Click Here to Return to Home Page

Acoustics FAQ
This enhanced version of the Acoustical FAQ file is provided by, acoustical consultants, as a public service to foster the worldwide dissemination of acoustical knowledge.
/////under minor editorial revision 9 JUL 01 AJC.

For global compatibility, only ASCII symbols are used. 


  • To make acoustics accessible to a wider public.
  • To encourage cooperation within the acoustics community. 
Disclaimer: No warranty is made for the accuracy of the contents of this FAQ.

Table of Contents
(Key Word Index is found in Section 7.)

0] Credits (see 10])

1] Resource Pointers

1.1 What acoustics related news groups and FAQs are there?
1.2 What World Wide Web sites are there?
1.3 What acoustics software is available on the Net?
1.4 What acoustics books and journals are there?

2] Basic Acoustics

2.1 What is sound?
2.2 What is a decibel (dB)?
2.3 How is sound measured?
2.4 What does dB(A) or "A-Weighted" mean?
2.5 How do sound levels add?
2.6 How does the ear work?
2.7 At what level does sound become unsafe?
2.8 What is sound intensity?
2.9 How does sound decay with distance?
2.10 What is the sound power level?
2.10.1 How is sound power measured?
2.11 What is the speed of sound in air, water ..?
2.12 What is meant by loudness?

3] Vibration

3.1 What is vibration?
3.2 How is vibration measured?
3.3 How is vibration isolated and controlled?
3.4 What is Seismic (Earthquake) protection?

4] Architectural & Building Acoustics

4.1 What is reverberation time?
4.2 What is the sound absorption coefficient?
4.3 What is the difference between insulation & absorption?
4.4 How is sound insulation measured?
4.5 How do I improve the noise insulation of my house/dwelling?
4.6 How does acoustics affect classrooms and meeting rooms?

5] Reserved

6] Miscellaneous Questions

6.1 What is active noise control?
6.2 What causes a sonic boom?
6.3 Can you focus sound?
6.4 What is sonoluminescence?
6.5 Why does blowing over a bottle make a note?
6.6 What is pitch?
6.7 What are musical intervals?
6.8 What causes "helium voice"?
6.9 What is structural acoustics?
6.10 What is the Doppler effect?
6.11 What is white noise, pink noise?
6.12 When should stranded wire be used for audio cables in a PA system? What is the "electrical skin effect"?


8] Weighting Tables

8.1 Formulae for computing A Weighting and 1/3-octave frequencies.
8.2 Table of A, C and U Weightings.

9] List of National Acoustic Societies

10] Composers

1] Resource Pointers

*** 1.1 What acoustic related news groups and FAQs are there?

news groups

news:alt.sci.physics.acoustics - started by Angelo Campanella - now the principal group for discussion of acoustics topics. Ang's CV is at URL http://www.CampanellaAcoustics.Com/angelo.htm

news:sci.physics - general physics but occasionally acoustics related questions are posted. - includes discussion on audio equipment, speakers etc. There are other groups which may be of interest. and - groups for sufferers of these complaints 

news:bionet.audiology - matters relating to hearing and hearing loss 

news:bit.listserv.deaf-l news:uk.people.deaf news:alt.society.deaf - usenet seems an ideal communication medium. 

news:comp.dsp - the group for people interested in computing digital signal processing solutions, FFTs FIRs IIRs etc. 

news:comp.speech - speech recognition and simulation - various discussion of use of internal sound cards in IBM compatible computers. 


The main archive site for all usenet FAQs is

A list of mirror sites (including html) for the Acoustics FAQ is at

The Active Noise Control FAQ by Chris Ruckman is at

The Tinnitus FAQ deals with a range of hearing disorders. It is available at

The Audio FAQ, with everything you ever wanted to know about the subject, from preamplifiers to speakers and listening room acoustics. It is located in the pub/usenet/* directories 

The comp.speech faq has information on speech processing and some software links

*** 1.2 What World Wide Web sites are there?
(virtual lib for acoustics & vibration with useful links)
(simple acoustics introduction from David Worrall)
(theoretical basic acoustics lecture notes; difficult stuff like the wave equation etc, in hypertext for browsing, or gzipped Postscript format for downloading)
(Acoustical Society of America home page with several links and comprehensive career section, book lists and Society info etc)
(Angelo Farina has published a variety of papers - some are available in zipped MSWord format)
(European Acoustics Association)
(Institute of Noise Control Engineering home page)
(Steve Ekblad's extensive audio related BBS and Internet list)
(Technical societies, conferences etc etc but not specifically acoustics related)
(main ISO standards page)
(national standards organizations addresses)
(official ANSI site)
ISO Technical Committee 43 - all areas of acoustics and acoustical measurements.
Sunbcommittee 1 deals with measurements including sound power.
Subcommitte 2 deals with acoustical properties of buildings.
American Society for Testing and materials (ASTM) Committee E-33 "Environmental Acoustics".
Deals with all aspects of building acoustics and some community noise measurements.

Some of the better search engines: (can also be used as Usenet posting gateway)

or use your nearest Archie site to look for files you want. 

*** 1.3 What acoustics software is available on the Net? - This is a computational acoustics resource site by Stephen Kirkup containing Fortran Software implementing the Boundary Element Method (BEM) for the solution of a range of acoustic problems. 

A range of programs available for downloading from the Simtel archive. 

Spectrogram 4.12 - Accurate real time Win95 spectrum analysis program (freeware) by Richard Horne is at a few sites including:

The comp.speech faq has several links to speech related software including speech recognition and text to speech programs. 

There are a few programs for various platforms listed at URL The programs listed are mainly for sound analysis and editing. 

Some software is available for audio systems design at URL

Odeon is a program for architectural acoustics. A demonstration version is available by ftp. The demo includes a large database for coefficients of absorption. A web page at URL describes the capabilities of the program and gives the ftp address. 

Also some interactive acoustics software (e.g. room acoustics, RT, decibel conversion etc.) is available at a couple of sites. 

CATT Auralization - demo version of CATT-Acoustic (room acoustics prediction / auralization). A free download version is available on the Web site, but it lacks a small key file which can be transfered via e-mail in return for name, address and company/organization affiliation. See . (4-98 per Bengt-Inge Dalenback * Mariagatan 16A * S-41471 Gothenburg * SWEDEN * phn/fax: +46 31145154) 

*** 1.4 What acoustics books and journals are there?

There is a large range of books available on the subject. Generally the choice of book will depend on which approach and subject area is of interest. A few books are listed below: 

>>Introduction to Sound
>>Speaks, C
Good foundation for acoustics principles 

>>Acoustics Source Book
>>Parker, S (editor)
Basic introductory articles on many topics discussed in the alt.sci.physics.acoustics group. Old book - technology a bit dated. 

>>The Science of Sound
>>Rossing, T
Introductory book on acoustics, music and audio 

>>Fundamentals of Acoustics
>>Kinsler, L Frey, A et al.
Good overall coverage of acoustics but includes lots of theory 

>>Acoustics ...
>>Pierce, A
Classic advanced text - lots of theory 

>>Engineering Noise Control
>>Bies, D & Hansen, C
Practically biased with examples. Partially updated and corrected. 

>>Handbook of Acoustical Measurements and Noise Control
>>Harris C (editor)
Comprehensive practical reference book. 

>>Vibration and Sound
Morse, P
Comprehensive theory of acoustic waves and vibration in materials. 
Good fundamentals reference book. 

A list of recently reviewed noise-related books is at URL

Some Journals

Applied Acoustics (UK - 12 per year)
Acoustics Bulletin (UK - every 2 months)
Acta Acustica (P.R.China)
Acta Acustica / Acustica (Europe - 6 per year)
Journal of the Acoustical Society of America (monthly)
Journal of the Acoustical Society of Japan (E) (English edn - 2 months)
Acoustics Australia (3 per year)
Journal of Sound & Vibration (UK - weekly)
Journal of the Audio Engineering Society (US - 10 per year)
Noise Control Engineering (US - every 2 months)
Technical Acoustics (

| Definitions used:
| 10^(-5) indicates 10 raised to the power of minus 5
| 1.0E-12 indicates 1.0 x 10^(-12)
| 1 pW indicates 1 picowatt i.e. 1.0E-12 Watt
| W/m^2 indicates Watts per square metre
| lg indicates logarithm to base 10
| sqrt indicates the square root of
| pi = 3.142
| Lw is sound power level, the w is subscripted

2] Basic Acoustics

*** 2.1 What is sound?

Sound is the quickly varying pressure wave within a medium that can travel widely in that medium. We usually mean audible sound, which is the sensation (as detected by the ear) of very small rapid changes in the air pressure above and below a static value. This "static" value is atmospheric pressure (about 100,000 Pascals) which does nevertheless vary slowly, as shown on a barometer. Associated with the sound pressure wave is a flow of energy. Sound is often represented diagrammatically as a sine wave, but physically sound (in air) is a longitudinal wave where the wave motion is in the direction of the movement of energy. The wave crests can be considered as the pressure maxima whilst the troughs represent the pressure minima. 

