Archive: A Primer on Noise in Computing

Table of Contents

 

October 28, 2003 by Mike Chin

A primer on noise and sound was one of the many items on my want list for core articles when Silent PC Review was first launched. There is so much misinformation on the topic that I felt it mandatory to provide some kind of baseline, an introduction to this complex subject. It is, in fact, a subject that seems simple only if you never scratch below the surface. Hopefully, this article serves well enough for its purpose: To provide guidelines for those who seek a quieter computing experience by which they can interpret noise specifications, commentary by others, and what their own ears tell them.

Revised slightly Nov 4, 2003: Section on “Why Such Noise Levels in Typical PCs?,” page 3.

Note: A large portion of the content for this article originates from a white paper I wrote for VIA entitled “Noise, Computing and VIA“, available at VIA’s web site.

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WHAT IS SOUND? AND NOISE?

Sound is what we hear. Technically, it is defined as the human perception of airborne pressure waves caused by mechanical vibrations emanating from any source. A pure sound, such as that made by a tuning fork, is a tone. When picked up with a microphone and displayed on an oscilloscope, such a tone looks like a sine wave. Every tone has two components: frequency or pitch, and amplitude or volume. Hertz (Hz) is the measure of sound frequency; the decibel (dB) is the measure of sound pressure level. Most sounds that we hear are not pure tones; they are many tones in complex combinations of frequency, amplitude and timing.

Noise is difficult to define technically – it can be almost any waveform, because fundamentally, noise is any unwanted sound. Unwanted being the operative word, noise can be a dripping faucet when you’re trying to sleep in a quiet room, a jackhammer being operated intermittently in the street while you try to read, or the whine of a computer’s cooling fans and hard drive as you try to write a paper. It can even be the sound of laughter when you are angry.

An important aspect of noise is that unlike microphones or sound level meters, people share with animals a keen ability to distinguish different kinds of sounds even when these sounds are actually quieter than the overall ambient level. You could call it focus: It is what allows us to pick out a single familiar voice in a noisy crowded restaurant. This phenomenon comes into play with noise perception as well, where an annoying sound is somehow audible even when it should be masked by other sounds. Noise is as much a psychoacoustic phenomenon as it is physical.

Some types of machine sounds can only be described as noise. The high-pitched limited bandwidth sound of small motors, such as an electric drill or a small high speed fan, is almost always perceived as unpleasant. It has high pitch and penetrating volume, worse than the buzzing of bees or wasps, which is about the closest comparison in nature.

RELATIVE SOUND LEVELS

The decibel follows a logarithmic scale, rather than a linear one. This is a complex subject, but for our purpose, it is sufficient to note:

  • 1 dB is generally the smallest difference that can be perceived by human beings
  • A 3 dB difference is clearly audible for just about anyone with normal hearing
  • A 10 dB difference is generally perceived as being twice or half as loud.

This means, for example, that if one source of noise is measured at point of perception at 85 dB, another source that measures 75 dB sounds half as loud. A 95 dB source sounds twice as loud as the 85 dB source, and four times louder than the 75 dB source.

Sounds are additive, but not in a simple linear way.

  • Two 30 dB noise sources make 33 dB
  • Four 30 dB noise sources make 36 dB
  • Eight 30 dB noise sources make 39 dB
  • Sixteen 30 dB noise sources make 42 dB

Each doubling of identical noise sources results in a 3 dB increase in noise.

NOISE REFERENCE TABLE

The following table shows Sound Pressure Levels for common sounds as a frame of reference to PC noise levels.

SPL (dB) TYPICAL ENVIRONMENT
AVERAGE
DESCRIPTION
140 30 meters from military
aircraft at take off
Threshold of pain
120 Boiler shop (maximum
levels)
Ships engine room (full speed)
Almost intolerable
100 Automatic lathe shop
Platform of underground station (maximum levels)
Printing press room
Extremely noisy
80 Curbside of busy street
Office with tabulating machines
Very noisy
60 Restaurant, Department
Store; Noisiest Gamer PC
Noisy
50 Conversational speech at 1
meter; Noisy workstation
Clearly audible
35 – 45 Quiet office or library;
Typical PC
Subdued
25 – 30 Bedroom at night, Quiet PC Quiet
20 – 25 Quiet whisper; Very quiet
PC
Background in TV and
recording studios
Very quiet
15 – 20 Super quiet / fanless PC Barely audible
<15 Sounds of internal organs Normally inaudible
0 ‘Normal’ threshold of
hearing
Not audible

HUMAN HEARING

The decibel scale gives sound of all frequencies equal weight, while human hearing does not. Our hearing sensitivity varies with frequency: It is most sensitive in the middle range (between 400~4000 Hz), but much less sensitive in the low frequencies, and less sensitive again in the high frequencies.

