single value representation of sound spectrum
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4. Single Value Representation of Sound Spectrum
Sometimes, a single numerical value is used to describe a sound which has a
spectrum over a wide frequency range. Many methods and parameters have
been derived to achieve this purpose. They are of course less precise and
sometimes may cause confusion. Nevertheless, they are quite useful because
of their simplicity. Some common examples are described below:
(a) NC, PNC & NR Curves
Noise-Criterion (NC) Curves
The set of curves, as shown in Fig. 7, were established in 1957 in
U.S. for rating indoor noise, e.g. noise from air-conditioning
equipment. For a given noise spectrum, the NC rating can be
obtained by plotting its octave band levels on the set of NC
curves. The noise spectrum is specified as having a NC rating
same as the lowest NC curve which is not exceeded by the
spectrum.
For example, a sound having the following octave-band noise :
Centre Frequency (Hz) 62.5 125 250 500 1K 2K 4K 8K
Band Pressure Level (dB) 41 45 48 50 46 42 40 38
is rated as NC-46 since when plotted in Fig. 7, it exceeds the NC-
45 curve by 1 dB at 500 Hz.
Preferred Noise-Criteria (PNC) Curves
The PNC curves was introduced in 1971 as a modification on the
NC curves in response to criticism that in offices designed to NC
curves the air-conditioning noise was too "rumbly" and "hissy".
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e curves are s own n g. . e a ove quote no se spectrum
has a PNC-47 rating as it exceeds the PNC-45 curve by about 2
dB at 4 kHz.
Figure 7 Noise Criteria (NC) Curves
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Figure 8 Preferred Noise Criteria (PNC) Curves
Table 3 illustrates some recommended noise criteria range for
steady indoor background noise.
NC curve PNC curve
1. Sleeping quarters 25 - 35 25 - 40
2. Living quarters 35 - 45 30 - 40
3. Office or
classroom
30 - 35 30 - 40
4. Recording studio 15 - 20 10 - 20
5. Retail store or
restaurant
35 - 50 35 - 45
6. Laboratory 40 - 45 40 - 50
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Table 3 Recommended Noise Criteria Range
for Steady Indoor Background Noise
Noise Rating (NR) Curves
These curves are developed in Europe to assess community noise complaints.
They are shown in Figure 9. Their use is similar to that for the NC and PNC
curves.
(b) The Weighted Scales
The weighted scales are designed to quantify sounds or noises by one single value
and yet do not have to refer to graphs or curves. The single numerical values are
called sound levels.
The octave-band pressure levels are adjusted individually before they are
combined to form one single number. The normalization is shown in Fig. 10, and is
intended to give a better subjective evaluation of the impact of noise or sound
upon the human ear.
Four weighting scales: A, B, C and D were introduced. These weighting curves
are in fact the inverse of equal loudness curves and taking the fact that the equal
loudness curves get flatter as sound pressure level increases. The A-weighting was
for sound pressure levels below 55 dB; B-weighting for levels between 55 and 85
dB; C-weighting for levels above 85 dB; and the D-weighting for even higher
levels. Nevertheless, the A-weighting is now used almost exclusively in
measurements that relate directly to human responses, both from the view point ofhearing damage and of annoyance.
The formula for converting octave-band sound pressure levels into sound levels on
the X-weighting scale, X being A, B, C, or D, is:
(1)
LX-weighting = sound level on the x-weighting scale, dB(X)
Lpi = sound pressure level for the ith octave band, dB
F= correction factor, dB
The values of the correction factors are given in Table 4.
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Figure 9 Noise Rating (NR) Curves
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Figure 10 Frequency Response for the A, B and C Weighting Networks
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Table 4 Sound Level Conversion Chart from
Flat Response to A, B and C Weightings
Example 1
Determine the total A-weighted sound level of the following set of
octave-band sound pressure levels :
Solution :
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For the dB conversion from a flat response to dBA for each of the octave
band :
Then sum the dBA in each of the bands for the total sound level :
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The use of sound levels to describe sounds or noises can be quite
misleading and may lead to confusion. In fact, it can be shown
that two sounds or noises of totally different spectra and hence
different impacts can have the same value of sound level.
There is no direct conversion from NC or NR rating (whichmeasures acceptability) to dBA value (which measures loudness).
However, a rough rule of thumb is:
(2)
This actually varies considerably, depending on spectrum shape.
The constant term could lie between 0 and +11.
(c) Equivalent Continuous Sound Level (LAeq)
This is the steady-state A-weighted sound level that has the same
acoustic energy as that of the time-varying sound averaged over
the specified time interval. See Fig. 11.
Figure 11 Equivalent Continuous Sound Level
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LAeq can be estimated from a record of A-weighted sound level
verse t ime by using the definition :
(3)
where LA(t ) = instantaneous A-level of sound
T = specified time period during which sound is sampled
By breaking the sound-level record into n nos of equal
increments of t ime , equation (3) can be approximated by :
(4)
where LAi = average A-level over the ith increment of t ime
Example 2
The one-minute measurement of a time-varying sound recorded that :
Lp = 60 dBA for 50 sec
= 80 dBA for 10 sec
LAeq = 10 log{(1/60) x [10(60/50) x 50 + 10(80/10) x 10]}
= 72.4 dBA