What is the difference between sound and noise? Clearly more than the loudness only. Although an aircraft is very noisy, a mosquito at night-time can be more than enough to spoil a good night’s sleep.
Instead of looking at the loudness only as a criterion for the degree of noisiness, we shall simply regard noise as what it is – viz. unwanted sound.
Since noise is unwanted sound, it is closely connected with the feeling of annoyance.
Noisiness is related to the loudness of a sound, which in turn must be regarded in connection with when and where it occurs (cf. mosquitos at daytime vs. night-time).
If noise becomes loud enough, the primary concern will be the risk of hearing impairment – not the annoyance.
In most countries governments have issued legislation to regulate the amount of noise permitted to occur as a result of different activities – such as industry, construction work, community activities etc. The aim of such legislation is to reduce the amount of hearing impairment among the members of the community, but also to offer the same people a better life, since secondary symptoms like high blood pressure etc. often occur as a result of long time exposure to noise.
This calls for the ability to assess the noise level to investigate whether there is a risk of hearing impair present, and any regulations have been violated. Hence noise must be measured.
Obviously, the way you measure noise must give you the information you need to assess the noise level. Your measurement procedure may therefore depend on the type of noise you measure. All measurements made on the same type of noise situation, e.g. industrial noise, must be made the same way, otherwise measurements will be incomparable. This calls for standardisation of measurement procedures.
Therefore, we must look into the nature of sound, as seen from a measurement point of view – which is what the following articles are all about.
What is sound really?
Sound is the mechanical vibration of a gaseous, liquid or solid elastic medium through which energy is transferred away from the source by progressive sound waves.
Transformation of vibrations into sound waves:
his is the strict physical definition of sound. More generally we restrict the term sound to be pressure variations which can be detected by the human ear.
The traditional way of measuring pressure is by means of a barometer. However, a barometer is too slow to detect the normal pressure variations in audible sound. Often, the sensitivity is too low as well.
The human hearing mechanism requires that the variations occur at least 20 times a second, but not more frequent than 20 000 times a second.
The number of variations per second is called the frequency of the sound and is expressed in hertz (Hz).
Hence, the human hearing is able to hear sound with frequencies ranging from 20 Hz to 20 000 Hz, the latter often written as 20 kHz.
Of course, pressure variations with frequencies lower than 20 Hz should also be regarded as sound. They are normally referred to as infrasound.
Sounds with frequencies higher than 20 kHz lie above the audible region and are referred to as ultrasound.
Note: The propagation speed of sound in air at ordinary temperatures is ca. 340 m/s, corresponding to about 1224 kilometres per hour. Given the speed of sound propagation we are able to calculate the wavelength at a certain frequency by using the following relation:
c = f × l
in which c is the speed of sound, f the frequency and l the wavelength. An inspection of this relation will reveal that the wavelength is inversely proportional to the frequency, i.e. low frequency means a large wavelength and vice versa.
Examples: at 20 Hz the wavelength is 17 m, while at 20 000 Hz it is merely 1.7 centimetres.
Assessing the sound level
Most sounds that you’re going to measure fluctuate in level. That immediately leaves you with two problems – how to measure these variations as accurately as possible, and how to be able to end up stating that the sound pressure level turned out to be, say 58 dB in a given situation?
The practical world is filled with trade-offs – you can’t always get it the way it ideally should be.
Instead you will have to look for quality and features sufficient to match the purpose, i.e. the errors or shortcomings introduced by the method or technology used should have as little significance as feasible for practical, economical or technical reasons.
Consider a Sound Level Meter with an analogue display (a deflecting needle or a bargraph). If the sound level fluctuates too rapidly, the needle or bargraph change so erratically that it is impossible to get a meaningful reading. On the other hand, if we introduce a damping of the needle deflection to slow down its movements and thus make it produce more meaningful results (to us, that is), we run the risk of missing rapid changes in the sound level.
Obviously, if two Sound Level Meters have different damping of the needle deflection, they will not give identical readings of the sound level when exposed to the same sound field. To circumvent this problem, standardised detector response times have been introduced.
