McGraw Hill Encyclopedia of Science & Technology

543 Pages·2007·15.75 MB·english

by  McGraw-Hill

S
S
Sorghum—Supramolecular chemistry
tall, late maturing, and generally unadapted. Since
Sorghum
itsintroductionintotheUnitedStates,thecrophas
Sorghum includes many widely cultivated grasses been altered in many ways, these changes coming
having a variety of names. Sorghum is known as asaresultofnaturallyoccurringgeneticmutations
guineacorninWestAfrica,KafircorninSouthAfrica, combinedwithhybridizationandselectionworkof
mtama in East Africa, and durra in the Sudan. In plantbreeders.Therapidexpansioninacreagecame
Indiasorghumsarecalledjuar,jowar,orcholam;in with the development of widely adapted varieties
China,kaoliang;andintheUnitedStates,milo.Culti- and later higher-yielding hybrids. The fact that hy-
vatedsorghumsintheUnitedStatesareclassifiedasa bridgrainsorghumswithhighyieldpotentialcould
singlespecies,Sorghumbicolor,althoughthereare be produced with stems that are short enough for
manyvarietiesandhybrids.Thetwomajortypesof harvestingmechanically(Fig.1)madethecropap-
sorghumarethegrain,ornonsaccharine,type,culti- pealingtomanyfarmers.
vatedforgrainproductionandtoalesserextentfor Grainsorghumisdifficulttodistinguishfromcorn
forage,andthesweet,orsaccharine,type,usedfor in its early growth stages, but at later stages it
forageproductionandformakingsyrupandsugar. becomes strikingly different. Sorghum plants may
tiller(putoutnewshoots),producingseveralhead-
GrainSorghum
bearing culms from the basal nodes. Secondary
GrainsorghumisgrownintheUnitedStateschiefly culmsmayalsodevelopfromnodalbudsalongthe
intheSouthwestandtheGreatPlains.Itisawarm-
season crop which withstands heat and moisture
stress better than most other crops, but extremely
high temperatures and extended drought may re-
duce yields. Sorghum responds well to optimum
growing conditions, fertility, and management to
produce large grain yields. It is extensively grown
inTexas,Kansas,Nebraska,Oklahoma,Missouri,Col-
orado,andSouthDakota.Thisgrainproductionisfed
to cattle, poultry, swine, and sheep primarily, with
lessthan2%goingintononagriculturalmarketssuch
asstarch,dextrins,flour,andindustrialpreparations.
Sorghumisconsiderednearlyequaltocorninfeed
value.
Originsanddescription. Sorghumsoriginatedinthe
northeastern quadrant of Africa. They have been
growninAfricaandAsiaformorethan2000years.
Introductionofasorghumcalledchickencornwas
made on the southern Atlantic coast in Colonial
American times, but it was not successfully culti-
vated.Thevarietyescapedandbecameaweed.Prac-
tically all grain sorghums of importance, until re-
Fig.1. DwarfgrainsorghumhybridsaregrownthroughoutthesorghumbeltoftheUnited
cent years, introduced into the United States were Statesbecausetheirshortstemsmakethemadaptabletomechanicalharvesting.
2 Sorghum
corn,andSudangrass)have10pairsofchromosomes
andfreelycross.
Varieties and hybrids. A combine-height grain
sorghumwasdevelopedbeforeWorldWarIbutwas
not accepted by farmers or agriculturalists. Accep-
tance of combine grain sorghums was stimulated
by the drought of the 1930s and by a farm labor
shortage during World War II. A number of widely
adapted productive varieties were developed dur-
ing this period. Nonetheless, varieties disappeared
rapidly when hybrids were introduced in the mid-
1950s(Fig.2).
The commercial production of seed of sorghum
hybridswasmadepossiblebythediscoveryofcyto-
plasmicmalesterilityintheearly1950s.Thistypeof
sterility,asusedincornandafewothercrops,pre-
ventsthedevelopmentofnormalpollengrainsand
makespossibletheformationofhybridseedbycross-
pollination.Becausetheflowersofsorghumareper-
fect,containingbothstaminate(male)andpistillate
(female)parts,theproductionofcommercialquanti-
tiesofhybridseedwasnotpossiblewithoutawork-
ablemale-sterilitymechanism.Thefirsthybridseed
inquantitywassoldtofarmersin1957,andwithina
periodoflessthan5yearshybridshadreplacedmost
ofthevarietiespreviouslygrown.Sorghumhybrids
yield at least 20% more than varieties, and concur-
rent improvements in cultural practices have com-
bined to boost per-acre yield over 50% since their
development.Theemphasisonresearchinfertiliza-
tion,irrigation,insectanddiseasecontrol,andother
areashasprovidedinformationtohelpaccountfor
theremarkableyieldandproductionincreasesover
theyears.