How small and rapid are the changes of air pressure which cause sound?
When the rapid variations in pressure occur between about 20 and 20,000 times per second (i.e. at a frequency between 20Hz and 20kHz) sound is potentially audible even though the pressure variation can sometimes be as low as only a few tens of millionths of a Pascal. Movements of the ear drum as small as the diameter of a hydrogen atom can be audible! Louder sounds are caused by greater variation in pressure. A sound wave of one Pascal amplitude, for example, will sound quite loud, provided that most of the acoustic energy is in the mid-frequencies (1kHz - 4kHz) where the human ear is most sensitive. It is commonly accepted that the threshold of human hearing for a 1 kHz sound wave is about 20 micro-Pascals. 

What makes sound?
Sound is produced when the air is disturbed in some way, for example by a vibrating object. A speaker cone from a high fidelity system serves as a good illustration. It may be possible to see the movement of a bass speaker cone, providing it is producing very low frequency sound. As the cone moves forward the air immediately in front is compressed causing a slight increase in air pressure, it then moves back past its rest position and causes a reduction in the air pressure (rarefaction). The process continues so that a wave of alternating high and low pressure is radiated away from the speaker cone at the speed of sound. 

*** 2.2 What is a decibel (dB)?

The decibel is a logarithmic unit for ratios that is used in a number of scientific disciplines. Other examples are the Richter scale for earthquake event energy and pH for hydrogen ion concentration in liquids. 

In all cases the logarithmic measure is used to compare the quantity of interest with a reference value, often the smallest likely value of the quantity. Sometimes that reference can be an approximate or average value.

Most often in common acoustics, the decibel is used to compare the sound pressure level  (SPL) in air with a reference pressure. The reference level for sound intensity (I), sound power level (PWL) and sound pressure in water are amongst others that are in common use: 

Reference sound pressure (in air) = 0.00002 = 2E-5 Pa (rms)

     "      "   intensity         = 0.000000000001 = 1E-12 W/m^2

     "      "     power           = 0.000000000001 = 1E-12 W

     "      "   pressure (water)  = 0.000001 = 1E-6 Pa

Acousticians use the dB scale for the following reasons: 
1) Quantities of interest often exhibit such huge ranges of variation that a dB scale is more convenient than a linear scale. For example, sound pressure radiated by a submarine may vary by eight orders of magnitude depending on direction; expression in linear uniits carryies with it the confusion of the location of the decimal point. Decibels vaues are characteristrically between only -999 to +999. 

2) The human ear interprets loudness more easily represented with a logarithmic scale than with a linear scale. 

*** 2.3 How is sound measured?

A sound level meter (SLM) is the principal instrument for general noise measurement. The indication on a SLM (aside from weighting considerations) indicates the sound pressure, p, as a level referenced to 0.00002 Pa, calibrated on a decibel scale. 

Sound Pressure Level = 20 x lg (p/0.00002) dB 

Often, the "maximum" level and sometimes the "peak" level of the sound being measured is quoted. During any given time interval the peak level will be numerically greater than the maximum level and the maximum level will be numerically greater than the (rms) sound pressure level; 


*** 2.4 What does dB(A) or "A-Weighted" mean? C-Weighted?

A sound level meter that measures the sound pressure level with a "flat" response will indicate the strength of low frequency sound with the same emphasis as higher frequency sounds. Yet our ear perceives low frequency sound to be of less loudness that higher frequency sound. The eardrum- stapes-circular window system behaves like a mechanical transformer with a finite pass band. In EE parlance, the "3 dB" rollover frequencies are approximately 500 Hz on the low end and 8 kHz on the high end. By using an electronic filter of attenuation equal to that apparently offered by the human ear for sound each frequency (the 40-phon response curve), the sound level meter will now report a numerical value proportional to the human perception of the strength of that sound independent of frequency. Section 8.2 shows a table of these weightings. 

Unfortunately, human perception of loudness vis-a-vis frequency changes with loudness. When sound is very loud - 100 dB or more, the perception of loudness is more consistent across the audible frequency band. "B" and "C" Weightings reflect this trend. "B" Weighting is now little-used, but C-Weighting has achieved prominence in evaluating annoying community noises such as low frequency sound emitted by artillery fire and outdoor rock concerts. C-Weighting is also tabulated in 8.2. 

The first electrical sound meter was reported by George W Pierce in Proceedings of the American Academy of Arts and Sciences, v 43 (1907-8) A couple of decades later the switch from horse-drawn vehicles to automobiles in cities led to large changes in the background noise climate. The advent of "talkies" - film sound - was a big stimulus to sound meter patents of the time, but there was still no standard method of sound measurement. "Noise" (unwanted sound) became a public issue. 

The first tentative standard for sound level meters (Z24.3) was published by the American Standards Association in 1936, sponsored by the Acoustical Society of America. The tentative standard shows two frequency weighting curves "A" and "B" which were modeled on the response of the human ear to low and high levels of sound respectively. 

With the coming of the Walsh-Healy act in 1969, the A-Weighting of sound was defacto presumed to be the "appropriate" weighting to represent sound level as a single number (rather than as a spectrum). With the advent of US FAA and US EPA interests in the '70's, the dBA metric was also adapted by them. (Along with the dBA metric has come an associated shortfall in precision in accurately presetning the capacity of a given sound to produce hearing loss and the capacity to create annoyance.) 

[Editor's Note: A single number metric such as dBA is more easily understood by legal and administrative officials, so that promulgation, enforcement and administrative criteria and actions are understandable by more parties, often at the expense of a more precise comprehension and engineering action capability. For instance, enforcement may be on a dBA basis, but noise control design demands the octave-band or even third-octave band spectral data metric.] 

The most commonly referenced weighting is "A-Weighting" dB(A), which is similar to that originally defined as Curve "A" in the 1936 standard. "C-Weighting" dB(C), which is used occasionally, has a relatively flat response. ""U-Weighting"" is a recent weighting which is used for measuring audible sound in the presence of ultrasound, and can be combined with A-Weighting to give AU-Weighting. The A-Weighting formula is given in section 8 of this FAQ file. 

In addition to frequency weighting, sound pressure level measurement can be time-weighted as the  "Fast", "Slow" or "Impulse" response. Measurements of sound pressure level with A-Weighting and fast response are also known as the "sound level". 

Many modern sound level meters can measure the average sound energy over a given time. this metric is called the "equivalent continuous sound level" (L sub eq). More recently, it has become customary in some circles to presume that this sound measurement was A-Weighted if no weighting descriptor is listed. 

*** 2.5 How are decibel sound levels added?

If there are two uncorrelated sound sources in a room - for example a radio producing an average sound level of 62.0 dB, and a television producing a sound level of 73.0 dB - then the total decibel sound level is a logarithmic sum i.e. 

Combined sound level = 10 x lg ( 10^(62/10) + 10^(73/10) ) 

= 73.3 dB 

Note: for two different sounds, the combined level cannot be more than 3 dB above the higher of the two sound levels. However, if the sounds are phase related ("correlated") there can be up to a 6dB increase in SPL. 

*** 2.6 How does the ear work?

The eardrum is connected by three small jointed bones in the air-filled middle ear to the oval window of the inner ear or cochlea, a fluid- filled spiral shell about one and a half inches in length. Over 10,000 hair cells on the basilar membrane along the cochlea convert minuscule movements to nerve impulses, which are transmitted by the auditory nerve to the hearing center of the brain. 

The basilar membrane is wider at its apex than at its base near the oval window; the cochlea tapers towards its apex. Groups of the delicate hair sensors on the membrane, which membrane varies in stiffness along its length, respond to different frequencies transmitted down the spiral. The hair sensors are one of the few cell types in the body which do not regenerate. They can therefore be irreparably damaged by large noise doses. Refer to the Tinnitus FAQ for more information on associated hearing disorders.

*** 2.7 At what level does sound become unsafe?

It is strongly recommended, to avoid unprotected exposure to sound pressure levels above 100dBA. Use hearing protection when exposed to levels above 85dBA (about the sound level of a lawn mower when you are pushing it over a grassy surface), and especially when prolonged exposure (more than a fraction of an hour) is expected. Damage to hearing from loud noise is cumulative and is irreversible. Exposure to high noise levels is also one of the main causes of tinnitus. 