The Sound Level Meter deflection must be fast enough to follow the fluctuations in the sound itself, yet slow enough to enable a read-out of the level:
Meter deflection due to damping
The signal itself
If the deflection is too slow, peaks like this may pass totally unnoticed
In order to be able to compare measurements made with different Sound Level Meters, the meters must have the same amount of damping of the meter deflection. The damping is called time constant.
Detector Response Time
A Sound Level Meter is always equipped with a detector. The purpose of the detector is to convert the measured sound pressure to a sound pressure level (a number of decibels above the threshold of hearing – which is 20 µPa). Two detector response times have been standardised. These are F (for Fast) and S (for Slow).
By detector response time we mean how rapidly the detector output signal changes for a sudden change in the detector input signal. The correct term for detector response time is time constant.
If the detector input signal changes suddenly, the time constant expresses the time it takes for the detector output signal to reach 63 % of its final value.
The F has a time constant of 125 milliseconds and provides a fast reacting display response enabling us to follow and measure not too rapidly fluctuating sound levels.
The S time constant, on the other hand, has been set to be eight times as slow – viz. one second. This will help to average out the display fluctuations on an instrument with a needle or bargraph, and make readings possible in situations where the F time constant setting would produce fluctuations impossible to read.
TIP: here is a way to circumvent this problem of display fluctuations. Most modern Sound Level Meters have digital displays where the sound level is presented as figures. These figures are typically updated once per second and indicate the sound level at the moment of sampling with the selected time constant.
RMS, Impulse and Peak
A term you will encounter frequently when measuring sound, is the RMS, or the root mean square, value. The RMS value is a special kind of mathematical average value which is directly related to the energy contents of the sound.
The energy contents of the sound is a fundamental part of hearing impair risk assessments. However, if the sound to be measured consists of impulses or contains a high proportion of impact noise, measuring RMS values with F or S time constant will not give results correlating very well with the perceived noise level.
To cope with this, a third time constant called I (for impulse) has been developed. The time constant of I is 35 milliseconds, which is sufficiently short to permit detection and display of transient (rapidly changing) noise in a way resembling the human perception of sound. To enable convenient read-out the decay-time for I is 1.5 seconds.
The perceived loudness is a function of the frequency and the sound level, but also a function of the sound duration. Sounds of short duration are perceived to be of a lower level than steady continuous sound of the same level.
The risk of hearing impair is in general not coupled to the perceived loudness. Therefore, precision Sound Level Meters like the Nor118 often include a circuit to measure the peak value of the sound.
TIP: What Is the RMS? The mains (line) voltage in your country will typically be 240 or 110 VAC (Alternating Current) with a frequency of 50 or 60 Hz. This AC voltage represents energy when you use it for illumination etc. How much depends on the amount of current you draw from the mains. But even DC voltage may be used for this, i.e. the energy term is applicable for this as well. The RMS term expresses what value an existing AC-signal should have – had it been a DC-signal – to develop the same amount of energy as the DC-signal would for the given configuration.
Energy Parameters – the Leq and the SEL
Sound is a form of energy. The risk of hearing impair depends not only on the level of the sound, but also on the amount of sound energy entering the ear. For a given sound level the amount of energy entering the ear is directly proportional to the duration of exposure.
Therefore, to assess the hearing damage potential of a sound environment, both the level and the duration must be taken into account. If the level is high enough, however, the duration will be irrelevant – the hearing impair will occur almost instantly.
To better understand the significance of the measured levels, we are always looking for data reduction. If we manage to boil down the data to one or a few numbers, without sacrificing the hearing damage potential or – if found to be a lower sound level – the degree of annoyance that they represent, we have succeeded.
We do that by introducing the equivalent continuous level or the Leq. The Leq is the constant level which has the same energy and consequently the same long term hearing damage potential as the actual varying, measured sound level. This will hold true if we for a moment disregard peak effects which may damage your hearing instantly.
Definition: Mathematically the Leq is defined as:
the average value with respect to time.
TIP: To understand the difference between RMS and the Leq consider the following: Although they both express an equivalent constant signal containing the same amount of energy as the actual time-varying signal itself, they cannot be substituted. The Leq expresses the linear energy average, while the RMS value expresses a weighted average where more recent events have more weight than older events.
