the A‐weighted sound pressure levels measured of the vehicle noise. The A‐weighted sound pressure level forms the basis of many other descriptors for determining human response to noise described later in Chapter 6. The A‐weighted sound pressure level descriptor is also used as a limit for new vehicles (Chapter 14) and noise levels in buildings (Chapter 12) in several countries. Although the A‐weighting filter was originally intended for use with low‐level sounds of about 40 dB, it is now commonly used to rate high‐level noise such as in industry where A‐weighted sound pressure levels may exceed 90 dB. At such high levels the A‐weighted sound pressure level and the loudness level are normally in disagreement.
Figure 4.15 Relation between subjective response and A‐weighted sound pressure level for diesel engine trucks undergoing an acceleration test: ●, values measured in 1960, ○, values measured in 1968.
(Source: Adapted from Refs. [37–39].)
Example 4.5
The factory noise spectrum (given in Table 4.1), was calculated to have a loudness level of 99 phon (see Example 4.2). Calculate the approximate A‐weighted sound pressure level from the octave band levels given in Table 4.1.
Solution
Since we do not have the directly measured A‐weighted sound level, we can calculate this approximately using Figure 4.14. The A‐weighting corrections at the octave band center frequencies have been read off Figure 4.14 and entered in Column 3 of Table 4.2. The so‐called A‐weighted octave band sound pressure levels have been calculated in Column 4 and these values have been combined to give the A‐weighted sound pressure level of 89.8, i.e. 90 dB. Note this A‐weighted sound pressure level is dominated by the A‐weighted band levels in the 500, 1000, and 2000 Hz octave bands. These three band levels combine to give 89.5 dB. Similar calculations of the C‐weighted and linear (nonfiltered) sound pressure levels give 91.9 and 92.0 dB, respectively. Thus we see that the A‐weighted sound pressure level is 9 dB below the level in phons and no closer than the linear unweighted sound pressure level of 92 dB. A‐weighted levels should not be used to calculate the loudness level unless the noise is a pure tone – then a good loudness level estimate can be made using the A, B, or C filters (depending on the noise level).
Table 4.2 Combination of octave‐band sound pressure levels of factory noise to give the A‐weighted sound pressure level.
| Octave band center frequency, Hz | Octave band level, dB | A‐weighting correction, dB | A‐weighted octave‐band levels, dB |
|---|---|---|---|
| 31.5 | 75 | −42 | 33 |
| 63 | 79 | −28 | 51 |
| 125 | 82 | −18 | 64 |
| 250 | 85 | −9.0 | 76 |
| 500 | 85 | −3.0 | 82 |
| 1000 | 87 | 0 | 87 |
| 2000 | 82 | +1.5 | 83.5 |
| 4000 | 75 | +0.5 | 75.5 |
| 8000 | 68 | −2.0 | 66 |
Figure 4.16 Loudness level in phons of a band of filtered white noise centered at 1000 Hz as a function of its bandwidth. The overall sound pressure level of each band of noise was held constant as its bandwidth was increased, and this level is shown on each curve. The dashed line indicates that the bandwidth at which the loudness starts to increase is about the same at all of the levels tested, except for the lowest level for which no increase in loudness occurs.
(Source: From Ref. [40]; used with permission.)
Figure 4.17 Dependence of loudness level LN (left ordinate) on duration Ti of 1‐kHz tone impulses of constant sound pressure level compared with measurements of A‐weighted sound pressure level LA (right ordinate) using the time constants “impulse,” “fast,” or “slow.” [17].
Another problem with A‐weighting is that it does not allow for the fact that loudness increases with the bandwidth of the noise and also with the duration of the noise event for very short impulsive‐type sounds of duration less than about 200 ms. The concept of the critical band is of fundamental importance in psychoacoustics. It is of concern in studies of loudness, pitch, hearing thresholds, annoyance, speech intelligibility, masking, and fatigue caused by noise, phase perception, and even the pleasantness of music.
Figure 4.16 shows the loudness level of bands of filtered white noise centered at 1000 Hz as a function of bandwidth for the different constant sound pressure levels shown on each curve. The curves were