To compensate for the non-linear frequency response of human hearing, the “A” weighting scale was developed for sound level measurements. Such measurements are expressed as dBA instead of dB and allow sounds of different frequency balances to be fairly compared for relative loudness. For example, a reading of 90 dBA of automotive traffic measured below a bridge (mostly low frequency sound) can be said to have the same loudness as a reading of 90 dBA of massed violins holding a note at 4 octaves above middle C (high frequency sound). Sound level meters (SLM) have the “A” weighting scale built in so that dBA can be read directly off the display.

Note that the “A” weighting scale is an attempt to compensate for non-linearities in average human hearing perception when compared to acoustic measuring devices such as SLMs, frequency spectrum analyzers and other machines. It is an educated approximation based on the research of Munson & Fletcher.

SOUND PRESSURE LEVEL (SPL) vs. SOUND POWER

Thus far, all the references to decibels have been in terms of sound pressure level. To obtain a SPL reading is relatively simple: position the meter at the specified point and measure in dBA. As long as the background noise is held at least ~6 dBA below the sound being measured, and the meter is accurate and calibrated, the result is clear. Because it is so simple to conduct, SPL measurement in decibels at 1-meter distance has become a de facto sound measurement standard, especially where a purpose-specific standard does not exist. However, this measurement is best likened to a single snapshot photograph of the object from one particular point of view. It cannot show the whole acoustic picture. The measured SPL for a device varies with angle, position and acoustical environment.

Sound power, while also a sound measurement expressed in decibels, is a more complete measurement that expresses the total amount of acoustic energy emitted by a sound source.

Think of it like a light bulb, which radiates light in every direction. If you could measure all the energy radiated by a bulb, then this would be the equivalent of sound power.

Noise generally emanates from most sources in some omnidirectional fashion, like light from a light bulb, although the intensity in different directions may vary considerably, unlike a light bulb. Measure all the acoustic energy radiated in every direction by a sound source: This is sound power.

Sound power is akin to a 3-D image compiled from many photographs. It involves multiple microphone measurements from many positions around the sound source, and calculations to convert these measurements into a single value. Unlike SPL measurements, it is not dependent on environmental factors. Sound power is a more accurate predictor of noise under a wide range of environments than SPL readings, and correlates better with human perception, especially for comparative purposes.

To distinguish sound power from SPL, sound power is commonly expressed in bel (a decibel is 1/10th of a bel). The A weighting scale is also generally applied to sound power measurements. For the purposes of this article I will use the A-weighted bel scale for sound power where possible, and refer to SPL in dBA @1M where applicable.


Used with permission from Tomas Risberg, creator of the pioneering web site, The Silent PC. The bel table is located on the ISO 9296 page, along with a detailed explanation of the items on it.

OTHER ASPECTS OF SOUND AND NOISE

Thus far we have focused on perceived and measured loudness, and touched on frequency. There are many other aspects of noise that affect human perception and reaction.

Variability: In other words, how a sound changes over time. One plain fact comes up over and over in dealing with noise: A variable noise that changes relatively quickly or dramatically over time is more noticeable and annoying than one that stays constant. Hence, a thermally-controlled fan that responds quickly to changes in temperature can be more intrusive than one that has a louder default noise level but stays constant. This is the reason why Seagate states in one of their white papers that minimizing the difference in noise level between idle and seek for hard drives is psychoacoustically more significant than achieving the lowest idle loudness.