NOTE: A few Words more on Annotation: LA means the A-weighted sound pressure level, LAeq, T means the A-weighted Leq, LAeq, T, I means the Impulse- & A-weighted Leq, LAE means the A-weighted SEL. The term dB(SPL) is often used to keep the “sound decibels” apart from “other decibels”.
Fig. shows the relationship between the SEL, the SPL and the Leq. The Leq is the constant level needed to produce the same amount of energy as the actual varying sound (the SPL).
The SEL is the Leq normalised to 1 second. It is what the Leq would be if everything took place during 1 second.
Calibrating
When you are going to make sound measurements, you will need to ensure that you measure the sound pressure level correctly. The procedure of making your sound level meter measure correctly is called calibration.
For sound measurements, calibration is no less than paramount since sometimes legal action will be taken based on the sound and noise levels measured!
The use of calibrators date back to those days when it was easier to design a stable calibrator than a stable sound level meter. Fortunately, this is no longer the case today, sound level meters are as stable as calibrators. However, the microphone is a delicate device designed to fulfil all specifications requested. Hence they are vulnerable and easily subject to damage unless great care is taken. One may therefore say that a calibrator is just as much a device for verification of appropriate operation as it is a device for readjustment of the sensitivity of the sound level meter.
As we have already pointed out, the demand for measurement results reproducibility requires measurements to be made in a standardised way. You will therefore have to act in compliance with applicable standards whenever you make a sound measurement.
Many standards require that you calibrate your sound level meter before and after the measurement session. In this way you are able ensure that all data are correctly acquired and that nothing has changed during the measurement session.
To calibrate a sound level meter we use what is called a sound calibrator — such as the Norsonic sound calibrator Nor1255 or Nor1256. A sound calibrator is designed to produce a known sound pressure level when used correctly together with the sound level meter. The actual calibration is then carried out by mounting the calibrator onto the microphone as shown below and then switch the calibrator on. If the sound level meter fails to indicate the correct sound pressure level, its sensitivity is adjusted until it indicates the correct value (some countries put restrictions on your right to adjust the meter, if your measurements shall comply with certain standards). The sound level meter is then said to be calibrated.
In case the level deviates significantly from earlier or nominal values and/or it is not possible to adjust the instrument to produce the correct results, a thorough check of the sound level meter will be needed.We have talked about the need to measure correctly. As we shall see this is strictly speaking not true, since a measuring device be it a speedometer or a sound level meter can only estimate the true, real value of the parameter it is measuring.
An uncertainty will always be present. The scope of the calibration is to bring this uncertainty to within given limits or tolerances. For sound level meters the width of this acceptable interval of estimates will depend on which type or class it belongs to.
Instrument Classes
According to the International standard for sound level meters IEC 61672-1, two performance categories are defined, class 1 and 2. In general, specifications for class 1 and 2 sound level meters have the same design goals and differ mainly in the tolerance limits and the range of operational temperatures: Class 1 as the most accurate — i.e. with the most narrow tolerances — and class 2 as the least accurate.
National and/or international standards applicable in your country may impose restrictions on which instrument types you may use for a given measurement task.
Obviously, the sound level meter cannot be the only part of this which is “infected” by uncertainties. The problem applies to sound calibrators as well. Hence, even these have been divided into several classes depending on their level accuracy and ability to maintain a stable level. This is to ensure that measurements made with high-quality precision sound level meters are not ruined by inaccurate calibration. Calibrators are specified in IEC 60942. In addition to class LS (laboratory standard) the calibrators also are specified as class 1 or class 2 devices. In general we recommend using a class 1 calibrator to calibrate a class1 sound level meter. A class 2 sound level meter may be calibrated with a class 1 or class 2 sound calibrator as appropriate.
Table showing permitted tolerances as defined by the IEC 60651. All tolerances are in decibels (dB)
Making sound level meters hear the way they do
Correlating sound measurements and the human hearing
A sound level meter must be designed so that it hears the sound level very much the same way as humans do.