The safety aspects of ultrasound scans are the subject of ongoing investigation. One metric that has been expressed is that exposure to utrasound should not exceed 85dB in the 16kHz octave band.

Health hazards also result from extended exposure to vibration. An example is "white finger" disease, which is found amongst workers who frequently use hand-held machinery such as chain saws. 

*** 2.8 What is sound intensity?

Sound intensity is expressed in decibels with respect to one pico-watt (10^-12 watts) per square meter. This is very nearly* numerically equal to the sound pressure level (SPL) in decibels when measures one foor from the noise source (viz. the inlet of a noisy fan) . An intenisty estimate using SPL-only presumes no standing waves or reflections where the effective impedance can differ from that of free space air. In its complete form, intensity include the unit vector of the propagation direction, i.e. intensity is a vector quantity. 

*For a plane wave, the sound power that passes through a surface of A square meters is defined as the ratio of the pressure squared to the air impedance 

I = p^2/(rho*c) 

When combined with the propagation unit vector, this defines the rate of sound energy transmitted in a specified direction per unit area normal to the direction. When measured in practical units, we can compute intensity after the relation that 

Numerically, the sound intensity is related to the sound power as follows: In free air space, a source emitting Lw dB re 1 picowatt produces the sound pressure level Lp at a distance R feet as 


At a one foot radius, that sound power is distributed over a surface of 4*pi = 12.57 square feet or (*.3048^2=.0920*) 1.17 square meters. 10log1.17=0.7dB. So within 0.1 dB, the coincidence exists that the sound intensity in picowatts per square meter is numerically equal to the sound pressure level in dB! 

NOTE: This identity holds true only when the impedance, rho*c is exactly 400 mks rayls. This occurs for sea-level at 39 degrees C. For 22 C, rho*c = 412; a 0.13 dB difference arises. But at higher elevations, air density decreases for a given temperature. At an elevation of 840 feet above sea level, rho*c reduces to 400 at 22 C. (fortunate for much of Midwestern US!). The 0.13 dB difference at sea level is not usually significant for acoustical measurements. 

Sound intensity meters are popular for determining the quantity and location of sound energy emission. 

*** 2.9 How does sound decay with distance?

At distances large compared to the size of the source, sound intensity diminishes according to the inverse square law. 

        I = Io/D^2 

This is relatively simple to reliably calculate, provided the source is small and outdoors where no echoes occur. (But indoor calculations in a reverberant field are rather more complex. )

If the noise source is outdoors and its dimensions are small compared with the distance to the monitoring position (ideally a point source), then as the sound energy is radiated it will spread over an area which is proportional to the square of the distance. This is an 'inverse square law' where the sound level will decline by 6dB for each doubling of distance. 

Line noise sources such as a long line of moving traffic will radiate noise in cylindrical pattern, so that the area covered by the sound energy spread is directly proportional to the distance and the sound will decline by 3dB per doubling of distance. 

Close to a source (the near field) the change in SPL will not follow the above laws because the spread of energy is less, and smaller changes of sound level with distance should be expected. 

If the observation position very close to the source, at a distance that is small compared to the size of the source, the sound level changes very little with location in that source area. One may be able to determine the "virtual center" of the whole sound field, whence inverse square law calculations can proceed in reference to that distance, for locations outside the source area. 

The surrounding environment, especially close to the ground, and in the presence of wind & vertical temperature gradients, has a great effect on the sound received at a distant location. Ground reflection affects sound levels more than a few feet away (distances greater than the height of the sound source or the receiver above the ground). Wind and air temperature gradients affect all sound propagation beyond 100 meters over the surface of the earth.  Sound propages well downwind (traveling with the wind), and very lirrle upwind. When the ground surface is cooler than the air  just above it ("inversion"), typically late at night and just before dawn, sound will travel great ditances across the landscape even without any wind. 

In addition it is always necessary to take into account attenuation due to the absorption of sound by the air, which may be substantial at higher frequencies. For ultrasound, air absorption may well be the dominant factor in the reduction. 

*** 2.10 What is the sound power level?

(See ACCULAB Reference Sound Source on this site:

Sound power level, Lw, is often quoted on machinery to indicate the total sound energy radiated per second. It is quoted in decibels with respect to the reference power level. The reference level is 1pico-watt (pW) [1x10^(-12) watts]. One watt of radiated sound power is represented as "Lw=120 dB re one picowatt". If the reported sound power is in terms of A-Weighted spectral weighting, a suffix, A, is applied to form dB(A). 

The sound pressure level (SPL) resulting from sound power (Lw) being radiated into free space, e.g. over a paved surface, is computed from 

SPL = Lw - 20*log(R) - 11 dB re 20 uPa   (R in meters)

SPL = Lw - 20*log(r) - 0.7 dB re 20 uPa   (r in feet)
If instead the sound is emitted over a reflecting plane such as a hard surface, three (3) decibels are added to the SPL. 

For example, a lawn mower with sound power level 100 dB(A) will produce at a sound pressure level (SPL) of about 89dB(A) at the operator (you) position over grass and 92 dB(A) when the mower is operated over a hard surface such as your driveway. At your neighbor's yard 50 feet (15m) away, the SPL will be is 65 dBA. 

*** 2.10.1 How is sound power measured?

Sound power is usually measured indirectly as the sound pressure level found at a specific distance, and in every direction that sound can be radiated. The sound power emitted by Items that can be carried to a laboratory is usually measured in a hemi-anechoic room or a reverberation room. 

Either the "comparison" or the "direct" method is used. 

In the comparison method, the SPL that the item causes in that room is compared the SPL created by a standard "Reference Sound Source" (see the 'Acculab' portion of this web page) to determine the sound power emitted by the item. This is the most common and economical method. 

In the direct method two processes may apply. For the hemianechoic method, the SPL is measured in every direction on a surface encompassing the test item. These measurements are then combined to compute the emitted sound power. For the reverberation room, the SPL is measured at several locations in the that room, then averaged. The sound power is computed from that average as:

PWL = SPL + 10Log(A)-C. 

A = absorption in the reverberation room, sabins or square meters.
C = 16.3 for A as sabins (square feet)
C = 6.2 for A in square meters. 

See ISO Technical Committee Web Site for acoustical measurement information. 

*** 2.11 What is the speed of sound in air & water  ?

**** AIR ****

A convenient formula for the speed of sound in air is 

c = 20*sqrt(273 + T), T in Centigrade and c in meters/sec 


c = 49*sqrt(459 + T), T in Fahrenheit and c in feet/sec 

The speed of sound in air at a temperature of 0 degrees C and 50% relative humidity is 331.6 m/s. The speed is proportional to the square root of absolute temperature and it is therefore about 12 m/s greater at 20 degrees C. The speed is nearly independent of frequency and atmospheric pressure but the resultant sound velocity relative to the ground may be substantially altered by wind velocity. 

A good approximation for the speed of sound in other gases at standard temperature and pressure can be obtained from 

    c = sqrt (gamma x P / rho) 

where gamma is the ratio of specific heats, P is 1.013E5 Pa and rho is the density. 

    **** WATER ****

The speed of sound in water is approximately 1500 m/s. It is possible to measure changes in ocean temperature by observing the resultant change in speed of sound over long distances. The speed of sound in an ocean is approximately: 

c = 1449.2 + 4.6T - 0.055T^2 + 0.00029T^3 + (1.34-0.01T)(S-35) + 0.016z 

T temperature in degrees Celsius, S salinity in parts per thousand
z is depth in meters 

See also CRC Handbook of Chemistry & Physics for some other substances and Dushaw & Worcester JASA (1993) 93, pp255-275 for sea water. 

*** 2.12 What is meant by loudness?

Loudness is the human impression of the strength of a sound. The loudness of a noise does not necessarily correlate with its sound level. Loudness level of any sound, in phons, is the decibel level of an equally loud 1kHz tone, heard binaurally by an otologically normal listener. Historically, it was with a little reluctance that a simple frequency weighting "sound level meter" was accepted as giving a satisfactory approximation to loudness. The ear senses noise on a different basis than simple energy summation, and this can lead to discrepancy between the loudness of certain repetitive sounds and their sound level. 

A 10dB sound level increase is perceived to be about "twice as loud" in many cases. The sone is a unit of comparative loudness with 

0.5 sone = 30 phons,

  1 sone = 40 phons,

 2 sones = 50 phons,

 4 sones = 60 phons etc.
The sone "10dB rule" is inappropriate at very low and high sound levels where human subjective perception does not follow it. 