Throughaprocessofconversionmanyofthebest
varietiesfromaroundtheworldarebeingchanged
(a) (b) fromtall,late,unadaptedtypestoshort,early,very
useful cultivars. From this program plant breeders
Fig.2. Headsofgrainsorghum.(a)Typicalvariety.(b)Typicalhybrid. areexpandinggerm-plasmutilizationandaredevel-
oping parents of hybrids for the entire sorghum-
main stem. The inflorescence (head) varies from a producingworld.SeeBREEDING(PLANT).
densetoalaxpanicle,andthespikeletsproduceper- Planting. Grain sorghum seeds are small and
fectflowersthataresubjecttobothself-andcross- shouldnotbeplantedtoodeepsincesorghumlacks
fertilization.Theamountofnaturalcross-pollination thesoil-penetratingabilityofcorn.Aseedingdepth
rangesfrom25to0%butaveragesabout5%.Mature of 1 in. (2.5 cm) is acceptable in moist and friable
grain in different varieties varies in size and color soil, but 2 in. (5 cm) may be necessary under dry
from white to cream, red, and brown. Color pig- soilconditions.Theseedsareplantedeitherinrows
mentsarelocatedinthepericarp(outercovering)of wide enough for tractor cultivation or in narrower
thegrainorinalayerofcellsbeneaththepericarp rowsifcultivationisnotintended.Rowplantersfor
calledthetesta.Insomevarietiesthetestaisabsent; corn,cotton,fieldbeans,andsugarbeetsmaybeused
whenthetestaispresent,however,theseedcoloris whenequippedwiththeproperseedplates.When
brownorsomevariationofbrown.Theendosperm wheatfarmingispracticed,muchgrainsorghumis
(starchportionoftheseed)iseitherwhiteoryellow. planted with a grain drill with alternate or various
Thereareendospermmodificationswhichcausethe feeder holes plugged to provide the desired row
starchtobesugaryorwaxy,ortoprocessahigher spacing. Soil temperature largely determines when
lysine content. The texture of the endosperm may theseedshouldbeplanted,assumingsoilmoisture
vary from completely corneous to full floury. Most conditions are adequate. Being tropical in origin,
sorghumsareintermediateinendospermtexture. sorghum should not be planted in the spring until
◦ ◦
Grain sorghums are classified into types desig- soiltemperature is65–70F(18–22C)atthe plant-
nated as milo, kafir, feterita, hegari, durra, shallu, ing depth and until there is little chance of subse-
kaoliang,andzerazera.Thisclassificationisbasedon quentlowertemperatures.Dry-landgrainsorghumis
morphological rather than cytological differences, plantedatarateof3–5lb/acre(3.3–5.5kg/hectare),
since all types (including forage sorghums, broom- andtherateisincreasedupto10lb/acre(11kg/ha)
Sorghum 3
whenplantedundermorefavorablemoisturecondi- although its ancestry traces back to Egypt. It is an
tionsandirrigation. annual,ratherdrought-resistantcrop.Theculmsare
Cultivation. Goodseedbedpreparationisessential from2to15ft(0.6to4.6m)tall,andthehardcortical
forfullstandsandforweedcontrol.Tillingfieldsim- layer,orshell,enclosesasweet,juicypiththatisin-
proves soil structure in most cases and often aids terspersedwithvascularbundles.Ateachnodeboth
inwarmingthesoil.Arotaryhoeiseffectiveincon- aleafandalateralbudalternateonoppositesides;
trollingweedswhentheplantsaresmall.Subsequent theinternodesarealternatelygroovedononeside.
cultivationsaremadeasneededwiththesameequip- Leavesaresmoothwithglossyorwaxysurfacesand
ment used for cultivating corn. Minimum tillage is have margins with small, sharp, curved teeth. The
practicedinmanyareaswherecontrolofweedswith leavesfoldandrollupduringdrought.Theinflores-
chemicalsisapartofthetechnologyofsorghumpro- cence is a panicle of varying size having many pri-
duction.Whenusedcorrectly,herbicidesareaboon marybrancheswithpairedellipsoidalspikeletscon-
to sorghum culture, but when used carelessly, dis- tainingtwofloretsineachfertilesessilespikelet.The
appointmentmayresult.Thereareseveralchemical plantisself-pollinated.SeeCORTEX(PLANT);PITH.
herbicidesregisteredandapprovedforweedcontrol Seed is planted in cultivated rows and fertilized
insorghum. similarly to corn. Maturity varies between 90 and
Harvesting. Nearlyallgrainsorghumisharvested 125 days. The juice contains about 12% sugar. The
standinginthefieldwithacombine(Fig.1).Harvest mainsorghum-syrup-producingareaisinthesouth-
begins in southern Texas in early June and slowly centralandsoutheasternUnitedStates(Fig.3).
proceeds northward. In the central and northern LeonardD.Baver
GreatPlains,thecropisusuallyharvestedafterfrost.
