Single Value Representation of Sound Spectrum

7/27/2019 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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personal.cityu.edu.hk/~bsapplec/single.htm 2

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

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Single Value Representation of Sound Spectrum