Sound level difference between Lr,1 and Lr,2 in dB(A)

Add dB(A) to the higher level
 
Fig. 2/7: Addition of sound levels
 

By adding only the addends L2 and L3 from the example above, you get:

40 dB(A) + 45 dB(A) = 46.2 dB(A)

From this we can conclude that the addend L1 = 35 dB(A) does not influence the sum level strongly and could have been ignored in the first place. The following significant rule can be deduced from the addition scale in figure 2/7:

If two sound levels differ by at least 10 dB, the lower level does practically not contribute to the sum level. We can therefore approximately conclude that (with or without the use of A-weighting):

65 dB(A) + 54 dB(A) = 65 dB(A)

43 dB(A) + 44 dB(A) + 58 dB(A) = 58 dB(A)

(since 43 dB(A) + 44 dB(A) can give at the most 47 dB(A) and this is 11 dB less than 58 dB(A))

The addition of two identical sound levels results in a sound level higher by three decibels, which means a doubling of the sound power due to the definitions given in section 2.4.1. So we can say that:

You can sum up sound levels online with the decibel calculator.

 
Energetic averaging

The process of averaging is analogous to the energetic addition of sound levels with the exception that after the addition of the elements 100,1L, we have to divide by the number of elements, and this before taking the logarithm.

In our example, the average sound level Lm is:

L1 = 35 dB(A), L2 = 40 dB(A), L3 = 45 dB(A)

Lm = 10 lg (1/3 (103.5 + 104.0 + 104.5))

Lm = 42 dB(A) (rounded up)

The example shows that the energetic average level of a series of different sound levels lies closer to the higher values than it would be in the case of arithmetic averaging.

As the averaging often concerns noises varying in time, the corresponding method of calculation can be adapted to this issue by dividing by the total observation or measurement period "T" instead of the number of values and by multiplying each of the addition elements 100,1L by the impact period "ti" of the sound level value Li during the total measurement period.

The calculation steps shall be illustrated using the example of a fictitious noise measurement during a measurement period T = 16 hours from 6 am to 10 pm. The following energetic average values are assumed for the individual hours:

6 am to 8 am : 60 dB(A) t1 = 2 h
8 am to 10 am : 45 dB(A) t2 = 2 h
10 am to 6 pm : 35 dB(A) t3 = 8 h
6 pm to 8 pm : 45 dB(A) t4 = 2 h
8 pm to 10 pm : 55 dB(A) t5 = 2 h

Which average sound level results for the whole daytime from 6 am to 10 pm (T = 16 h)?

Lm = 52 dB(A) (rounded down)

This result also shows that the highest sound level values (in our example the six loudest hours) influence the result of the average sound level the most.

The following statements can easily be deduced from the rules of energetic addition and averaging of sound levels:

- Halving (doubling) the impact period of a noise leads to a decrease (increase) of its average level by 3 dB.

- Halving (doubling) the sound power of a noise also leads to a decrease (increase) of its average sound level by 3 dB.
 

Decreasing sound level during sound propagation

The sound pressure level decreases with increasing distance from the source of the sound. The theoretical description of the decreasing sound level assumes that the point source of a sound emits sound waves in the form of a spherical wave to all directions of a room. This means that the sound power from a sound source spreads to an always growing spherical surface with increasing distance. This leads to the following ratio for the sound level decrease L if the distance between r1 and r2 is increased:

∆L = 20 lg (r₂/r₁)

This means that the sound level decreases by 6 dB each time the distance is doubled, provided that there is no loss during sound propagation and that the sound comes from a point source (figure 2/8 ).

In the case of line sources (figure 2/9), which have a wide linear expansion in comparison to the considered distance and which run in a straight line, the sound is radiated in the form of a cylindrical wave. This leads to the following ratio for the sound level decrease L if the distance between r1 and r2 is increased: