sound pressure levels, Lp."/>
Figure 3.4 Some typical sound pressure levels, Lp.
3.4.2 Sound Power Level
The sound power level of a source, LW, is given by
(3.23)
where W is the sound power of a source and Wref = 10−12 W is the reference sound power.
Some typical sound power levels are given in Figure 3.5.
Figure 3.5 Some typical sound power levels, LW.
3.4.3 Sound Intensity Level
The sound intensity level LI is given by
(3.24)
where I is the component of the sound intensity in a given direction and Iref = 10−12 W/m2 is the reference sound intensity.
3.4.4 Combination of Decibels
If the sound pressures p1 and p2 at a point produced by two independent sources are combined, the mean square pressure is
(3.25)
where 〈〉t and the overbar indicate the time average
Except for some special cases, such as two pure tones of the same frequency or the sounds from two correlated sound sources, the cross term 2〈p1 p2〉t disappears if T → ∞. Then in such cases the mean square sound pressures
Let the two mean square pressure contributions to the total noise be p2rms1 and p2rms2 corresponding to sound pressure levels Lp1 and Lp2, where Lp2 = Lp1 − Δ. The total sound pressure level is given by the sum of the individual contributions in the case of uncorrelated sources, and the total sound pressure level is given by forming the total sound pressure level by taking logarithms of Eq. (3.26)
where Lpt is the combined sound pressure level due to both sources, Lp1 is the greater of the two sound pressure level contributions, and Δ is the difference between the two contributions, all in dB. Equation (3.27) is presented in Figure 3.6.
Example 3.2
If two independent noise sources each create sound pressure levels operating on their own of 80 dB, at a certain point, what is the total sound pressure level?
Solution
The difference in levels is 0 dB; thus the total sound pressure level is 80 + 3 = 83 dB.
Example 3.3
If two independent noise sources have sound power levels of 70 and 73 dB, what is the total level?
Solution
The difference in levels is 3 dB; thus the total sound power level is 73 + 1.8 = 74.8 dB.
Figure 3.6 and these two examples do not apply to the case of two pure tones of the same frequency.
Note: For the special case of two pure tones of the same amplitude and frequency, if p1 = p2 (and the sound pressures are in phase at the point in space of the measurement):
(3.28)
Example 3.4
If p1 = p2 = 1 Pa and the two sound pressures are of the same amplitude and frequency and in phase with each other, then the total sound pressure level
Example 3.5
If p1 = p2 = 1 Pa and the two sound pressures are of the same amplitude and frequency, but in opposite phase with each other, then the total sound pressure level
For such a case as in Example 3.2 above, for pure tone sounds, instead of 83 dB, the total sound pressure level can range anywhere between 86 dB (for in‐phase sound pressures) and −∞ dB (for out‐of‐phase sound pressures). For the