Diseases
The grain threshes freely from the head when the
seedmoisturecontentis20–25%orlower.Thegrain Sorghums are plagued by a variety of diseases that
should not contain more than 12% moisture to en- varyinimportancefromyeartoyearandamongloca-
suresafestorageafterharvest.Graindryersareoften tionsbecauseoftheenvironment,plantgenotypes,
usedwhenthegrainatharvestisnotdryenoughfor culturalpractices,variationsinpathogens,orthein-
optimumstorage.Properstoragemustbemaintained teractionofanyofthesefactors.Thesediseasesmay
untilthegraincanbemarketed.Theindustry’seco- beclassifiedintofivegeneralcategories:thosethat
nomichealthliesintheabilitytoprovidegrainofthe rottheseedorinjureseedlingroots;thosethatattack
rightqualityintherightquantityatthepropertime theleaves,makingtheplantslessproductive;those
andplace. FrederickR.Miller that attack or destroy the grain in the heads; those
thatcauserootandstalkrots;andthosecausedby
SweetSorghum
virusesorviruslikeorganisms.
Commonlyknownassorgo,sweetsorghumwasin- Fungi causing seed rotting and seedling diseases
troduced into North America from China in 1850, may be seed-borne or soil-inhabiting and are most
destructiveafterplanting,whenthesoiliscoldand
wet.SpeciesofFusarium,Pythium,Helminthospo-
rium,andPenicilliumarethemostimportantfungi
involved. Damage may be considerably reduced by
plantingsoundhybridseedtreatedwithanapproved
fungicideinsoilwarmenoughtoensurepromptger-
mination.
Leafdiseasesarecausedbythreespeciesofbacte-
riaandatleasteightspeciesoffungi.Manyofthese
pathogensarefavoredbyhightemperaturesandhu-
midconditions,butafewarefavoredbycool,humid
conditions. Disease lesions occurring as discolored
spots or streaks may coalesce to involve the entire
leaf. Rotation, seed treatment, and the use of resis-
tantvarietiesarerecommendedcontrolmeasures.
Three of the four known smuts of sorghum are
foundintheUnitedStates;coveredkernel,looseker-
nel,andheadsmut.Kernelsmuts,whilehistorically
important,arenowcontrolledbyroutineseedtreat-
ments.Headsmut(Fig.4)destroystheentirehead
andcontinuestocausemajorcroplosses.Resistant
hybridsareprovidingcontrol,althoughnewstrains
of the fungus pathogen require the periodic devel-
opmentofnewresistanthybrids.
Sorghum downy mildew (Fig. 5) has spread
throughout the southern and central sorghum-
growing regions. Losses result when the disease
Fig.3. SweetsorghuminOklahoma.Thescaleindicates
feet.1ft=0.3m.(USDA) systemically invades the plant. Diseased plants are
4 Sound
barren.Fortunately,excellentresistancehasbeende-
velopedandused.
Maize dwarf mosaic, caused by an aphid-
transmitted virus, spread throughout the sorghum-
growingregionsduringthe1970s.Hosttolerancere-
duceslossescausedbythisprevalentdisease.Yellow
sorghumstunt,causedbyamycoplasmalikeorgan-
ism and transmitted by leafhoppers, rarely reaches
economicallysignificantproportions.
Several diseases of the roots and stalks are of
primary importance. Periconia root and crown
rot, which caused extensive damage to milo and
darso sorghums, is controlled by resistant vari-
eties. Pythium graminicola causes a major root
rot during periods of frequent rainfall in dryland
sorghums.Charcoalrot,mostevidentastheplantap-
proachesmaturityunderextremeconditionsofheat
or drought, causes shredding of the stalks and ex-
tensivelodging.Anthracnose,orredrot,developsin
susceptiblehybridsduringwetyears;plantslodgeat
thebaseofthepeduncle.Developmentofresistant
ortoleranthybridsappearstobetheonlyeffective
methodofcontrolofthestalkrotsifirrigationisnot
possible.
Fig.5. Sorghumdownymildew,aseriousfungusdisease
Grainmoldisadiseaseofmaturegraincausedby
thatsystematicallyinvadessorghumplants,causing
species of Fusarium and Curvularia. These fungi strippedleavesandbarrenstalks.
infect at the flowering stage and rot the seed as it
matures,particularlyduringwetweatheratharvest
time.SeePLANTPATHOLOGY. RichardA.Frederiksen
Bibliography. W. F. Bennett et al., Modern Grain
SorghumProduction,1990;H.Doggett,Sorghum,
1970;J.R.Quinby,SorghumImprovementandthe
GeneticsofGrowth,1974;J.S.WallandW.M.Ross,
Sorghum Production and Utilization, 1970;R. J.
Williams, R. A. Frederiksen, and G. D. Bengston,
Proceedings of the International Sorghum Dis-
ease Workshop,InternationalCropsResearchInsti-
tute for the Semi-Arid Tropics, Hyderabad, 1980;
R. J. Williams, R. A. Frederiksen, and J. C. Girard,
Sorghum and Pearl Millet Disease Identification
Handbook, International Crops Research Institute
fortheSemi-AridTropics,Inform.Bull.2,Hyderabad,
1978.
Sound
The mechanical excitation of an elastic medium.
Originally, sound was considered to be only that
which is heard. This admitted questions such as
whetherornotsoundwasgeneratedbytreesfalling
where no one could hear. A more mechanistic ap-
proachavoidsthesequestionsandalsoallowsacous-
tic disturbances too high in frequency (ultrasonic)
tobeheardortoolow(infrasonic)tobeclassedas
extensionsofthoseeventsthatcanbeheard.