If a Sound Level Meter neither attenuates nor accentuates any part of the audible frequency range, it is then said to have a flat frequency response. For obvious reasons such a sound level meter cannot be used for hearing impair risk assessments since it doesn’t hear sounds the way we do.
This calls for a need to approximate the way the human hearing works. The unlinearities of our hearing can also be expressed as that our hearing puts more emphasis or weight on some parts compared to other parts.
Hence an electronic circuit – often referred to as a network – doing very much the same, could be called a spectral weighting circuit or a spectral weighting network. A sound level meter with such a weighting network built-in, can then be used to make weighted measurements.
To make measurements comparable, the hearing approximations – normally called weighting curves – have been standardised.
Originally, three different weighting curves were made to reflect the fact that the human hearing has a level-dependent frequency dependence. The three curves approximate the hearing at different levels and were called A, B, and C. Measurements made with a weighting network employing weighting curve A, are then said to be A-weighted measurements.
This calls for a need to approximate the way the human hearing works. The unlinearities of our hearing can also be expressed as that our hearing puts more emphasis or weight on some parts compared to other parts.
Hence an electronic circuit, often referred to as a network, doing very much the same, could be called a weighting circuit or a weighting network. A Sound Level Meter with a weighting network built-in, can then be used to make weighted measurements.
To make measurements comparable, the hearing approximations, normally called weighting curves, have been standardised.
If we make a sound level meter with a circuitry simulating the basic aspects of human hearing vs. level/frequency, a better correlation between perceived loudness and the measured results will be obtained. The circuitry is referred to as a weighting network and the measurement are referred to as weighted, since more weight is put on some frequency regions than others.
Note: The above Fig. shows the most popular two spectral weighting functions. The C-weighting curve differs from flat (linear or unweighted). Substituting one for the other will not give identical results.
Spectral weighting networks
Historically, the most well-known spectral weighting networks have been designed to be used as follows:
The A-curve has been designed to follow approximately the equal loudness curve of 40 phons.
The B-curve has been designed to follow approximately the equal loudness curve of 70 phons.
The C-curve has been designed to follow approximately the equal loudness curve of 100 phons.
The D-curve has been designed to match the perceived noise for such things as single event aircraft noise measurements.
The equal loudness curves were based on measurements using pure tones. It soon turned out that with the exception of the A-curve, none of the approximations correlated very well with the perceived loudness of real-world complex sounds. Hence, all but the A-curve were abandoned for most applications and up to recently, the A-curve has been the only weighting curve used.
However, the C-weighting is now being brought back to life again, not because of correlation properties hitherto overlooked, but simply because of its shape. The difference between the sound pressure level measured with A-weighting employed and the sound pressure measured with C-weighting employed will tell you something about the spectral properties of the sound you’re measuring.
All the four weighting curves (A,B,C & D) have the same value at 1kHz (0dB attenuation).
Example, illustrating the use of weighting curves: Consider the level difference C-A. If C-A > 0, the spectrum is dominated by low-frequency sound components, simply because the C-curve attenuates less than does the A-curve in the frequency region below 1kHz. However, if C-A < 0, the spectrum is dominated by high-frequency sound components. The more negative this latter value is, the higher in frequency the dominant part is located. If the difference is very small, the dominating component will be located around 1kHz.
The difference between the A-weighted and the C-weighted levels provides information about the spectral properties of the sound measured. In addition, the C-weighting is often used for measuring the peak value of a sound in order to access the risk for hearing impairment.
Note: The C-weighting curve differs from flat (linear or unweighted). Substituting one for the other will not give identical results.
All the four weighting curves (A,B,C & D) have the same value at 1kHz (0dB attenuation).
Example, illustrating the use of weighting curves: Consider the level difference C-A. If C-A > 0, the spectrum is dominated by low-frequency sound components, simply because the C-curve attenuates less than does the A-curve in the frequency region below 1kHz. However, if C-A < 0, the spectrum is dominated by high-frequency sound components. The more negative this latter value is, the higher in frequency the dominant part is located. If the difference is very small, the dominating component will be located around 1kHz.