Loudness level calculations take account of "masking" - the process by which the audibility of one sound is reduced due to the presence of another at a close frequency. The redundancy principles of masking are applied in digital audio broadcasting (DAB), leading to a considerable saving in bandwidth with no perceptible loss in quality. 

3] Vibration

*** 3.1 What is vibration?

When something moves periodically about a static position it can be said to vibrate. Examples of unwanted vibration are the movement of a building near a railway line when a train passes, or the vibration of the floor caused by a washing machine or spin dryer. Floor vibration can be reduced with vibration isolators, sometimes at the risk of increased machinery vibration and subsequent deterioration. 

*** 3.2 How is vibration measured?

Vibration is often measured with an accelerometer. This is a device that is securely attached to the surface under investigation. The accelerometer produces an electrical charge proportional to the surface acceleration, which is then amplified by a charge amplifier and recorded or observed with a meter. The frequencies of interest are generally lower than sound, and range from below 1 Hz to about 1 kHz. 

It is sometimes more useful to know the vibrational velocity or displacement. Often, moving coil transducers are used to directly measure vibrational velocity. A single integration of that signal provides a measure of displacement. 

If only an accelerometer is available, it is necessary to integrate the acceleration signal once for velocity and twice for displacement. If the vibration is sinusoidal at a known frequency, f, then an integration is calculated by dividing the original by 2 x pi x f (noting that there is also an associated phase change). 

Example: A machine is vibrating sinusoidally at 79.6 Hz with an rms acceleration of 10 m/s^2. 

Its rms velocity is therefore 10/(2 x pi x 79.6) = 20 mm/s
Its rms displacement is 10/(4 x pi^2 x 79.6^2) = 0.04 mm 

The final result may also be expressed in terms of zero-to-peak, which is found as the square root of two [sqrt(2)] times the rms value. The peak-to-peak value is twice again that. 

Thus, one has three measures (acceleration, velocity, displacement) and three scales (rms, 0-p, p-p) totalling nine possible explicit measures of one and the same vibration. Couple that with three possible directions (E-W, N-S, up-down) one faces 27 separate possible values... and then there are inches, mils, microns and millimeters... Needless to say, one must be eternally vigilant and explicit in their vibration measurement and reporting nomenclature! 

*** 3.3 How is vibration isolated or controlled?

Vibration problems are solved by considering the system as a number of connected springs and masses with damping. The vibration source is included within, e.g. the engine of a motor car, or the environment on which this assembly is mounted is presumed to vibrate, e.g. a scanning electron microscope. 

If the vibration is produced by a motor inside a machine, it is necessary that the natural frequency of the supporting system is well below frequency of motor oscillations (the forcing frequency). This is achieved by increasing the mass or decreasing the stiffness of the system as appropriate. 

The method of vibration isolation is demonstrated with a weight held from a rubber band. If the band is moved up and down very slowly the suspended weight will move by the same amount. At resonance the weight will move much more and possibly in the opposite direction. But as the frequency of vertical movement is further increased, the weight will become almost stationary. Springs are more often used in compression than intension. 


Intuitive attempts to reduce vibration from machinery can sometimes instead aggravate the problem. This is especially true when care was originally taken to minimize vibration at the time of design, manufacture and installation. 

Another method of vibration control is to cancel the forces involved using a Dynamic Vibration Absorber. Here an additional "tuned" mass-spring combination is added so that it exerts a force equal and opposite to the unwanted vibration. They are only appropriate when the vibration is of a fixed frequency. 

Recently, "Active Vibration Control", using techniques akin to Active Noise Control has evolved. This senses the unwanted vibration of a structural member to produce a reversed phase signal to drive a transducer attached to the same member to counter the motion. In that way, for instance, the vibration of rolling wheels of a vehicle is prevented from being transmitted into the body of that vehicle through the chassis

*** 3.4 What is Seismic (Earthquake) protection?  Earthquates can produce vertical and sidewise vibrations up tp perhaps one G or more, though it is usually much less. The immedaite concerns can be divided into two categories,"operating, basic earthwuake" (OBE) and "safe shutdown earthquake" (SSE). OBE protection seeks to have equipment operate during and survive an earthquake. SSE protection merely assures that equipment that shuts down dring an earthquake will survive to be used another day. Unfortunately, the amount of vibration items experience in a bulding can be worsened by that building, the higher in the building, the worse the vibration amplitude, since the elasticity of the joists and columns act as springs, only to resonate  with the masses supported at anywhere from 5 Hz to 15 Hz. The best place to be is in the basement, on bedrock.  Equipment bolted to the floor and walls ("hard-mounted"), survive best, provided the bolts, walls or floor do not break. Equipent mounted on isolator springs are particulaly vulnerable since those soft isolators easily allow the equipment to sway due to the earthqauke, only to suddenly crash into the spreing stops or nearby objects. Special seismic isolator springs containing soft stops (like the rubber stops accompanying automobile suspension springs) that cushion the impact.

4] Architectural & Building Acoustics

*** 4.1 What is reverberation time?

The time for sound in a room to decay 60 decibels. Scientific work on room acoustics was pioneered by Wallace Clement Sabine 1868-1919 (see his Collected Papers on Acoustics, 1922). The reverberation time, T, is defined as the time taken for sound energy to decay in a room by a factor of one million  in energy (60 dB). It is dependent on the room volume and the total amount of sound absorption contained in the room. In metric units 

                              0.161 x room Volume

          T =  ----------------------------------------------

               sum of Surface areas x absorption coefficients
In US English units, dimensions are in feet and the constant is 0.049. 

*** 4.2 What is the sound absorption coefficient?

The absorption coefficient of a material is ideally the fraction of the randomly incident sound power which is absorbed, or otherwise not reflected. It is standard practice to measure the coefficient at the preferred octave frequencies over the range of at least 125Hz - 4kHz. 

It can be determined on small material samples with an "impedance tube" or on large samples in a laboratory "reverberation room". The impedance tube evaluates sound absorption at normal incidence only, and produces absorption values that are sightly lower than those found in the reverberation room where the "Sabine coefficient" is measured over a wide range of incidence angles. 

For the purposes of architectural design, the Sabine coefficient is preferred, though the normal incidence absorption may be used in the absence of any other information. Interestingly some absorbent materials are found to have a Sabine coefficient in excess of unity at higher frequencies. This is due to diffraction effects. Where this occurs the value can be taken at face value for small material patches and as 1.0 for very large absorbers (entire walls). The Odeon computer program includes a file of absorption coefficients. 

*** 4.3 What is the difference between sound absorption & sound insulation ?

There is often confusion between sound insulation and sound absorption. 

Sound is absorbed when it encounters a material which will convert some or all of it into heat, or which allows it to pass through not to return. For this reason good sound absorbers do not of themselves make good sound insulators. Sound insulators rarely absorb sound. Sound absorbers contribute little to sound insulation. They are treated separately in sound control design. 

Sound insulation prevents sound from traveling from one place to another, such as between apartments in a building, or to reduce unwanted external noise inside a concert hall. Heavy materials like concrete are the most effective materials for sound insulation - doubling the mass per unit area of a wall will improve its insulation by about 6dB. It is possible to achieve good insulation over most of the audio frequency range with less mass by instead using a double leaf partition (two independent walls separated by an airgap filed with a sound absorber). 

*** 4.4 How is sound insulation measured?

////The measurement method depends on the particular situation. There are standards for the measurement of the insulation of materials in the laboratory, and for a number of different field circumstances. Usually 

Test procedures (e.g. ASTM E-90 in the lab and E336 in the field) generate a loud and consistent broadband spectrum of steady noise on one side of a partition or specimen of the material under test, then measure the amount of this sound that passes through that material. The ratio of the incident sound to the transmitted sound is the "noise reduction", usually expressed as 10 time the logarithm of this ratio. If the noise reduction is also corrected for the amount of sound absorption to be found in the receiving room, 10 times the logarithm of the corrected ratio is called the "transmission loss. This is performed for 1/3 octave bands of noise from 100 to 4000 Hz. 

A single-number rating of that range of noise reductions or transmission losses van be had by fitting them to a segmented curve. 

In North America, this procedure is ASTM E413. The fitted range is from 125-4000 Hz. The value of that curve at 500 Hz is called the Noise Isolation Class (NIC) or Sound Transmission Class (STC) respectively. Internationally, ISO140-3 produces the noise reduction and transmission loss data in the same way. But the single number rating is according to ISO 717 which uses data in the 100-3150 Hz range. This single number rating is called "R'" and "R" respectively. 