A source of sound undergoes rapid changes of
shape, size, or position that disturb adjacent ele-
ments of the surrounding medium, causing them
to move about their equilibrium positions. These
Fig.4. Sorghumheadsmut,adiseasethatcompletelydestroysthenormalheadand
replacesitwithmassesofsmutspores. disturbances in turn are transmitted elastically to
Sound 5
neighboring elements. This chain of events propa- Harmonic waves. A most important plane wave,
gates to larger and larger distances, constituting a both conceptually and mathematically, is the
wave traveling through the medium. If the wave smoothlyoscillatingmonofrequencyplanewavede-
contains the appropriate range of frequencies and scribedbyEq.(4).TheamplitudeofthiswaveisP.
impinges on the ear, it generates the nerve im- (cid:3) (cid:1) (cid:2)(cid:4)
x
pulses that are perceived as hearing. SeeHEARING p=Pcos 2πf t− (4)
c
(HUMAN).
Thephase(argumentofthecosine)increaseswith
AcousticPressure
time, and at a point in space the cosine will pass
A sound wave compresses and dilates the mate- throughonefullcycleforeachincreaseinphaseof
rial elements it passes through, generating associ- 2π.TheperiodTrequiredforeachcyclemustthere-
ated pressure fluctuations. An appropriate sensor forebesuchthat2πfT=2π,orT=1/f,sothatf=1/T
(a microphone, for example) placed in the sound canbeidentifiedasthefrequencyofoscillationofthe
field will record a time-varying deviation from the pressure wave. During this period T, each portion
equilibriumpressurefoundatthatpointwithinthe of the waveform has advanced through a distance
fluid. The changing total pressure P measured will λ=cT,andthisdistanceλmustbethewavelength.
vary about the equilibrium pressure P0 by a small This gives the fundamental relation (5) between
amount called the acoustic pressure, p = P − P .
0
The SI unit of pressure is the pascal (Pa), equal λf =c (5)
to 1 newton per square meter (N/m2). Standard at-
mospheric pressure (14.7 lb/in.2) is approximately the frequency, wavelength, and speed of sound in
1bar=106dyne/cm2=105Pa.Foratypicalsound anymedium.Forexample,inairatroomtemperature
in air, the amplitude of the acoustic pressure may thespeedofsoundis343m/s(1125ft/s).Asoundof
be about 0.1 Pa (one-millionth of an atmosphere); frequency1kHz(1000cyclespersecond)willhave
mostsoundscauserelativelyslightperturbationsof a wavelength of λ = c/f = 343/1000 m = 0.34 m
thetotalpressure.SeeMICROPHONE;PRESSURE;PRES- (1.1 ft). Lower frequencies will have longer wave-
SUREMEASUREMENT;PRESSURETRANSDUCER;SOUND lengths: a sound of 100 Hz in air has a wavelength
PRESSURE. of 3.4 m (11 ft). For comparison, in fresh water at
room temperature the speed of sound is 1480 m/s
PlaneWaves
(4856 ft/s), and the wavelength of 1-kHz sound is
One of the more basic sound waves is the travel- nearly1.5m(5ft),almostfivetimesgreaterthanthe
ingplanewave.Thisisapressurewaveprogressing wavelengthforthesamefrequencyinair.
throughthemediuminonedirection,saythe+xdi- Because of many close analogies between sound
rection,withinfiniteextentintheyandzdirections. andelectricity,itisoftenconvenientinpracti√ceto
Atwo-dimensionalanalogisoceansurfadvancingto- definetheeffectivepressureamplitudeP =P/ 2in
e
wardaverylong,straight,andevenbeach.Thesurf awavesuchasthatofEq.(4).Similarly,thefrequency
lookslikealong,corrugatedsurfaceadvancinguni- is often represented by the angular frequency
formlytowardtheshorebutextendingtransversely ω=2πfandthewavelengthexpressedreciprocally
in a series of parallel peaks and troughs. A plane by the wave number k = 2π/λ. With these defini-
wave has acoustic pressure controlled by the one- tions,Eq.(4)couldbewrittenasEq. (6),andEq.(5)
dimensionalwaveequationincartesiancoordinates, asEq.(7).
Eq. (1). An appropriate solution to this equation is √
Eq.(2),withfanyfunctiondifferentiabletwicewith p= 2Pecos(ωt−kx) (6)
∂2p 1 ∂2p ω
∂x2 = c2 ∂t2 (1) k =c (7)
(cid:1) (cid:2)
x
p=f t− (2)
c SeeALTERNATING-CURRENTCIRCUITTHEORY.
respecttoxort.Thissolutionhasthepropertythat Transient and continuous waves. Monofrequency
theacousticpressurephasasinglevalueforallpairs wavesarethebuildingblocksformorecomplicated
ofxandtsuchthatthephase(t−x/c)isconstant. wavesthatareeithercontinuousortransientintime.
