This enhanced version of the Acoustical FAQ file is provided by CampanellaAcoustics.com,
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.
Aims:
- 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"?
7] KEY
WORD INDEX
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.
news:rec.audio.tech -
includes discussion on audio equipment, speakers etc. There are other rec.audio
groups which may be of interest.
news:alt.support.hearing-loss
and news:alt.support.tinnitus - 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
news:comp.sys.ibm.pc.soundcard.misc
- various discussion of use of internal sound cards in IBM compatible computers.
FAQs
The main archive site for all
usenet FAQs is ftp://rtfm.mit.edu/pub/usenet/
A list of mirror sites (including
html) for the Acoustics FAQ is at
http://extra.newsguy.com/~consult/Acoustics_FAQ_mirrors.html
The Active Noise Control FAQ
by Chris Ruckman is at http://www.xis.com/~ruckman/
The Tinnitus FAQ deals with a
range of hearing disorders. It is available at
http://www.cccd.edu/faq/tinnitus.html
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/rec.audio.*
directories
The comp.speech faq has information
on speech processing and some software links
http://www.speech.su.oz.au/comp.speech/
*** 1.2 What
World Wide Web sites are there?
http://www.ecgcorp.com/velav/
(virtual lib for acoustics &
vibration with useful links)
http://online.anu.edu.au/ITA/ACAT/drw/PPofM/INDEX.html
(simple acoustics introduction from
David Worrall)
http://www.mme.tcd.ie/~m.carley/Notes/
(theoretical basic acoustics lecture
notes; difficult stuff like the wave equation etc, in hypertext for browsing,
or gzipped Postscript format for downloading)
http://asa.aip.org/
(Acoustical Society of America home
page with several links and comprehensive career section, book lists and
Society info etc)
http://pcfarina.eng.unipr.it/
(Angelo Farina has published a variety
of papers - some are available in zipped MSWord format)
http://eaa.essex.ac.uk/eaa/
(European Acoustics Association)
http://users.aol.com/inceusa/ince.html
(Institute of Noise Control Engineering
home page)
http://wssh.net/~wattsup/Audio%20related%20Site%20list.html
(Steve Ekblad's extensive audio
related BBS and Internet list)
http://www.techexpo.com/
(Technical societies, conferences
etc etc but not specifically acoustics related)
http://www.iso.ch/
(main ISO standards page)
http://www.iso.ch/addresse/membodies.html
(national standards organizations
addresses)
http://www.ansi.org/
(official ANSI site)
http://www.ds.dk/public/isotc43/default.htm
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.
http://www.ASTM.org/COMMIT/e-33.htm
American Society for Testing and
materials (ASTM) Committee E-33 "Environmental Acoustics".
Deals with all aspects of building
acoustics and some community noise measurements.
http://www.noisenet.org/Noise_home.htm
http://www.noisenet.org/Vibration_Introduction.htm
Some of the better search
engines:
http://www.infoseek.com/
http://altavista.digital.com/
http://www.dejanews.com/
(can also be used as Usenet posting gateway)
http://www.excite.com/
http://www.hotbot.com/
http://www.yahoo.com/
http://www.lycos.com/
or use your nearest Archie site
to look for files you want.
*** 1.3 What
acoustics software is available on the Net?
http://www.soundsoft.demon.co.uk
- 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:
ftp://ftp.simtel.net/pub/simtelnet/win95/sound/gram412.zip
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
http://www.cisab.indiana.edu/CSASAB/index.html
The programs listed are mainly for sound analysis and editing.
Some software is available for
audio systems design at URL
ftp://ftp.uu.net/usenet/rec.audio.high-end/Software
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 http://www.dat.dtu.dk/~odeon/index.html
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
www.netg.se/~catt
. (4-98 per Bengt-Inge Dalenback * Mariagatan 16A * S-41471
Gothenburg * SWEDEN catt@netg.se
* 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 http://users.aol.com/inceusa/books.html
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 (http://webcenter.ru/~eeaa/ejta/)
| 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;
peak>max>rms.
*** 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.
http://www.mankato.msus.edu/dept/comdis/kuster2/audiology.html
http://oto.wustl.edu/cochlea
ftp://rtfm.mit.edu/pub/usenet/news.answers/medicine/tinnitus-faq
*** 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
Lp=Lw-20logR-0.6
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:
http://www.point-and-click.com/campanella_acoustics/rssman.htm
)
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
or
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.
Important:-
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:
http://www.erols.com/ruckman/
*** 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 (kplotkin@access2.digex.net)
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:
http://ne43.ne.uiuc.edu/ans/sonolum.html
http://www.wdv.com/Sono
James Davison (TKGN58A@prodigy.com)
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
(9:8)
D
(10:9)
E
(16:15)
F
(9:8)
G
(10:9)
A
(9:8)
B
(16:15)
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:-
http://capella.dur.ac.uk/doug/noisecols13.txt
*** 6.12 When
should stranded wire be used for audio cables in a PA system? What is the
"electrical skin effect"?