Similar methods are applied to impact ("footfall") noise (a problem in multifamily residential buildings). A standard tapping machine is used to hammer on the floor, lightly and steadily at the rate of 10 taps per second. The sound pressure level in the room below are measured. ASTM E492 and ISO 140-4 and 717 apply. (See ASTM e-33 Web Site .) 

*** 4.5 How do I improve the noise insulation of my house/dwelling?

This is one of the most commonly asked questions of noise consultants. Firstly you should consider whether it is noise insulation or sound absorption (see 4.3) that is really required. Sound insulation is most often asked for in order to keep out unwanted noise, but is occasionally requested for the purpose of minimizing disturbance to others. 

The method of noise insulation will depend on the exact situation; generalities are extremely difficult to devise. Situations are more often than not unique, depending on the nature of the building infrastructure that the architect or his informal successors have devised. More often than not, successful noise isolation improvement requires the advice of a competent and experiences person and at an early stage of the renovation. The following ideas may serve as initial guidelines. 

When the noise is from an external source such as a main road it may be possible, if planning authorities permit, to screen with a noise barrier. These can be effective providing that the direct line of sight between traffic and house is concealed by the barrier. 

The weak point for sound transmission to and from a building is most often via the windows. Double glazing will usually afford noticeably better protection than single glazing, but in areas of high external noise it might be preferable to have double windows with a large air gap (25 to 100 mm) and acoustic absorbent material on the perimeter reveal around that gap. For a few people, the resultant lower room background noise level can make noise transmitted through party walls more apparent. The fitting of new windows may reduce the level of air ventilation, and it will be vital to compensate for this, if necessary with by improving the noise insulation of certain party walls. 

Noise through party walls can be reduced by the addition of a false wall. This is constructed from a layer of sound insulating material, commonly plasterboard, separated from the party wall by a large void containing acoustic quilting. The false wall must not be connected to the party wall because that would allow sound transmission paths. The quality of construction is an important consideration if optimal levels of attenuation are desired. It is advisable to contact an independent noise consultant before allowing any building works to commence. 

*** 4.5 How does acoustics affect classrooms and meeting rooms?

This question is less common, but now known to be a significant factor in modern public education. Basically, the degree that we hear well in a room depends on the background noise level and the reverberation of sound in that room. An example of a good listening environment is outdoors in a quiet back yard in the country . Here, the background noise level can be as low as 35 dBA and the reverberation time will be  a tiny fraction of a second, if any. A class or meeting of 20 to 30 persons will proceed quite well, the group acting in harmony most if not all of the time. Reparte` vital to learning can be rapid and 2-way.
/////recompose the following
The weak point for sound transmission to and from a building is most often via the windows. Double glazing will usually afford noticeably better protection than single glazing, but in areas of high external noise it might be preferable to have double windows with a large air gap (25 to 100 mm) and acoustic absorbent material on the perimeter reveal around that gap. For a few people, the resultant lower room background noise level can make noise transmitted through party walls more apparent. The fitting of new windows may reduce the level of air ventilation, and it will be vital to compensate for this, if necessary with by improving the noise insulation of certain party walls. 

Noise through party walls can be reduced by the addition of a false wall. This is constructed from a layer of sound insulating material, commonly plasterboard, separated from the party wall by a large void containing acoustic quilting. The false wall must not be connected to the party wall because that would allow sound transmission paths. The quality of construction is an important consideration if optimal levels of attenuation are desired. It is advisable to contact an independent noise consultant before allowing any building works to commence. 

6] Miscellaneous Questions

*** 6.1 What is active noise control?

ANC is an electronic method of reducing or removing unwanted sound by the production of a pressure wave of equal amplitude but opposite sign to the unwanted sound. When the electronically produced inverse wave is added to original unwanted sound the result is nil sound at that location. 

This method of noise control is sometimes considered a "cure-all" for noise problems. But this is not the case. Noise cancellation in 3D spaces such as living areas is difficult to impossible to achieve. However it can be more successful locally, e.g. for a passenger sitting in an aircraft or car. Many institutions world wide are developing technology to increase the circumstances where ANC can be effective. The award winning "Active Noise Control FAQ" is maintained by Chris Ruckman and available at a number of sites worldwide including:

*** 6.2 What causes a sonic boom?

(from "Aircraft Noise" by Michael T Smith, Cambridge, 1989) 

" .. When the speed of an aircraft is supersonic, the pressure waves cannot get away ahead of the aircraft as their natural speed is slower than that of the aircraft. Slower, in this context, means just over 1200 km/hr at sea level and about 10% less at normal cruising altitude. Because they cannot get away, the pressure disturbances coalesce and lag behind the airplane, which is in effect travelling at the apex of a conical shock wave. The main shock wave is generated by the extreme nose of the airplane, but ancillary shocks are generated by all the major fuselage discontinuities. .. " 

Ken Plotkin ( on 24th July 1995 wrote: 

[snip] .. A body moving through the air pushes the air aside. Small disturbances move away at the speed of sound. Disturbances from a slowly moving body go out in circles, like ripples from a pebble in a pond. If the body moves faster, the circles are closer in the direction of travel. If the body is supersonic, then the circles overlap. The envelope of circles forms a cone. The vertex angle of the cone is determined by its vertex moving in the travel direction of, and with the speed of the body, while the circles grow at the sound speed. [snip] The existence of the "Mach cone", "Mach waves" and the corresponding angle, was discovered by Ernst Mach in the nineteenth century. [snip] 

*** 6.3 Can you focus sound?

Sound can be focused like light, but in the case of sound the "optics" must be much larger because you are dealing with longer wavelengths. This effect is heard in some domed buildings such as the Capitol in Washington, and St. Paul's Cathedral in London providing noise background conditions permit. 

Large parabolic reflectors 1/2 meter or more in diameter can be used to send and receive sound over significant distances. Your local science museum or exploratorium may have a demonstration of this method. It is also possible to refract and focus sound with an "acoustical lens. The lens is constructed from parallel plates which locally decrease the speed of sound. Also, a large thin bubble, say 2 metres across, filled with carbon dioxide will focus sound. The effect is not very pronounced. 

Sound can be directed by assembling several loudspeakers in an organized array. See "Acoustics" by Leo Beranek, 1954 and 1986, pp 93-115. This principle is used in column speakers, and commercial systems for reducing noise levels outside the dance floor area of discos. 

*** 6.4 What is sonoluminescence?

In the early 1930s Frenzel and Schultes discovered that photographic plates became "fogged" when submerged in water exposed to high frequency sound. More recent experiments have succeeded in suspending a single luminous pulsating bubble in a standing wave acoustic field, visible in an undarkened room. Generally sonoluminescence is light emission from small cavitating bubbles of air or other gas in water or other fluids, produced when the fluid is acted upon by intense high frequency sound waves. The mechanism is not completely understood, but very high pressures and temperatures are thought to be produced at the center of the collapsing bubbles. 

See "Science" 14 October 1994 page 233, "Scientific American" (International Edition) February 1995 Page 32 or "Physics Today" September 1994 Page 22, all quite readable articles. 

See also the following URLs:

James Davison ( on 28th June 1995 wrote: 

[snip] .. I have been sufficiently interested to reconstruct the apparatus for producing this effect -- using a pair of piezoelectric transducers, an old oscilloscope and a signal wave generator -- materials costing only a few hundred dollars. 

I am proud to say that tonight I managed to reproduce this effect -- the tiny bubble has the appearance of a tiny blue star trapped in the middle of the flask. It is distinctly visible to the unadapted eye in a dark room, and it is a very startling thing to see. [snip] 

*** 6.5 Why does blowing over a bottle make a note?

Resonance in acoustics occurs when some mass-spring combination is supplied with energy. Many musical instruments rely on air resonance to improve their sonority. If you blow across the mouth of a bottle you can often get a note. The bottle behaves as a Helmholtz resonator. The main volume of air inside the bottle is analogous to a spring, whilst the "plug" of air in the neck acts as an attached mass. The resonant frequency is roughly given by: 

f = { c sqrt (S/LV) } / 2pi 

c is velocity of sound
S is the surface area of the neck opening
V is bottle volume
L is the effective length of the neck i.e. the actual length plus ends correction. Ends correction ~ 1.5 times radius of neck opening 

Example: A 75 cl (7.5E-4 m^3, approx. a "fifth") sized wine bottle with neck diameter 19 mm, bottle neck length 8 cm, air temp = 20 degrees C. The calculated resonant frequency is 109Hz, actual resonance was 105Hz. 