Pure Tones Vs. Broadband: The plucking of a guitar string was cited as an example of a pure tone. It is one that decays, unlike a held key on an electronic organ, which is also a pure tone. The undecaying steady tone is much more common in computers, with rotating devices like fans and hard drives. The sound of a waterfall or of the surf heard from a distance is broadband; it is composed of random noise in the entire audible frequency spectrum. Such broadband noise that occurs in nature can generally be described as pink noise – its loudness decreases with increasing frequency. Most machine-generated broadband noise has a flatter frequency balance, with equal loudness at high and low frequencies. This is called white noise, usually perceived as more intrusive than pink. Most human beings are more comfortable with broadband noise than with pure tones, if there is little loudness difference between them. So the “wooosh” of air blown by a fan is less intrusive than the high frequency “whine” that can emanate simulutaneously from that same fan if it is small and spinning at high speed.

Directionality: Low frequency sounds emanate from any source in an omnidirectional pattern. As we move up in frequency, the sound becomes more and more directional. In other words, it cannot bend around corners, al though it can reflect off hard adjacent surfaces to reach around corners. High frequency directionality explains, for example, why the high pitch whine that comes from some CRT monitors is not always audible from every angle. If you own such an afflicted monitor, you will have had the experience of moving your head a few inches or turning your head and finding that the noise has disappeared – only to reappear when you put your head back to another position. Directionality can be exploited with baffles in PC cases to contain higher frequency noise.

Decrease with Distance: Distance makes the sound grow fainter. Sound reduces in intensity at the rate of 6 decibels for each doubling of distance when there are no reflective surfaces, such as when a loudspeaker is suspended 50 feet up in mid-air in the middle of a field. In an enclosed space like a room, the sound that radiates away from you, which would not be heard outdoors, reflects off walls to reinforce the direct sound. This explains why indoors, sound generally reduces in intensity by the slower rate of 3 dB for each doubling of distance.

Mechanical Vibrations: All sound is caused by modulation of the air by a moving, vibrating object. Most noise measurement techniques isolate the noise source so that its mechanical vibration does not interfere with the airborne noise that is being measured. But even if those vibrations do not translate directly into noise, when the object is coupled to – bolted, screwed, glued or even set down upon – another object. A fan or hard drive in free air sounds different compared to when it is firmly screwed into chassis of a PC case. Generally, panels in the PC case resonate easily in response to the low frequency vibrations in the fan or hard drive — caused usually by imperfectly balanced bearings or uneven weight distribution of the moving mass.

Room Acoustics: The particular acoustic qualities of a room can have an additive or subtractive effect on noise. Obviously, if your office is an anechoic chamber, you’ll probably hear less noise from your computer. But things such as heavy carpeting or bare wooden floors, overstuffed furniture or glass and metal furniture, drapes and curtains or bare glass windows and walls, and the asymetry or symmetry of your room — these can all affect dramatically the noise that a listener perceives.

MEASUREMENT LIMITATIONS

Despite the efforts of scientists and engineers to advance the metrology of acoustics, there is still no single objective or numeric summation that tells about the quality of a sound. By the term quality, I do not mean how good it sounds, but rather, the nature of a sound. This is best illustrated with an example:

The sound of a gas lawn mower a few houses away is measured at the point of reception as 50 dBA average SPL. The sound of the distant surf is measured at the point of reception as 50 dBA average SPL. The measurements are correct; the SPL values are the same. Do they have the same value, meaning or effect on human beings? No. Most of us perceive these sounds as fundamentally different. A sound level meter does not. It takes sophisticated frequency spectrum analysis plotted over time, and someone trained enough to interpret the data in order to identify roughly what you and I can hear and characterize in seconds.

In my work, I repeatedly encounter compelling evidence that while measurements are important, they only tell half of the acoustic story. There is simply no substitute as yet for a careful, trained listener who can describe accurately what is heard and correlate that description to an analysis of its source.

HEALTHY NOISE LEVELS

It’s well known that long exposure to noise levels above ~70 dBA can cause noise-induced hearing loss. There is also considerable recent evidence that much lower levels of noise have a real impact on learning, stress, and productivity.

Cornell University researchers published a study in the Journal of Applied Psychology in 2000 on the effects of what would be considered moderate levels of noise on workers in the common open-office environment. They found that there was psychological, motivational, and observational evidence of elevated stress. They concluded that chronic exposure to even low-intensity noise may have the potential to cause serious health problems such as heart disease (due to elevated levels of epinephrine, a stress hormone) and musculoskeletal problems.

Workplace stress is no joking matter. The Confederation of British Industry (1992) estimates that, in the UK, 360 million working days are lost each year through illness. The Health and Safety Executive calculates that at least 50% of those lost days are due to stress.