Atsomepointx andtimet ,theacousticpressurep Forexample,asawtoothcontinuouswavehasacous-
0 0
hasthevaluep =f(t −x /c).Astincreasesfromt tic pressure which, during each cycle, begins at
0 0 0 0
tpoost0iti+on(cid:2)xt,0t+he(cid:2)vxa,luwehpe0rwei(cid:2)llxmaonvde(cid:2)frotmarex0retloataednebwy wa ipthostitimivee)vtaoluaenPemgaax,tivdeecvraelausees−uPnmiafxoramtltyhe(liennedarolyf
Eq.(3).Solvingfor(cid:2)xintermsof(cid:2)tgives(cid:2)x/(cid:2)t=c, theperiodT,andthenjumpsinstantaneouslyback
tothepositivevalueP ,repeatingthiscycleindefi-
(x +(cid:2)x) x max
(t +(cid:2)t)− 0 =t − 0 (3) nitely.Itisadirectconsequenceofthewaveequation
0 c 0 c that this waveform can be described equivalently
so that the specific value p is translated through asaFouriersuperposition,orsummation,ofwaves
spacewithaspeedofpropa0gationc.Thus,cisthe p1+p2+p3+···,eachoftheformofEq.(8),where
(cid:3) (cid:1) (cid:2)(cid:4)
speed of sound of the wave. See WAVE (PHYSICS); 2 P x
WAVEEQUATION;WAVEMOTION. pn= π mnax sin 2πnf t− c (8)
6 Sound
thefundamentalfrequencyf=1/Tgivestherepeti- position.ThisisrelatedtothepressurebyNewton’s
tionrateofthewaveformandnhasintegervalues1, second law. With the neglect of some small non-
2,3,....Thewavesp constitutetheovertonesof linear and viscous terms, this law can be written
n
thewaveform.Inthiscasethefrequenciesnfofthe as Eq. (12), where ρ is the equilibrium density of
0
overtones are integer multiples of the fundamental −→
∂u
frequencyf,andtheovertonesaretermedharmon- ρ =−∇p (12)
o ∂t
ics.Anysignalthatisnonrepeatingorisnonzeroonly
withsomelimiteddurationoftimecanbewrittenas thefluidand∇ isthegradientoperator.SeeCALCU-
asummationofwavesthatarenotharmonicallyre- LUSOFVECTORS;FLUID-FLOWPRINCIPLES;NEWTON’S
latedor,intheextreme,anintegrationofwaveforms LAWSOFMOTION.
ofallfrequencies.Asanillustration,averysharppos- Foraone-dimensionalplanewavemovinginthe
itivepulseofpressuretravelinginthexdirectionand +x direction, the acoustic pressure p and particle
lastingforaninfinitesimallyshortdurationoftimeis speeduareproportionalandrelatedbyp/u=ρ c.
0
represented by the Dirac delta function δ(t − x/c). The product ρ c is a basic measure of the elastic
0
This function, which has unbounded value where propertiesofthefluidandiscalledthecharacteris-
t=x/candiszeroelsewhere,canbeexpressedasan ticimpedance.Thisisanindexoftheacoustic“hard-
integral,asinEq.(9).Theseconsiderationsshowthat ness”or“softness”ofafluidorsolid.(Thetermchar-
(cid:1) x(cid:2) (cid:5) ∞ (cid:3) (cid:1) x(cid:2)(cid:4) acteristicimpedanceisrestrictedtotheplane-wave
δ t− =2 cos 2πf t− df (9) valueofρ c;moregenerally,thetermspecificacous-
c c 0
0 ticimpedanceisused.)Somerepresentativevalues
astudyofmonofrequencysoundwavesissufficient ofthespeedofsound,thedensity,andthespecific
todealwithallsoundwaves,andthatthefundamen- acousticimpedancearegiveninTable1.Significant
talconceptsoffrequencyandwavelengthpermeate differencesamongthesequantitiesforgases,liquids,
allaspectsofsound.SeeFOURIERSERIESANDTRANS- andsolidsareevident.SeeACOUSTICIMPEDANCE.
FORMS; HARMONIC (PERIODIC PHENOMENA); NONSI- Because fluids cannot support shear (except for
NUSOIDALWAVEFORM;WAVEFORM. smalleffectsrelatedtoviscosity),theparticleveloc-
Standingwaves. Inmanysituations,soundisgen- ity of the fluid elements is parallel to the direction
erated in an enclosed space that traps the sound ofpropagationofthesoundwaveandthemotionis
withinorbetweenboundaries.Forexample,ifthere longitudinal. In contrast, solids can transmit shear-
is a boundary that causes the pressure wave given ingorbendingmotion—reeds,strings,drumheads,
byEq.(4)tobecompletelyreflectedbackonitself, tuningforks,andchimescanvibratetransversely.
then there is an additional wave given by Eq. (10),
DescriptionofSound
(cid:3) (cid:1) (cid:2)(cid:4)
x
p(cid:4)=Pcos 2πf t+ (10) Thecharacterizationofasoundisbasedprimarilyon
c
humanpsychologicalresponsestoit.Becauseofthe
whichrepresentsamonofrequencyplanewavetrav- nature of human perceptions, the correlations be-
elinginthe−xdirection.Thiswavecombineswith tweenbasicallysubjectiveevaluationssuchasloud-
theincidentwave,resultinginastandingwavewitha ness,pitch,andtimbreandmorephysicalqualities
pressuredependencep givenbyEq.(11).Thiskind suchasenergy,frequency,andfrequencyspectrum
T
(cid:6) (cid:7) aresubtleandnotnecessarilyuniversal.
