted value, which is widely used in surveys, is given the symbol L_{Aeq}.

Table 2.1 Result of adding to a sound level L_{p}, of X dB a second level L_{p2}

Adding X dB and:

Result

X dB

X + 3 dB

X + 1 dB

X + 3.5 dB

X + 2 dB

X + 4.1 dB

X + 3 dB

X + 4.8 dB

X + 4 dB

X + 5.5 dB

X + 5 dB

X + 6.2 dB

X + 6 dB

X + 7.0 dB

X + 7 dB

X + 7.8 dB

X + 8 dB

X + 8.6 dB

X + 9 dB

X + 9.5 dB

X + 10 dB

X + 10.4 dB

X+ 11 dB

X + 11.3 dB

X + 12 dB

X + 12.3 dB

X + 13 dB

X + 13.2 dB

X + 14 dB

X + 14.2 dB

X + 15 dB

X + 15.1 dB

X + 16 dB

X + 16.1 dB

Are we done then? Of course not. For the same L_{eq} value the temporal fluctuations of a noise can be very different, and people can be sensitive to such variations. For example, a 65 dB(A) L_{Aeq} value can be reached close to a major highway where it is a continuous rumble, but it can also be reached close to a country road if a single motorcycle passes by [14]! Clearly enough, something else is needed. One then uses the notion of statistical sound levels, given the symbol L_{x}, which states the sound level reached or exceeded for x% of the analysis time. Several standards and regulations currently use L_{50} (which will be less than the L_{eq} value for a fluctuating noise), as well as L_{10} (which gives a fair idea of the highest noise levels) and L_{90} (which gives a fair idea of the lowest noise levels), with the difference giving the dynamic of the noise.

What about the fluctuations of noise over a whole day? Legal writers and standard writers have eventually come up with the notion of day-evening-night, where the energetic sum is weighted according to the period of the day (i.e., there is a penalty of 5 dB for evening noise and 10 dB for night noise):

where L_{d}, L_{e}, and L_{n} are the day (7:00 a.m to 7:00 p.m.), evening (7:00 p.m. to 11:00 p.m.), and night (11:00 p.m. to 7:00 a.m.) values, respectively, of the noise levels. Please note that while the durations of each period are clearly defined in the European Union, each member state can adjust the corresponding time limits.