Helmholtz resonators are sometimes employed as a means of passive noise control in air conditioning ducts. They may also be hidden in the wall design of auditoria and offices in order to improve the acoustics. 

*** 6.6 What is pitch?

The term "pitch" has both a subjective and an objective sense. Concert pitch is an objective term corresponding to the frequency of a musical note A (at present 440Hz). Using such a standard will define the pitch of every other note on a particular musical scale. For example, with Equal Temperament each semi-tone is higher or lower in frequency than the previous semi-tone by a factor of 2^(1/12). An octave is a pitch interval of 2:1. Many sounds with no obvious tonal prominence are considered by musicians to be of indeterminate pitch; for example, the side drum, cymbals, triangle, castanets, tambourine, and the spoken word. 

Pitch is also a subjective frequency ordering of sounds. Perceived pitch is dependent on frequency, waveform and amplitude or changing amplitude. Numbers can be assigned to perceived pitch relative to a pure frontal tone of 1000Hz at 40dB (1000 mels) thereby establishing a pitch scale. 

*** 6.7 What are musical intervals?

An interval is the fractional frequency ratio between musical notes. 

The ratio of frequency intervals for Just Intonation is demonstrated below in the scale of C major, though the same ratios apply to all the major keys: 

C <- Octave

The interval between E & F and between B & C is a semi-tone, whilst the other intervals are tones. The interval between any two notes above can be found by multiplying the intervening ratios; thus if all the above ratios are multiplied together the resultant is 2 because an octave is twice the original frequency. 

Intervals are also sequentially labeled; the interval. For instance, in the scale of C major: C D E F G A B C, the note 'E' is the third note of the scale and the interval from C to E is therefore called a third. For the scale D major: D E F# G A B C# D, the third will be F#. The term 'interval' can also be used to indicate that the notes are sounded together, in which case there are consonant intervals and dissonant intervals. 

The notes of minor scales differ from their major counterparts; one important difference being the flattened third. E flat is a minor third above the note C. 

The use of Just Temperament causes serious problems of intonation when music modulates between keys. Equal Temperament is nearly always used as a compromise to the problem of tuning (see question 6.6). 

See The Oxford Companion to Music, Percy A Scholes, "interval". 

*** 6.8 What causes "helium voice"?

Many people, on hearing the voice of someone who has breathed helium, believe that the person's speech pitch has increased. 

WARNING - Breathing helium can be very dangerous.

A cavity will have certain resonant frequencies. These frequencies depend on the shape and size of the cavity and on the velocity of sound within the cavity. Human vocal cords vibrate impulsively (pulse rate is the voice fundamental) in the vocal tract, generating a range of frequencies above that fundamental. The vocal tract and cavities enhances various frequency components imparting the recognizable voice spectrum. 

The velocity of sound in helium is more than twice that in air. The characteristic resonant frequencies of the vocal tract cavities will be raised in that ratio. The mechanical resonant frequency of any solid or fleshy tract component will not be altered by helium, but the result of the higher resonance frequency of the several vocal tract cavities is to alter substantially the relative amplitudes of the voice spectrum components and harmonics thus leading to a significant voice timbre change and also an apparent pitch change. 

*** 6.9 What is structural acoustics?

Structural acoustics is concerned with the coupled dynamic response of elastic structures in contact with non-flowing fluids into which vibrations or sound is consequentially emitted. Conversely, sound in the fluid can excite vibrations in the structure. 

The fluid, although non-flowing, undergoes small-amplitude vibration relative to some equilibrium position.) For heavy fluids like water, the coupling is two-way, since the structural response is influenced by the fluid response, and vice versa. For lighter fluids like air, the coupling may be either one-way (where the structural vibration affects the fluid response, but not vice versa) or two-way (as occurs, for example, in the violin. 

Structural acoustics problems of interest involving water include the vibration of submerged structures, acoustic radiation from mechanically excited, submerged, elastic structures; acoustic scattering from submerged, elastic structures (e.g., sonar echoes); acoustic cavity analysis; and dynamics of fluid-filled elastic piping systems. These problems are of interest for both time-harmonic (sinusoidal) and general time-dependent (transient) excitations. Water hammer in pipes can be thought of as a transient structural acoustics problem. 

Structural acoustics problems of interest involving the air medium include determining and reducing noise levels in automobile and airplane cabins. 

Reference (for simple geometry problems): "Sound, Structures, and Their Interaction," Second Edition, by M.C. Junger and D. Feit, MIT Press, Cambridge, Mass (1986). 

*** 6.10 What is the doppler effect?

When a sound source is moving, a stationary observer will hear a frequency that differs from that which is produced by the source. The doppler effect will be noticed as a marked drop in pitch when a vehicle passes at high speed. An interesting fact is that doppler for any straight line movement always sweeps down in pitch! 

If one approaches a sound source by moving toward it with a velocity, v, the frequency of the sound heard is F=Fo(c+v)/c, where Fo is the emitted sound frequency, c is the speed of sound in still air and v is the speed of the observer or the moving source. if one moves away from a sound source, the sign of v is reversed. 

But for an approaching sound source, the frequency of the sound heard is F=Fo*c/(c-v). For a receding source the sign of the velocity, v, term is reversed. 

The speed of sound in air is approximately 340 m/s (see 2.11). 

Example 1: A sound source, S, emits 1000 waves per second (1 kHz) and is moving directly towards an observer, O, at a speed of 100 metres per second (equivalent to approximately 225 miles per hour). 

After 1 second the wave front, which is travelling at the speed of sound, will have travelled 340 metres from the original source position. Also after that second the sound source will have moved 100 metres towards the observer. 

  0 m                                            340 m

S |     |     |     |     |     |     |     |     |          O

  <--------------  1000 waves   ------------------>

                 100 m                           340 m

                S |   |   |   |   |   |   |   |   |          O

                  <-------  1000 waves   --------->
Therefore the same number of waves will occupy a space of 340-100 = 240 metres and the wavelength will be 240/1000 = 0.24 metres. To the observer the frequency heard will be the speed of sound divided by its wavelength = 340/0.24 = 1416.7 Hz. 

Example 2: An observer moving at 100 metres per second directly approaches a stationary sound source, S, which is emitting 1000 waves per second (1 kHz). In this example there is no change in wavelength. In one second, the observer will hear the number of waves emitted per second plus the number of waves which s/he has passed in the time (1000+100/0.34) = 1294.1 Hz. 

Note the interesting result - a stationary observer with moving source will not hear the same frequency as a would a moving observer with a stationary source. 

Interesting corollaries are that if one is confined to movement velocities equal to or less than the speed of sound, on approaching a sound source, one will observe frequencies up to only twice the radiating frequency, but if one is stationary and approached by a sound source, there is no upper frequency limit. 

Thought teaser: Apply these principles to light, aether, red shift and quasars. What would cause a "blue shift"? 

*** 6.11 What is white noise, pink noise?

The power spectral density of white noise is independent of frequency. There is the same amount of energy within any two different but identically sized frequency intervals. E.g. 84-86Hz and 543-545Hz. A narrow band FFT analysis of white noise will show as flat. However octave band analysis will show the level to rise by 3dB per octave because each band has twice the frequency range of the preceding octave. 

Pink noise is produced by filtering white noise to have the same power within each octave. Narrow band analysis will show a fall in level with increasing frequency, but third-octave band or octave band analysis results will be "flat". 

see Joseph S. Wisniewski's Colors of noise FAQ at:-

*** 6.12 When should stranded wire be used for audio cables in a PA system? What is the "electrical skin effect"?

Q:Tim <> wrote: When should solid core or stranded audio cables be used in the public addressing system that broadcasts an audio with sound bandwidth 7kHz? Any reasons for the choice? 

A: Art Ludwig - - provided the following answer and analysis: 

For higher audio frequencies, the "skin effect" in practical conductors forces the current to be close to the surface. This increases the effective resistance of that wire. The "Skin depth" - for planar geometry and wire diameters much larger than this depth - is where the ac current diminishes to 1/e of the surface value. Round wire conductors should be less than three times that planar skin depth in diameter for there to be a "small" effect. 

One way to circumvent the problem is to use stranded wire, each stand insulated from the other and woven in a special pattern that varies the radius and thus the magnetic linkage. This is called "Litz wire". 

Audio designers may bundle several smaller gauge insulated wires, stranded or solid, to form a larger capacity conductor with minimal skin effect. Also, thinner or stranded wire has a nice flexibility and workability. 

The skin depth, delta, is given by: delta = a/sqrt(f) where delta is in meters, f in Hertz. The constant, a, is .0642 for silver, .0660 for copper, .0826 for aluminum, .127 for brass, and .185 for a representative solder. My reference is "Fields and Waves in Communications Electronics," Ramo, Whinnery, and Van Duzer, Wiley, 1965, page 289. 