The US Federal agency National Institute for Occupational Safety and Health (NIOSH) identifies job stress as a major cause of ailments and productivity loss, and lists noise as one of the main contributors to workplace stress.

A comprehensive 1999 study for the World Health Organization recommends:

“In schools and preschools, to be able to hear and understand spoken messages in class rooms, the sound pressure level should not exceed 35 dBA during teaching sessions.”

The WHO study specifies the same maximum level of 35 dBA for the interior of homes, to “maintain comfortable speech intelligibility and avoid annoyance.” While no comparable recommendation was made for office environments, it is easy to see how the mentally challenging work conducted in many offices is similar to that done in classrooms, and there is no reason why a similar standard for maximum noise in the work environment shouldn’t apply.

One other simple fact is that noise begets more noise. If the background noise is low, then people speak softly and communicate well whether in person or on the phone. As the ambient noise level increases, people speak louder in order to be heard. When the background noise in an open-office is high, then everyone speaks louder, and the overall noise level is far higher than in a quiet ambient.

In short, the intuitive knowledge most of us have that a quiet environment is conducive to reduced stress, improved learning, higher productivity, and finally, better health, both mental and physical, is confirmed by scientific authorities.

COMPUTER NOISE

Cooling fans (in the power supply, the CPU heatsink, motherboard chipset, VGA card and the case itself), hard drives and optical drives are the noise sources in typical PCs. Typical current PCs emit 3.0 to >5.0 bel sound power . Even PCs at the bottom of this noise range (3.0 bel) can be heard in a classroom, office or living room because:

In a classroom or office, it’s rarely just one PC but rather, at least several and often dozens; in concert, even 3.0 bel PCs clearly become a source of noise. In a living room, the ambient noise is often low enough that it does not mask that level of noise.

PCs closer to the middle of the range, say 4.0 bel, are easily heard in most class, office or home environments.

Realizing that system noise is an important issue, hard drive manufacturers have already fully embraced sound power as a noise declaration standard. Large PC makers are also becoming slowly aware of noise. Dell and HP both began in mid-2002 to include sound power and sound pressure data in the specifications for some of their PC systems, although this information still requires digging on their web sites to find. The vast majority of PC makers do not have consistent standards for noise emission declaration.

WHY SUCH NOISE LEVELS IN TYPICAL PCs?

The relationship between computing power and noise is not direct, but closely related. As the central processing unit (CPU), random access memory (RAM), the hard drive (HDD) and other components run at faster speeds, they inevitably emit more heat. The most cost-effective way to cool hot electronic components is with heatsinks and fans.

The CPU is the toughest cooling challenge, because it produces so much heat in such a small area. The core die of a typical modern CPU is no bigger than one square centimeter, yet some Intel P4 variants have already exceeded 100W heat dissipation. The heat density is incredibly high! Large copper heatsinks with high-speed fans have become virtually mandatory in powerful desktops for this very reason. Add to that the processor found in modern VGA cards, which are now approaching 75W.

The amount of heat generated inside a PC is generally evacuated by cooling fans. Small DC fans are the cheapest way to remove heat from a PC.

An Aside: To be fair, these wattage numbers represent the most conservative estimate of system power requirements, as they are the very highest peak levels that can be reached with a system of comprised of these components. In typical usage for desktop applications, average power is usually 50% of the numbers cited. Consider the discussion here most relevant for worst-case scenarios. Still this is the approach that AMD and Intel both take to estimating power needs. Also, the document in question is 18 months old; both VGA and CPU power dissipation have jumped ~50% since then.

An AMD document, Builders Guide for Desktop/Tower Systems, suggests that the total power for a typical system based around their XP1800+ processor “needs a power supply of at least 162.47 W.” The same document calculates that a “High Performance” system based on their XP2100+ processor “needs a power supply of at least 241.91 watts.” This AMD document is being cited, but the numbers for Intel processors are just as high, in fact, even higher as their P4 processors ramp up beyond 3.0 GHz clock speed.

The AMD XP1800+ processor has a typical power dissipation of 60.7W, is similar to the 61W rating of the Intel P4-2.5G; the AMD XP2100+ processor has a typical power dissipation of 64.3W, similar to the 66.1W rating of the Intel P4-2.67G. There is little reason to doubt that the Intel CPU of similar speed rating in similar systems would have power supply requirements very similar to the aforementioned AMD systems. Keep in mind that none of these processors are the fastest and hottest of either line at this time.