2πx
p =p+p(cid:4)=2P cos cos(2πft) (11) Intensity, loudness, and the decibel. The strength
T λ
of a sound wave is described by its intensity I.
From basic physical principles, the instantaneous
of wave would be found within a sounding organ
rateatwhichenergyistransmittedbyasoundwave
pipeandisanalogoustoavibratingguitarstring.The
throughunitareaisgivenbytheproductofacous-
pressure waveform p is zero at positions x = λ/4,
T ticpressureandthecomponentofparticlevelocity
3λ/4,5λ/4,....Thesenodes(pressurenulls)occur
perpendiculartothearea.Thetimeaverageofthis
every half-wavelength in space. Midway between
quantityistheacousticintensity,asinEq.(13).Fora
themareantinodesatwhichthepressurewaveform (cid:5)
oscillates in time between its maximum and min- 1 t
I = pudt (13)
imum values of ±2P. More complicated standing t
0
wavescanbeformedfromwavestravelinginanum-
ber of directions. For example, vibrating panels or planemonofrequencytravelingwave,thisisgivenby
drumheadssupportstandingwavesintwodimen- Eq.(14)inthedirectionofpropagation.Ifallquanti-
sions, and steady tones in rooms can excite three- 1 P2 P 2
dimensionalstandingwaves.SeeVIBRATION. I = 2ρ c = ρec (14)
0 0
ParticleSpeedandDisplacement
tiesareexpressedinSIunits(pressureamplitudeor
Assoundpassesthroughafluid,thesmallfluidele- effective pressure amplitude in Pa, speed of sound
mentsaredisplacedfromtheirequilibriumrestposi- inm/s,anddensityinkg/m3),thentheintensitywill
tionsbythefluctuatingpressuregradients.Themo- beinwattspersquaremeter(W/m2).
tion of a fluid element is described by the particle Becauseofthewaythestrengthofasoundisper-
velocityu(cid:5)withwhichitmovesaboutitsequilibrium ceived, it has become conventional to specify the
Sound 7
∗∗
TABLE1.Density,speedofsound,andspecificacousticimpedanceinselectedmaterials
Gases Density(ρ0),kg/m3 Speedofsound(c),m/s
Air 1.21 343
Oxygen(0°C;32°F) 1.43 317
Hydrogen(0°C;32°F) 0.09 1,270
Liquids Density(ρ0),kg/m3 Speedofsound(c),m/s
Water 998 1,481
Seawater(13°C;55°F) 1,026 1,500
Ethylalcohol 790 1,150
Mercury 13,600 1,450
Glycerin 1,260 1,980
Specificacousticimpedance
Speedofsound(c),m/s (ρ0c),N.s/m3
Density(ρ0),
Solids kg/m3 bar bulk bar bulk
Aluminum 2,700 5,150 6,300 13.9 17.0
Brass 8,500 3,500 4,700 29.8 40.0
Lead 11,300 1,200 2,050 13.6 23.2
Steel 7,700 5,050 6,100 39.0 47.0
Glass 2,300 5,200 5,600 12.0 12.9
Lucite 1,200 1,800 2,650 2.2 3.2
Concrete 2,600 — 3,100 — 8.0
∗Temperature(cid:1)20°C(cid:1)68°Funlessotherwiseindicated.Pressure(cid:1)1atm(cid:1)101.3kPa(cid:1)14.7lbf/in.21kg/m3(cid:1)0.0624lbm/ft3;1m/s(cid:1)
3.281ft/s;1N .s/m3(cid:1)6.366(cid:2)10(cid:3)3lbf.s/ft3.
SOURCE:AfterL.E.Kinsleretal.,FundamentalsofAcoustics,3ded.,Wiley,1982.
intensity of sound in terms of a logarithmic scale teristicthatreducingthevolumeofrecordedmusic
with the (dimensionless) unit of the decibel (dB). causesittosoundthinortinny,lackingbothhighs
Anindividualwithunimpairedhearinghasathresh- andlowsoffrequency.SeeDECIBEL;LOUDNESS.