Tip: When working with noise control your noise abatement measures will depend entirely on the spectral properties of the noise. High-frequency noise is much easier to cope with than low-frequency noise. However, improvements effective on high-frequency noise are generally not effective on excessive low-frequency noise. The normal procedure is then to make a frequency analysis using fractional octave filters (typically using 1/3 octave filters). Observe, however, that what you do by looking at the difference between the C- and the A-weighted level is in fact a miniature frequency analysis.
The level of sound (dB)
Introducing the decibel
In the early days of telephony, a frequent problem of using long wires was the severe attenuation imposed on the transmitted signal by the transmission wires.
This loss of signal-strength could be so significant that even calculating the percentage of received signal compared to transmitted resulted in very inconvenient numbers.
Then somebody came up with the idea of taking the logarithm to the ratio between received and transmitted signal strength.
When the logarithm used is to the base of 10, the logarithm of the ratio between two amounts of power is said to be expressed in bels (B), named after Alexander Graham Bell, inventor of the telephone.
However, the bel is frequently too large to be of practical use. Hence a unit one-tenth of the bel was introduced, viz. the decibel.
The decibel (abbreviated dB) uses – when applied to describe sound in air – the hearing threshold (20 µPa) as reference pressure. This level is defined as 0 dB.
By converting sound pressure levels in pascals to decibels, a scale spanning no less than 10 000 000 : 1 is conveniently reduced to a value between 0 and 140.
Note: Physically doubling the sound pressure means to increase the sound pressure level by 6dB, while ten-folding it (×10) means to increase it by 20 dB.
On the other hand, if you reduce the sound pressure by 50% (e.g. from 1 to 0.5 Pa) the level has been reduced by 6 dB, denoted as a -6 dB change, and a reduction to 1/10 corresponds to a decrease of 20 dB, denoted as a -20 dB change.
Observe the use of negative signs to denote a level reduction.
Calculus as we thought we knew it doesn’t work with decibels. Let us look into a few aspects of this:
Since the dB expresses a ratio, a variation of x dB represents the same relative variation anywhere along the dB scale. This is similar to how percentage calculations work. The similarity ends, however, when it comes to the logarithmic nature of the dB.
An important fact, justifying the use of dB is the way our senses work. The sensation of hearing is like most other human senses of a differential nature. Changes are given priority rather than information on steady state conditions.
However, this will only hold true as long as the level of sensation is well below levels putting your health in jeopardy.
How much is a dB? As a general rule a sound pressure level variation of 1 dB is about the smallest variation detectable by the human hearing.
A pressure variation of 3 dB is clearly audible, but not much more.
Sound Pressure versus Sound Power
Let’s begin with an allegory; if you place an electrical oven in a room, connect it to the mains and turn it on, the room will gradually get warmer.
The heat comes from the electrical power being transformed to heating (thermal) power and emitted by the oven. The final temperature in the room will depend on the outside temperature as well as the room size and the amount of insulation preventing the heat to “escape” from the room. For simplicity we ignore that the heat may be unevenly distributed about the room.
Similarly, if you put a noise source in a room, it will emit a certain sound power which in turn will put up a certain sound pressure. The sound pressure level will depend on such things as the amount of reflections of sound from the wall, the amount of sound being transmitted into adjacent rooms (and thus not returning) etc.
Again we ignore any uneven sound pressure distribution about the room.
With a thermometer you can measure the heat (the temperature) in the room; while with a Sound Level Meter you measure the sound pressure level in the room.
Unless we have a special room at our disposal, we cannot use a thermometer to assess the emitted power of the electrical oven. (What we do instead is to measure the electrical power consumed by the oven. Since electrical ovens have an efficiency of 100 %, we are able to calculate the power.)
We feel temperature and prefer to use that as a criterion, rather than thermal power (ignoring radiation effects).
Similarly, we hear sound pressure, rather than sound power. For assessment of hearing impair, sound pressure is the correct parameter to measure.
The decibel is defined in the power domain, but through mathematics, we can also use it for sound pressure levels.
All decibels large and small
When two completely independent sound sources are put in the same room, the resulting sound pressure is not the sum of the individual sound pressures. Instead, the resulting sound power will be the sum of the sound power emitted by each of the two sources.