It is important to note that for a wire diameter comparable to the skin depth, The current does not fall off nearly as rapidly as for the planar case. The Bessel function solution must be used to get reasonable accuracy. >From the same reference, define T=sqrt(2/j)/delta. The current in a cylindrical conductor is proportional to J0(Tr) where J0 is the Bessel function of order zero, and r is the radius. For a wire 3.2 skin depths in diameter, the current at the skin deoth is 73% that at the surface, and it is not much lower at the center. (For a planar surface, current at the skin depth is only 37% of that at the surface and drops further with depth.) The table below indicates the increase of resistance and inductance caused by the skin effect for a single strand of solid copper wire 20,000 Hz. The values of resistance and inductive reactance are given as fractions of the DC resistance. The results are a function of the wire radius in skin-depths, so the results can be scaled to other frequencies by scaling the diameter by sqrt(20000/freq) 

AWG    diameter(in.)   Resistance Ratio   Inductive Reactance Ratio 

 8      .1285            2.02                       1.72

10      .1019            1.65                       1.34

12      .0808            1.35                       1.00

14      .0641            1.17                        .70

16      .0508            1.07                        .46

18      .0403            1.03                        .30    
(Ed. Notes: 1-Lowering the frequency increases the effective diameter at which each ratio cited applies. Viz the 18 gauge 20 kHz effect would be the same for a wire of diameter 0.0641 (14 gauge) at 8 kHz.) 

2-From the cefficient, a, it is apparent that: Silver conductors will perform about the same as copper conductors. The skin depth is about 25% greater in aluminum (0.0826 vs 0.0660) so that for instance the relative skin effect in #12 aluminum wire is the same as in #14 copper wire. For brass and solder, the skin depth is double that of copper or silver.) 

Art Ludwig concludes with: "Litz wire - a bundle of woven insulated wires - is designed to reduce the skin effect. Ordinary stranded wire will not help since the wire strands are in electrical contact and tend to stay at the same radius from the center. 

"My web site contains a Glossary including entries on skin effect and Litz wire, in addition to other sound data. The address is 

"A Matlab program is available (Requires Matlab 5) for computing skin depth effects, current density, effective resistance, etc., etc. for cylindrical copper wires of any diameter and at any frequency. Easily changed for other conductors. It is available on request from . 


A-Weighting 2.4 2.12 8.1 8.2
absorption coefficient 4.1 4.2
accelerometer 3.1
acoustic energy 2.1 2.8 2.10 4.1 4.3
Acoustical Society of America 2.4
active noise control 6.1
active vibration control 3.3
addition of sound 2.5
air absorption 2.9
ANC 6.1
atmospheric attenuation 2.9
atmospheric pressure 2.1 2.11
audibility 2.1 2.12
auralization 1.3
C-Weighting 8.2
column speaker 6.3
concert pitch 6.6
dB(A) 2.4 8.1
decibel (dB) 2.2 2.3 2.4
Doppler effect 6.10
dynamic vibration absorber 3.3
ear 2.1 2.2 2.6 2.7
elastic structures 6.9
equal temperament 6.6 6.7
equivalent continuous sound level 2.4
focusing sound 6.3
frequency 2.1 2.4 2.12 6.6 6.7
hearing conservation 2.7
hearing damage 2.6 2.7
Helmholtz resonator 6.5
historical notes 2.4 2.12
insulation 4.3 4.4 4.5
interference 6.3
interval (music) 6.6 6.7
inverse square law 2.9
just intonation 6.7
Leq 2.4
logarithmic scale 2.2 2.3
loudness 2.1 2.2 2.12
loudspeaker 2.1 6.3
longitudinal wave 2.1
Lw 2.10
major and minor keys 6.7
masking 2.12
mel 6.6
musical scale 6.6 6.7
ocean sound velocity 2.11
octave 6.6 6.10
PA cable 6.12
pascal 2.1 2.2 2.8
passive noise control 6.1 6.5
peak level 2.3
phon 2.12
physical constants
Pierce, George W 2.4
pink noise 6.11
pitch 6.6 6.8
resonance 6.5 6.8
reverberation time 4.1
Sabine, Wallace C 4.1
semi-tone 6.6 6.7
skin effect 6.12
sone 2.12
sonic boom 6.2
sonoluminescence 6.4
sound 2.1
sound absorption 4.1 4.2 4.3
sound cancellation 6.1
sound decay 2.9
sound insulation 4.3 4.4 4.5
sound intensity 2.2 2.8
sound intensity meter 2.8
sound level 2.4 2.5 2.12
sound level meter 2.3 2.4 2.8 2.12
sound power level 2.10
sound pressure 2.1 2.2
sound pressure level 2.3 2.4 2.5
speech 6.6 6.8
speaker 2.1 6.3
speed of sound 2.1 2.11 6.8 6.11
structural acoustics 6.9
supersonic 6.2
tapping machine 4.4
third-octave band 8.2
tinnitus 2.6 2.7
U-Weighting 8.2
ultrasound 2.9
ultrasound scans 2.7
velocity of sound 2.1 2.11 6.8 6.10
vibration & Seismic (3.4) 2.1 2.7 3.1 3.2
vibration control 3.3
voice 6.6 6.8
wave 2.1
weighting 2.4 2.12 8.1
white finger 2.7
white noise 6.11

8] Weighting Tables

*** 8.1 A-Weighting

A-Weighting can be found from the following formulae 

For A-Weighting: A(f) = 

                              12200^2 f^4


(f^2 +20.6^2) (f^2 +12200^2) (f^2 +107.7^2)^0.5 (f^2 +737.9^2)^0.5
The weighting in dB relative to 1000Hz is now given by 

          20 lg -------        where  A(1000) = 0.794

It is convenient to list A-Weighting at nominal octave or 1/3-octave ("third-octave") frequencies, for example 1250 Hz or 2500 Hz. Ideally weightings should be calculated for the exact frequencies which may be determined from the formula 1000 x 10^(n/10), where n is a positive or negative integer. Thus the frequency shown as 1250 Hz is more precisely 1258.9 Hz etc. 

At these precise frequencies, the A- and C-Weighting values are as follows: 

*** 8.2 A, C & U Weighting Table (dB)

   Nominal         Exact

  Frequency      Frequency    A-Weight  C-Weight  U-Weight


     10             10.00     -70.4     -14.3       0.0

     12.5           12.59     -63.4     -11.2       0.0

     16             15.85     -56.7     - 8.5       0.0

     20             19.95     -50.5     - 6.2       0.0

     25             25.12     -44.7     - 4.4       0.0

     31.5           31.62     -39.4     - 3.0       0.0

     40             39.81     -34.6     - 2.0       0.0

     50             50.12     -30.2     - 1.3       0.0

     63             63.10     -26.2     - 0.8       0.0

     80             79.43     -22.5     - 0.5       0.0

    100            100.00     -19.1     - 0.3       0.0

    125            125.9      -16.1     - 0.2       0.0

    160            158.5      -13.4     - 0.1       0.0

    200            199.5      -10.9       0.0       0.0

    250            251.2      - 8.6       0.0       0.0

    315            316.2      - 6.6       0.0       0.0

    400            398.1      - 4.8       0.0       0.0

    500            501.2      - 3.2       0.0       0.0

    630            631.0      - 1.9       0.0       0.0

    800            794.3      - 0.8       0.0       0.0

   1000           1000.0        0.0       0.0       0.0

   1250           1259        + 0.6       0.0       0.0

   1600           1585        + 1.0     - 0.1       0.0

   2000           1995        + 1.2     - 0.2       0.0

   2500           2512        + 1.3     - 0.3       0.0

   3150           3162        + 1.2     - 0.5       0.0

   4000           3981        + 1.0     - 0.8       0.0

   5000           5012        + 0.5     - 1.3       0.0

   6300           6310        - 0.1     - 2.0       0.0

   8000           7943        - 1.1     - 3.0       0.0

  10000          10000        - 2.5     - 4.4       0.0

  12500          12590        - 4.3     - 6.2     - 2.8

  16000          15850        - 6.6     - 8.5     -13.0

  20000          19950        - 9.3     -11.2     -25.3

  25000          25120                            -37.6

  31500          31620                            -49.7

  40000          39810                            -61.8
* There is some reason to believe that a very low frequency rollover frequency of 4 Hz may be appropriate for instruments that are to be used to measure sound affecting humans. 

9] List of National Acoustical Societies

For standards organizations addresses see section 1.2 

Please let us know if any information in this list needs amending. 