Whatever power is drawn by the components is dissipated as heat. The power supply mentioned above also produces heat. We can safely say that power supplies used in desktop systems have an average AC/DC conversion efficiency of about 65%. Of the AC power drawn by the PSU, 65% is delivered to the components as DC power; the remaining 35% is lost as heat within the power supply itself. The following table shows this simply:

Type of system DC Power Lost in PSU Total AC Power
Typical XP1800+ 162.47 W 87.55 W 249.95 W
Performance XP2100+ 241.91 W 130.26 W 372.17 W

The total amount of power used by the system may or may not surprise you. What is really interesting:

Total AC Power is a very good estimate of the total heat generated in a PC.

Even if a relaxed approach to power requirement is taken, and the total AC power numbers are dropped by 50%, we’re still looking at 125~185W of heat in the case. It’s not a surprise that conventional PCs make as much noise as they do, given the airflow required to remove all that heat!

The noise from fans is exacerbated by case and system designs that fail to provide optimized airflow paths to maximize the cooling power of those fans. High airflow impedance invariably causes higher noise from fans and from air turbulence.

MONKEY NO HEAR

All this is part and parcel of the general prevailing attitude in the industry that, somehow, noise is not an issue, and more importantly: Quiet is not a sellable feature.

Simple things such as soft mounting of hard drives, optical drives and fans that can dramatically reduce noise have routinely been ignored — as have 90% of the quieting solutions considered, discussed and formulated in the pages of Silent PC Review (SPCR). It’s only in the past year or so that manufacturers have begin to notice the noise made by silence seekers. While there has been a increase in the number of genuinely useful quiet components, the number of dubiously marketed so-called silent products has also mushroomed, and quiet prebuilt PC are still hard to find. The enthusiasts at SPCR remain far in advance of the industry in finding and implementing solutions to reduce PC noise.

The single most important reason that PCs are not quieter is that management has not demanded engineering to consider low noise as a primary goal. I wrote in the article The State of Computer Noise: January 2003,

Given what do-it-yourself enthusiasts can achieve with just creativity, desire and minimal funds, it seems clear that if the industry focused its enormous resources on the noise issue, it could be solved overnight at minimal cost to them or to the consumer.

In a broad industry-wide sense, until management and sales are convinced that a quieter PC is a more sellable PC, we will not see this shift in focus. Some individuals, some divisions and maybe even some entire companies in the PC industry are beginning to hear and listen. We’ll see how long it takes for the entire industry to uncover their ears.

EXTREME COOLING SOLUTIONS

In the last few years, PC makers have resorted to all kinds of extreme techniques to cool increasingly hotter components.

  • Large, heavy copper heatsinks for CPUs that require special mounting and transportation techniques in order to avoid damage to the motherboard.
  • Extremely noisy, high-speed fans on CPUs, video card heatsinks, and multiple high-speed fans for case cooling.


    What price cooling? Massive CPU cooler with 80 cfm fan rated for 53 dBA/1meter noise!

  • Intel now mandates an intake opening on the case cover near the CPU for additional cooling air, which opens another direct escape path for noise.
  • Water cooling – a pump circulates water through a closed loop in order to carry the heat from the CPU and other hot component parts to a radiator, often located outside the PC case and cooled by forced air with 2 or more 80~120mm fans.


    Watercooled system by Koolance uses 3 top mounted fans: A direct sound path to the PC user’s ears.

  • Complex heatsinks integrating heat pipes to wick heat away from the CPU to another point in the case where it can be dissipated more efficiently; it is a kind of passively pumped water-cooling system, but requires customization.
  • Refrigeration technology, the ultimate liquid cooling. Complete with compressor pump, copper piping, Freon-substitute, etc.


Is it a fridge? An air conditioner? No, it’s a computer!

The above cooling solutions add considerable expense, complexity, maintenance and noise. Some are so extreme as to be acceptable only for the fanatical or for highly specialized applications. All for the sake of increased clock speeds. One can’t help ask: Is maximum clock speed a necessity for all computers?