old of perception near 10−12 W/m2 between about Since most sound-measuring equipment detects
2and4kHz,thefrequencyrangeofgreatestsensi- acoustic pressure rather than intensity, it is conve-
tivity.Astheintensityofasoundoffixedfrequency nient to define an equivalent scale in terms of the
is increased, the subjective evaluation of loudness sound pressure level. Under the assumption that
alsoincreases,butnotproportionally.Rather,thelis- Eq. (14) is valid for most commonly encountered
tenertendstojudgethateverysuccessivedoubling sound fields, a reference effective pressure ampli-
oftheacousticintensitycorrespondstothesamein- tudeP =20micropascals(µPa)generatestherefer-
ref
crease in loudness. This is conveniently expressed enceintensityof10−12W/m2inair(atstandardtem-
by Eq. (15), where the logarithm is to base 10, I perature and pressure) and a sound pressure level
(cid:6) (cid:7) (SPL) can be defined by Eq. (16), where P is the
L =10log I (15) (cid:6) (cid:7) e
I Iref SPL=20log Pe (16)
P
ref
is the intensity of the sound field in W/m2, I is
ref
10−12 W/m2, and L is the intensity level in dB re effective pressure amplitude in µPa. The intensity
I
10−12W/m2.Onthisscale,theweakestsoundsthat level and sound-pressure level are usually taken as
can be perceived have an intensity level of 0 dB, identical,butthisisnotalwaystrue(theselevelsmay
normalconversationallevelsarearound60dB,and notbeequivalentforstandingwaves,forexample).
hearing can be damaged if exposed even for short Forunderwatersounds,thesoundpressurelevelis
timestolevelsaboveabout120dB.Everydoubling alsoexpressedbyEq.(16),butthereferenceeffec-
of the intensity increases the intensity level by 3 tivepressureisdefinedas1µPa.
dB. For sounds between about 500 Hz and 4 kHz, Frequencyandpitch. How “high” sound of a par-
theloudnessofthesoundisdoublediftheintensity ticularfrequencyappearstobeisdescribedbythe
levelincreasesabout9dB.Thisdoublingofloudness senseofpitch.Afewminuteswithafrequencygen-
correspondstoaboutaneightfoldincreaseininten- eratorandaloudspeakershowthatpitchisclosely
sity. For sounds lying higher than 4 kHz or lower relatedtothefrequency.Higherpitchcorresponds
than500Hz,thesensitivityoftheearisappreciably to higher frequency, with small influences depend-
lessened.Soundsatthesefrequencyextremesmust ing on loudness, duration, and the complexity of
havehigherthresholdintensitylevelsbeforetheycan thewaveform.Forthepuretones(monofrequency
beperceived,anddoublingoftheloudnessrequires sounds)encounteredmainlyinthelaboratory,pitch
smallerchangesintheintensitywiththeresultthatat andfrequencyarenotfoundtobeproportional.Dou-
higherlevelssoundsofequalintensitiestendtohave blingthefrequencylessthandoublesthepitch.For
moresimilarloudnesses.Itisbecauseofthischarac- themorecomplexwaveformsusuallyencountered,
8 Sound
however,thepresenceofharmonicsfavorsapropor- nonconsonantovertonespresent,dyingawayatdif-
tionalrelationshipbetweenpitchandfrequency.See ferentrates,sothatthesoundseemstoshiftinpitch
PITCH. and timbre, and may appear nonmusical or merely
Consonanceanddissonance. Twotonesgenerated noisetosome.Itistheabundanceofharmonicsand
together cannot be distinguished from each other overtones,thedistributionofintensityamongthem,
if their frequencies are the same. If their frequen- and how they preferentially die away in time that
ciesf and(slightlyhigher)f arenearlybutnotex- provide the subjective evaluation of the nature or
1 2
actlyidentical,theearwillperceiveaslowbeating, timbreofthesound.SeeMUSICALACOUSTICS.
hearing a single tone of slowly and regularly vary-
ing amplitude. The combination yields an equiva- PropagationofSound
lent signal given by Eq. (17), which is heard as a
Planewavesareaconsiderablesimplificationofan
(cid:8) (cid:9) (cid:8) (cid:9)
actualsoundfield.Thesoundradiatedfromasource
cos 2πf t +cos 2πf t
1 2 (suchasaloudspeaker,ahandclap,oravoice)must
(cid:6) (cid:7) (cid:6) (cid:7) spreadoutwardmuchlikethewideningcirclesfrom
=2cos 2πf2−f1 t cos 2πf2+f2 t (17) apebblethrownintoalake.
2 2 Sphericalwaves. Asimplemodelofthismorereal-
isticcaseisasphericalsourcevibratinguniformlyin
singletonehavingafrequencythatistheaverageof
alldirectionswithasinglefrequencyofmotion.The
the frequencies of the two individual tones and an
sound field must be spherically symmetric with an
amplitudethatvariesslowlyaccordingtothediffer-
amplitudethatdecreaseswithincreasingdistancer
ence of the two frequencies. As f increases more,
2 from the source, and the fluid elements must have
thebeatingwillquickenuntilitfirstbecomescoarse
particle velocities that are directed radially. A solu-
and unpleasant (dissonant) and then resolves into
tion of the wave equation with spherical symme-
twoseparatetonesofdifferentpitches.Withstillfur-
try describing this kind of motion for an outgoing
therincrease,asenseofbeatinganddissonancewill
monofrequencytravelingwaveisgivenbyEq.(18),
reappear,leadingintoablendingorconsonancethat
thenbreaksagainintobeatsanddissonance,andthe p= Acos(ωt−kr) (18)
wholecycleofeventsrepeats.Theseislandsofcon- r
sonancesurroundedbybeatinganddissonanceare
where ω = 2πf is the angular frequency and k =
attainedwhenevertheratioofthetwofrequencies
becomesthatofsmallintegers,f /f =1/1,2/1,3/2, 2π/λ the wave number. The pressure amplitude is
2 1
A/randdiminishesinverselywithdistancefromthe
4/3,....Thelargertheintegersintheratio,themore
source. If the spatially dependent pressure ampli-
subtletheeffectsbecome.SeeBEAT.