To provide an in-depth explanation of why this is the case is beyond the scope of this article.
All right, you may say, sound power can be used to find the resulting noise level when two sources are brought together in the same room, but why can’t we add the two the sound pressure levels together as well?
Sound power is proportional to the square of the sound pressure. This means that if the sound pressure is doubled (two times the initial value), the sound power is quadrupled (four times the initial value). This leaves us with only one option, viz. to familiarise ourselves with the sound power as well.
Earlier we postulated that a dB is a dB. From the above, we may now deduce that a change of +6 dB gives a sound pressure level twice the initial and a sound power level four times the initial. In other words, for sound power levels, the dB’s “count more” than they do for sound pressure levels – which justifies talking about “Large” and “Small” decibels.
Note: The sound power may be calculated directly from sound pressure level measurements, provided that certain precautions are made.
To calculate the level in decibels
in which
is the measured sound pressure, and
is the threshold of hearing (20 µPa).
Since decibels are generally defined and not restricted to be used with sound, decibels using 20 µPa as reference level are normally referred to as dB SPL (Sound Pressure Level). Note the use of squared values in the first line. This is because the decibel is defined in the power domain. However, the rules of mathematics tell that you the two equations in fact are identical.
Adding sound sources
When you start to measure noise, you are going to encounter situations where you need to add sound pressure levels.
For example, you may be engaged in noise measurements in a workshop without being able to measure with all machines running simultaneously – maybe just a few of them are running at the time. If you stay there for a while, you will get the data you for all machines, but not the overall sound pressure level in the room when all machines are running.
What do you do then? Well, if you are good at mathematics, you may of course start calculating the resulting sound pressure level based on the level of each machine. The rest of us don’t do that. There are easier ways. We simply use a graph made specifically for this.
The graph is used to calculate the sum of two noise levels. It can be used for more sources, of course, but they must be added two and two. To add three sources, you just add two of them and the result is then added with the third.
Observe that no machine must be measured more than once. Otherwise the graph procedure won’t work correctly.
To add two sound pressure levels coming from two independent sources, a special graph is used.
Example of use: Measure the sound pressure levels of machine Nos. 1 and 2. Assume these turn out to be L1 = 85dB and L2 = 88dB. The difference is then 88 – 85 = 3dB. Find the 3dB point along the horizontal axis. Go up until you intersect the graph and then into the vertical axis. You will find a delta L value of approximately 1.8dB. Add this value to the level of noisiest machine (the sum must be louder than the noisiest) and get a resulting level of 88 + 1.8 = 89.8dB approximately 90dB!
Background noise compensation
Assume that you are going to make measurements on a machine. If there is so much other noise present that the noise of the machine will be “drowned out”, your measurement will not reflect the noise level of the machine.
Obviously the noise level of “your” machine must be higher than the background noise level. For reliable results, at least 3 dB higher. However, a correction will be needed to compensate for the influence of the background noise on the overall noise level – even if the level difference is higher than 3 dB.
The “smart guy” could always calculate the compensation. The rest of us rely comfortably on the graph below.
This graph also tells that when the level difference increases beyond 10 dB, the correction factor drops below 0.5 dB and therefore becomes insignificant.
In many cases, the machine you want to measure, simply cannot be turned off. Paper and pulp machinery, for instance, are often so expensive that stopping them to measure the background level is out of the question.
What to do then?
One solution could be to attempt to stop the other machinery – i.e. the background noise and so to speak try a backdoor into the problem. The procedure will be the same, the difference is just that background level and machine level swap places in the calculations.
Example of use: Measure the sound pressure level L(S+N) with the machine running. Switch off the machine and measure the background level L(N). Assume you found these levels to be L(S+N) = 72 dB and L(N) = 65 dB. The difference between these amounts to L(S+N) – L(N) = 72 – 65 = 7 dB. Locate this on the horizontal axis, go up until you intersect the graph and then go to the vertical axis to the left. In this case you will find that delta L(N) = 1 dB. Subtract this value from the overall level — the L(S+N) — and you get the machine sound pressure level, i.e. 72 – 1 = 71 dB.