The answer is no. Maximum clock speed is not a primary requirement for the vast majority of today’s PC applications. Increasingly, the compelling requirements of a PC include:

  • Application performance
  • Ergonomic compatibility: access, operation, maintenance, noise
  • Aesthetics and physical design: size, shape, look and fit
  • Low total cost of ownership

Maximum clock speed is not a prerequisite for any of the above. In fact, maximum clock speed makes it more difficult to reach most of the above requirements.

Individual system builders and buyers of custom-built computers can take a different approach. A computer that performs well for your applications and needs makes a lot more sense than one that’s been built for some idealized “everyman” consumer imagined by the industry.

NOISE EMISSION DECLARATIONS

The complexities of noise measurements and the importance of noise as a fundamental health, productivity and lifestyle issue leads us to the question of noise emission declaration standards. That is to say, how PC and PC component noise should be measured, and how that noise information should be reported.

  • Except for hard drive makers, noise emission reporting practices in the industry are spotty and inconsistent.
  • Fan makers generally provide only 1-meter (no load) SPL measurements.
  • Among the few power supply makers who report noise, many incorrectly cite the SPL data provided by the makers of fans used in their products. Even when the fan data is accurate, this does not reflect the actual noise that the PSU emanates, because of close-proximity turbulence effects of the impedances around the fan.
  • Makers of mainboards, video cards and optical drives rarely provide noise data, despite the fact that they all make noise – mainboards and video cards due to embedded fans often used for cooling, and optical drives due to their intrinsic motor-driven, spinning nature.
  • Suppliers of cases often include fans, but never provide any noise information. The fans never emit the same level of noise as specified by the makers, as mounting in a case causes mechanical vibrations that usually result in higher levels of noise.

Sound power and bel are already utilized by an important sector of the PC industry, hard drive manufacturers. It is also the primary metric used in the most applicable standards for PC noise:

ISO 7779 specifies operating and installation conditions in an acoustical lab in order to have reproducible and repeatable values. The two noise metrics in ISO 7779 are the A-weighted sound power level and the A-weighted sound pressure level at specified locations.

ISO 9296 specifies the declaration of noise emissions from information technology products. ISO 9296 specifies reporting statistical maximum values of the A-weighted sound power levels based on measurements taken according to ISO 7779.

SPCR urges all participants in the PC industry to join together in making noise emission declaration a standard practice for all components and systems. Acoustics labs are available all over the world, and with enough demand and testing in batches, costs can be made modest. The broader goal is the creation of a saner, healthier, more productive computing world.

This standard noise emission practice could be extended into all industries so that all human-made products bear the same noise labeling, allowing consumers to make intelligent choices based on apples-to-apples comparisons. In a related and perhaps more difficult challenge, I personally urge the industry to develop an acoustics metrology that integrates a qualitative yet objective appraisal of the noise emission.

COMPUTING NOISE CONCLUSIONS

Ever-increasing noise seems an inescapable byproduct of the machines, the technologies and the infrastructure support mechanisms we employ in our work and leisure time. As computers in their various forms become more pervasive in everyone’s lives, they add increasingly to the universal din.

PC devices don’t have to create the high noise levels they do and further contribute to the noise problem. Rather than employ noise reduction solutions after the fact, the best methodology is to use and end encourage the development of computer components that are quiet from the beginning of the design cycle – for both cost and environmental reasons. VIA’s high efficiency C3 processor and Mini-ITX platform, AMD’s speed/voltage adjusting Athlon 64 CPU, and Intel’s high efficiency Pentium M processor are all positive recent movements towards this more enlightened direction.

Increased consumer awareness, education by institutions such as the World Health Organization, and the work of advocates (including
Silent PC Review) is beginning to force manufacturers to address noise emission levels. Companies that wish to market effectively to noise sensitive environments, schools, offices and living rooms will be forced to reduce the noise of their products.

Hard drive manufacturers have provided useful noise data as part of their product specifications for some time, and the competition amongst them have helped lower the general noise level of hard drives. Cooling fans arguably create the most unnecessary system noise.

To create a level playing field for comparing products, that adherence to a standardized noise measurement system is imperative. As described earlier, Sound Pressure Level measured at 1 meter in dBA is a reasonable indicator of noise, but Sound Power (bel) measurements are more accurate and better correlate with human perception of noise. Qualified sound testing laboratories with anechoic chambers that provide the most suitable testing environments for sound measurements should be used to determine official results.

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