Argentina Acoustical Association
Asociacion de Acusticos Argentinos
c/o Prof A. Mendez, Laboratorio de Acustica, Camino Centenario Y 506, 1897 - Gonnet, Argentina
Tel: +54 21 84 2686 Fax: +54 21 71 2721

Australian Acoustical Society
Private Bag 1, Darlinghurst, NSW 2010
Tel: +61 2 331 6920 Fax: +61 2 331 7296

Austrian Acoustics Association
c/o Prof Ewald Benes, Technische Universitat Wien, Institut fur
Allgemeine Physik, Wien, Austria
Tel: +43 1 58801-5587 Fax: +43 1 5864203

Belgian Acoutics Assosciation (ABAV)
Av. P Holoffe 21, 1342 Limelette, Belgium
Tel: +32 2 653 88 01 Fax: +32 2 653 07 29

Sociedade Brasileira de Acustica
Attn Prof Samir Gerges, Universidade Federal de Santa Catarina,
Departamento de Engenharia Mecanica, Campus Univeritario, C.P 476
CEP 88040-900, Florianopolis - SC, Brazil
Tel: +55 48 2344074 Fax: +55 48 2341519

Canadian Acoustical Association
PO Box 1351, Station F, Toronto, Ontario, M4Y 2V9, Canada
Tel: +1 514 343 7559 or +1 613 993 0102

Sociedad Chilena de Acustica
San Francisco # 1138, Santiago, Chile
. Tel/Fax: +56 2 555 63 66 or +56 2 551 79 20
e-mail: with copy (Cc) to:

China (PRC)
Acoustical Society of China
17 Zhongguancun St., Beijing 100080, China

Czech Republic
Czech Acoustical Society
Technicka 2, 166 27 Prague 6, Czech Republic.
Tel: +420 2 24352310 Fax: +420 2 3111786

Acoustical Society of Denmark
c/o Department of Acoustic Technology, Bldg. 352 - Technical University
of Denmark, DK-2800 Lyngby, Denmark
Tel: +45 4588 1622 Fax: +45 4588 0577

Acoustical Society of Finland
c/o Helsinki University of Technology, Acoustics Laboratory,
Otakaari 5 A, FIN-02150 Espoo, Finland
Tel: +358 9 451 2499 Fax: +358 9 460 224

French Acoustical Society
Societe Francaise d'Acoustique
23 avenue Brunetiere, 75017 Paris, France
Tel +33 1 48 88 90 59 Fax: +33 1 48 88 90 60

German Acoustical Society
Deutsche Gesellschaft fur Akustik
c/o Department of Physics Acoustics, University of Oldenburg,
D-26111 Oldenburg, Germany
Tel: +49 441 798 3572 Fax: +49 441 798 3698

Hellenic Acoustical Society
Patision 147, 112 51 Athens, Greece
Tel or Fax: +30 1 8646 065

Hong Kong
Hong Kong Institute of Acoustics
PO Box 7261
Hong Kong
Fax: +852 2886 3777

Scientific Society for Optics, Acoustics... (OPAKFI)
Fo utca 68, H-1027 Budapest, Hungary
Tel/Fax: +36 1 202 0452
e-mail (c/o Andras Illenyi):

Acoustical Society of India
c/o Dr S Agrawal, CEERI Centre, CSIR Complex, Hillside Road,
New Delhi-110012, India
Tel: +91 11 5784642
e-mail (c/o National Physical Lab):

Associazione Italiana di Acustica
Istituto di Acustica "O.M. Corbino"
Area della ricerca di Roma Tor Vergata
Via del Fosso del Cavaliere
00133 Roma Italy
Tel. +39 6 49934480 (ask Mrs. Cappelli)
Fax: +39 6 20660061

Acoustical Society of Japan
Nippon Onkyo Gakkai
4th Floor, Ikeda Building, 2-7-7 Yoyogi, Shibuya-ku, Tokyo, Japan
Tel: +81 3 3379 1200 Fax: +81 3 3379 1456

Korean Republic
The Acoustical Society of Korea,
c/o 302-B, The Korean Federation of Science and Technology,
635-4, Yeoksam-dong, Kangnam-gu, Seoul-city, 135-080, Rep. of Korea
Tel: +82 2 565 1625 Fax: +82 2 569 9717

Mexican Institute of Acoustics
Instituto Mexicano de Acustica
c/o Sergio Beristain, P.O. BOX 75805,
Col. Lindavista 07300 Mexico, D.F.
Tel +52 5 682 28 30 Fax: +52 5 523 47 42

Netherlands Acoustical Society
Nederlands Akoestisch Genootschap
Postbus 162, NL-2600 AD, Delft, Netherlands
Tel: +31 15 26 92 442 Fax: +31 15 26 92 111

New Zealand
New Zealand Acoustical Society
c/o J. Quedley, CPO Box 1181, Auckland, New Zealand
Tel: +64 9 623 3147 Fax: +64 9 623 3248

Acoustical Society of Norway
Norsk Akustisk Selskap
Sintef Telecom and Informatics, N-7034 Trondheim, Norway
Tel: +47 73 59 26 45 Fax: +47 73 59 14 12

Acoustical Society of Peru
Sociedad Peruana de Acustica
Garcilazo de la Vega 163, Salamanca de Monterrico, Lima 3, Peru
Tel: +51 1 4351151 Fax: +51 1 4675625

Polish Acoustical Society
Polskie Towarzystow Akustyki
Instytut Akustyki, Uniwersytet Adama Mikiewicz, ul J.Matejki 48/49,
60-769 Poznan, Poland
Tel or Fax: +48 61666 420

Portuguese Acoustical Society
SPA - CAPS/Instituto Superior Tecnico, Av. Rovisco Pais
1096 Lisboa CODEX, Portugal
tel: +351 1 841 9393/39 fax: +351 1 352 3014

Romanian Acoustical Society
Societatea Romana de Acustica
c/o Nicolae Enescu, Universitatea Politehnica Bucuresti,
Splaiul Independentei nr. 313, 77206 Bucuresti, Romania
Tel: +40 1 4101615 Fax: +40 1 4104488

East-European Acoustical Association (
44, Moskovskoe Shosse, Saint Petersburg, 196158, Russia
Fax: +7 (812) 1279323

Russian Acoustical Society
4 Shvernik ul, Moscow, 117036 Russia
Tel: +7 095 126 7401 Fax: +7 095 126 8411

Society of Acoustics Singapore
c/o W Gan, Acoustical Services Pte Ltd
209-212 Innovation Centre, NTU
Nanyang Ave, Singapore 639798
Fax +65 791 3665

Slovak Acoustical Society
c/o Prof Stefan Markus, Racianska 75, PO Box 95, 830 08 Bratislava 38,
Tel: +421 7 254751 Fax: +421 7 253301

South Africa
South African Acoustics Institute
c/o John R. Hassall
Acoustics, Noise and Vibration Consultancy
Tel: +27 11 403 1163

Spanish Acoustical Society
Sociedad Espanola de Acustica
Serrano 144, E-28006 Madrid, Spain
Tel: +34 1 5618806 Fax: +34 1 4117651

Swedish Acoustical Society
Svenska Akustiska Sallskapet
c/o Ingemansson AB, Box 47 321
S-100 74 Stockholm, Sweden
Tel: +46 8 744 5780 Fax: +46 8 18 26 78

Schweizerische Gesellschaft fur Akustique
Societe Suisse d'Acoustique
Postfach 251, 8600 Dubendorf
Tel: +41 1 823 4743 Fax: +41 1 823 4793

Turkish Acoustical Society - TAS
Y.T.U. Mimarlik Fakultesi
Yildiz, 80750, ISTANBUL/TURKEY
Tel: +90 212 259 70 70 ext: 2772
Fax: +90 212 26105 49

Institute of Acoustics
5 Holywell Hill, St Albans, Herts, AL1 1EU, UK
Tel: +44 1727 848195 Fax: +44 1727 850553

Acoustical Society of America
500 Sunnyside Blvd., Woodbury, NY 11797, USA
Tel: +1 516 576 2360 Fax: +1 516 576 2377

10] FAQ Contributors

Angelo Campanella*
Michael Carley
Gordon Everstine
Johan L Nielsen
Torben Poulsen
Larry Royster
Chris Ruckman
Asbjoern Saeboe
Jesper Sandvad
Andrew Silverman**

* Acoustics FAQ file Editor January 1998 ff
** Originator and original architect of this acoustics FAQ file! 

Last updated 23-Apr-2002.
Web Site by Point & Click Software, Inc.