acceptance of the new designation of the octave bands, the SIL was adapted to new octave bands and renamed preferred speech interference level (PSIL). PSIL is defined as the arithmetic average of SPL in the 500, 1000, and 2000 Hz octave bands [4,7]:

PSIL Lp500 þ Lp1000 þ Lp2000

3

PSIL curves

9.4Weighted Sound Pressure Level

Weightings were developed as a method to better subjectively evaluate the impact of noise on the human ear. The human ear is more sensitive to sounds at certain frequency ranges. Therefore, we apply weighting corresponding to sensitivity at different frequencies.

As mentioned in Sect. 9.2.5, weighting cannot be applied in SPL in the time domain. The weighted SPL can only be calculated in the frequency domain. The

formula for calculating RMS pressure, which is used for calculating SPL, in the frequency domain is derived by Parseval’s theorem as shown in the flowchart below. Parseval’s theorem was proved in Sect. 9.2.5:

9.4.1Logarithm of Weighting

A weighted RMS pressure is an RMS pressure multiplied by a weighting factor W as:

P2RMS,w ¼ P2RMS ∙ W

Note that the weightings are applied to the square of RMS pressure. Assume that an RMS pressure PRMS has a sound pressure level of Lp as:

The weighted sound pressure level Lp, w of the weighted RMS pressure is:

¼ Lp þ 10 log 10ðWÞ

Based on the equations above, there are two ways to calculate the weighted sound pressure level Lp, w:

1.Applying the weighting W by multiplying P2RMS ∙ W:

2.Applying the weighting W by adding 10log10(W)

It is easier to calculate the weighted sound pressure level Lp, w by adding 10log10(W) as a gain or loss of dB than by multiplying P2RMS ∙ W.

9.4.2A-Weighted Decibels (dBA)

There are three weightings that were initially introduced for noise levels corresponding to different ranges.

A-weighting is for levels below 55 dB.

B-weighting is for levels between 55 and 85 dB.

C-weighting is for levels above 85 dB.

However, A-weighting is used today to evaluate the response of human hearing at all levels. The three weightings 10log10(W) in dB to be added as a gain/loss for different frequencies are shown in the figure below. The table below also gives the A-weighting for some frequencies.

When sound pressure levels are measured, their spectrum is applied by the weighting attenuation at different frequencies to generate weighted sound pressure levels. The resulting spectral levels can be added by the dB addition rule to find the total (combined) weighted sound pressure levels. Weighted SPLs have units in dB, with the weighting letter appended (i. e., dBA) to indicate the type of weighting. A-weighting can be applied to narrow or m-octave band spectrums and can be either an analog filter or, in the case of digital equipment, simply an attenuation applied to the calculated spectrum.

Example 9.7

Given the octave band spectrum below:

(a)What is the PSIL and communication voice level at a distance of 1.2 m between the speaker and the listener?

(b)Determine the A-weighted spectrum.

(c)Calculate the A-weighted sound pressure levels.

Example 9.7: Solution

(a) Preferred speech interference level (PSIL) is calculated based on the three bands:

In PSIL curves of Sect. 9.3.3, based on PSIL¼67.3 dB and Distance ¼ 1.2 m., the voice level required is approximately “very loud voice”; see figure below: