Noise Measurement Briefing
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Contents
3. Frequency Weighting Filter Characteristics
1. Sound Pressure Level (SPL)
The frequency of a vibration is expressed as the number of vibrations per second (i.e. inversely proportional to the period) in Hertz (Hz). Audible sound for fit, healthy young people is from 20Hz-20,000Hz, with maximum sensitivity at around 3,000Hz. Frequencies below 20Hz are called 'infrasound' and those above 20,000Hz 'ultrasound'. The numerical magnitude of a sound is normally expressed as the sound pressure level in logarithmic decibel units (dB):
where P is the sound pressure being measured and P0 the reference sound pressure, normally taken as 0.0002µbar (=20µPascals).
This gives a nominal range of 0-120dB, with zero as the reference minimum threshold and 120dB as the approximate threshold of pain.
A sound level change of 1dB can just be detected by the human ear, an increase of 10dB within the hearing range is perceived as a doubling in loudness, a decrease of 10dB as a halving in loudness. In addition, since the decibel is a logarithmic unit, a doubling in the number of noise sources means an increase of 3dB in the sound pressure level (if the noise sources are independent); a further doubling raises it another 3dB, and so on.
Sound may consist of a single frequency, or pure tone, but mostly contains tones of varying frequencies and intensities. The disturbance caused by a sound is dependent on both the frequency and level of the sound. A pure tone causes more disturbance than a complex sound at the same level.
2. Frequency weighting
The basic instrument for objectively measuring sound is the sound level meter. In its simplest form it is calibrated to read sound level over a short period of time with a similar response to all frequencies, that is a 'linear' weighting. Since the human ear is not uniformly sensitive to all frequencies, several weighting scales have been developed to simulate the various sensitivities. These weightings are known as A, B, C or D weightings (see figure 1).
Figure 1: A, B, C and D Weightings
The A, B and C weightings mainly differ in the degree of sensitivity at lower frequencies, relative to 1000Hz. The least sensitivity to lower frequencies is provided by the A-scale, the most by the C-scale. The D-scale gives an indication of perceived noisiness and is used in aircraft noise measurements (IEC 537).
Measurements of sound pressure levels with a weighted response are usually referred to as 'sound levels with the appropriate suffix' (i.e. dB(A), dB(B), dB(C) or dB(D)). The A-weighted sound level has been shown to correlate with subjective responses and two sounds judged to be of similar loudness would produce similar dB(A) values, although their unweighted dB values would vary considerably. The A-weighting compares well with other noise sources. It is, therefore, the most widely used. All four weightings are internationally standardised.
3. Frequency weighting filter characteristics
Note that all frequency weighting filter characteristics are normalised to have a gain of 1 (0dB) at 1 kHz.
A-weighting
The A-weighting characteristic is ideally realised by a filter with the following characteristics:
- Four differentiating zeros
- Two poles at -20.6 Hz (-129.4 /s)
- One pole at -107.7 Hz (-676.7 /s)
- One pole at -737.9 Hz (-4636 /s)
- Two poles at -12200 Hz (-76655 /s)
and therefore has the following transfer function:
B-weighting
The B-weighting characteristic is ideally realised by a filter with the following characteristics:
- Three differentiating zeros
- Two poles at -20.6 Hz (-129.4 /s)
- One pole at -158.5 Hz (-995.9 /s)
- Two poles at -12200 Hz (-76655 /s)
and therefore has the following transfer function:
C-weighting
The C-weighting characteristic is ideally realised by a filter with the following characteristics:
- Two differentiating zeros
- Two poles at -20.6 Hz (-129.4 /s)
- Two poles at -12200 Hz (-76655 /s)
and therefore has the following transfer function:
D-weighting transfer function
The D-weighting characteristic is ideally realised by a filter with the following characteristics:
- One differentiating zero
- Two zeros at -519.8±j876.2 Hz (-3266±j5505.3 /s)
- One pole at -282.7 Hz (-1776.3 /s)
- One pole at -1160 Hz (-7288.5 /s)
- Two poles at -1712±j2628 Hz (-10757±j16512 /s)
and therefore has the following transfer function:
4. Time weighting
Different, internationally recognised, meter damping characteristics are available on sound level measuring instruments: 'Slow' (S), 'Fast' (F) and 'Impulse' (I) (IEC 651, 1979; BS 5969, 1983). The 'Slow' characteristic gives an effective averaging time of approximately 1 second, the 'Fast' characteristic, approximately 0.125s.
The 'Slow' characteristic is mainly used in situations where the reading with the 'Fast' response fluctuates too much (more than about 4dB) to give a reasonably well-defined value. Modern digital displays largely overcome the problem of fluctuating analogue meters by indicating the maximum r.m.s. value for the preceding second.
The 'Impulse' characteristic is about four times faster than the 'Fast' response. It has a very fast rising time constant (approximately 35 milliseconds) and a very slow falling time constant. This characteristic presents a value representative of the loudness of a short duration sound, and is therefore used to determine annoyance rather than hearing damage risk.
The 'Peak' characteristic, on the other hand, measures the actual peak sound pressure level of a short duration sound, as short as 50 microseconds, and is therefore used to determine hearing damage risk. There is little standardisation of criteria for assessing hearing damage risk due to impulsive noise. Some national standards suggest impulse noise limits in terms of dB(A) 'Impulse' level; ISO suggests the addition of 10dB(A) to the measured 'Slow' dB(A) value for a series of impulse sounds but does not cover the single impulse situation. The Occupational Safety and Health Administration (OSHA), which is the accepted standard in parts of North America and Europe, classes repetitive events as 'steady noise' if the interval between events is less than 0.5s, and as 'impulses' if the interval is greater than 0.5s. They also set a maximum limit of 140dB peak sound pressure level for up to 100 impulses a day, with a 10dB decrease in allowable level for a 10-fold increase in the number of impulses.
For impact noise, the OSHA requires measurements to be made using a sound level meter with a linear frequency response, a peak detection circuit and a response time which is approximately 1000 times faster than the 'Impulse' response. This facility is only available on specialised impulse sound-level meters.
5. Background noise
One factor that may substantially affect the accuracy of environmental measurements is the level of background noise in relation to the noise being measured. In practice, no correction is necessary if the difference between the measured noise and the background noise is greater than 10dB. If the difference is less than 3dB the background noise is too high for accurate measurement. For differences between 3dB and 10dB a correction is necessary, as illustrated in figure 2.
If the spectra of the source and background noise are very different, it may still be possible to provide useful information concerning the source, despite comparable overall noise levels.
Figure 2: Correction for background noise (LS+N is the total noise level and LN is the background noise level)