Q:Tim <2207leung@hknet.com>
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 - aludwig@silcom.com
- 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 http://www.silcom.com/~aludwig
"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 aludwig@silcom.com .
7] INDEX
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
http://asa.aip.org/
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
http://oto.wustl.edu/cochlea/
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
http://www.globaldialog.com/~nhca/index.html
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
http://physics.nist.gov/PhysRefData/contents.html
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
A(f)
20 lg ------- where A(1000) = 0.794
A(1000)
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
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
e-mail:
ciclal@gba.gov.ar
Web:
http://www.eie.fceia.unr.edu.ar/~acustica/adaa/index.htm
LABORATORIO DE ACÚSTICA Y
ELECTROACÚSTICA:
http://www.eie.fceia.unr.edu.ar/~acustica/
Australia
Australian Acoustical Society
Private Bag 1, Darlinghurst, NSW
2010
Tel: +61 2 331 6920 Fax: +61 2 331
7296
Austria
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
Belgium
Belgian Acoutics Assosciation (ABAV)
Av. P Holoffe 21, 1342 Limelette,
Belgium
Tel: +32 2 653 88 01 Fax: +32 2
653 07 29
e-mail:
bbri.lim@pophost.eunet.be
Brazil
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
e-mail:
gerges@mbox1.ufsc.br
Canada
Canadian Acoustical Association
PO Box 1351, Station F, Toronto,
Ontario, M4Y 2V9, Canada
Tel: +1 514 343 7559 or +1 613 993
0102
Chile
Sociedad Chilena de Acustica
San Francisco # 1138, Santiago,
Chile
. Tel/Fax: +56 2 555 63 66 or +56
2 551 79 20
e-mail: acusticos@entelchile.net
with copy (Cc) to: crooke@cmet.net
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
e-mail:
csas@feld.cvut.cz
Denmark
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
e-mail:
atc.das@dat.dtu.dk
Finland
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
e-mail:
akustinen.seura@hut.fi
France
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
e-mail:
sfa@cal.enst.fr
Germany
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
e-mail:
dega@aku.physik.uni-oldenburg.de
Greece
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
e-mail:
hkioa@hk.super.net
Hungary
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):
illenyi@sparc.core.hu
India
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):
Agrawals%npl@sirnetd.ernet.in
Italy
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
E-mail:
aia@idac.rm.cnr.it
Japan
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
Mexico
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
e-mail:
SBERISTA@vmredipn.ipn.mx
Netherlands
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
e-mail:
nag@tpd.tno.nl
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
e-mail:
mms@bitz.co.nz
Norway
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
e-mail:
truls.gjestland@informatics.sintef.no
Peru
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
e-mail:
cjim@mail.cosapidata.com.pe
Poland
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
e-mail:
ula@phys.amu.edu.pl
Portugal
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
e-mail:
capsist@alfa.ist.utl.pt
Romania
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
e-mail:
enescu@cat.mec.pub.ro
Russia
East-European Acoustical Association (http://webcenter.ru/~eeaa/)
44, Moskovskoe Shosse, Saint Petersburg, 196158, Russia
Fax: +7 (812) 1279323
e-mail: eeaa@online.ru
Russian Acoustical Society
4 Shvernik ul, Moscow, 117036 Russia
Tel: +7 095 126 7401 Fax: +7 095
126 8411
e-mail:
bvp@asu.acoins.msk.su
Singapore
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
e-mail:
wsgan@singnet.com.sg
Slovakia
Slovak Acoustical Society
c/o Prof Stefan Markus, Racianska
75, PO Box 95, 830 08 Bratislava 38,
Slovakia
Tel: +421 7 254751 Fax: +421 7 253301
e-mail:
markus@umms.savba.sk
South Africa
South African Acoustics Institute
c/o John R. Hassall
Acoustics, Noise and Vibration Consultancy
Email:
jhassall@pixie.co.za
Tel: +27 11 403 1163
Spain
Spanish Acoustical Society
Sociedad Espanola de Acustica
Serrano 144, E-28006 Madrid, Spain
Tel: +34 1 5618806 Fax: +34 1 4117651
e-mail:
a.perezlopez@mad.servicom.es
Sweden
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
e-mail:
sas@ingemansson.se
Switzerland
Schweizerische Gesellschaft fur
Akustique
Societe Suisse d'Acoustique
Postfach 251, 8600 Dubendorf
Tel: +41 1 823 4743 Fax: +41 1 823
4793
e-mail:
kurt.heutschi@empa.ch
Turkey
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
e-mail:
takder@ana.cc.yildiz.edu.tr
UK
Institute of Acoustics
5 Holywell Hill, St Albans, Herts,
AL1 1EU, UK
Tel: +44 1727 848195 Fax: +44 1727
850553
e-mail:
Acoustics@clus1.ulcc.ac.uk
USA
Acoustical Society of America
500 Sunnyside Blvd., Woodbury, NY
11797, USA
Tel: +1 516 576 2360 Fax: +1 516
576 2377
e-mail:
asa@aip.org
10] FAQ Contributors
Angelo Campanella*
a.campanella@worldnet.att.net
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!
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