tudeisdefinedbyEq.(19),thentheintensityisstill
Frequency spectrum and timbre. Sounds can be
characterized by many subjective terms such as A
clean, nasal, edgy, brassy, or hollow. Each term at- P(r)= (19)
r
tempts to describe the nature of a complex wave-
formthatmaybeofveryshortorlongdurationand givenbyEq.(1√4),butwithPandPeinterpretedas
that consists of a superposition or combination of A/r and (A/r)/ 2, respectively. Thus, the intensity
a number of pure tones. The sound of a person’s fallsoffwithdistanceas1/r2.Thisisconsistentwith
whistlingorofafluteplayedsoftlyoftenhasapure, conservation of energy. The acoustic power sent
clean,butsomewhatdullquality.Thesesoundscon- throughasphereofradiusrsurroundingthesource
sistmainlyofapuretonewithfewornoharmonics. istheintensityofthewavemultipliedbythesurface
Asdescribedabove,complexrepetitivewaveforms area through which it passes. This yields 4πr2I =
are made up of a fundamental tone and a number 4πA2/(2ρ c),whichisindependentofr.
0
of harmonics whose frequencies are integer multi- Whiletheparticlevelocityforthiswaveisarela-
plesofthefundamentalfrequency.Blownorbowed tivelycomplicatedfunctionofr,atdistancesr(cid:1)λ
instruments such as flute, bowed violin, oboe, and theratiop/uapproachesρ c,thesameasforatrav-
0
trumpet provide good examples. Other sounds are elingplanewave.Further,inthislimitthesurfaces
transient, or nonrepetitive, and usually consist of a ofconstantphase,forwhich(t−r/c)hasconstant
fundamentalplusanumberofovertoneswhosefre- value,becomemoreandmoreplanar.Thus,atsuf-
quenciesarenotintegermultiplesofthelowest.Pi- ficient distances from the source a spherical wave
ano,tympani,cymbals,andpluckedviolingenerate becomesindistinguishablefromaplanewavewhen
thesekindsofsounds. viewedoverregionsofthespacewhosedimensions
Animportantfactoristhewayinwhichasound aresmallwithrespecttor.Thisasymptoticbehavior
commences.Whenachimeisstruck,thereisaclear allowsuseofthesimpleplane-waverelationshipsfor
sharponsetmuchlikeahammerhittingananvil;the manysituations.
higher overtones are quite short in duration, how- Directional waves. Not all sources radiate their
ever,andquicklydieout,leavingonlyafewnearly sound uniformly in all directions. When someone
harmonic lower overtones that give a clear sensa- isspeakinginanunconfinedspace,forexamplean
tionofpitch.Pluckingaguitarstringnearthebridge openfield,alistenercirclingthespeakerhearsthe
withafingernailyieldsasimilareffect.Agonggives voice most well defined when the speaker is fac-
averycompleximpressionbecausetherearemany ingthelistener.Thevoicelosesdefinitionwhenthe
Sound 9
speakerisfacingawayfromthelistener.Higherfre- isgivenapproximatelybyEq.(20).Thisequationis
quenciestendtobemorepronouncedinfrontofthe
Akd
speaker, whereas lower frequencies are perceived p= (cosθ) sin(ωt−kr) (20)
r
moreorlessuniformlyaroundthespeaker.
Dipolesource. Thefieldsradiatedbysourcesofmore validwhenthewavelengthofsoundismuchlarger
complicatedshapeandsizecanbecalculatedbycon- than the distance separating the sources (kd < 1)
sideringthecomplicatedsourceasbeingmadeupof and r is much larger than d. The amplitude of the
acollectionofsmallsphericalsources,eachradiat- pressureP(r)isgivenby(Akd/r)|cosθ|.Inanyfixed
ingapressurewavelikethatgivenbyEq.(18),and direction, the amplitude of the pressure falls off as
thenaddingthepressurefieldstogether.Asimpleex- 1/r, but at a fixed distance the pressure amplitude
ampleisthedipolesource,consistingoftwosmall ismodulatedindirectionby|cosθ|.Inthedirection
sources spaced very closely together and radiating θ = 0 (or θ = π radians), the two sources lie one
◦
180 outofphase,sothatoneisshrinkingastheother behindtheotherandthecancellationisleastcom-
is expanding, and vice versa. The two sources will plete. If θ = π/2, then the two sources lie side by
nearlycancelbecauseasoneisgeneratingapositive side and the cancellation is total. There is a nodal
pressure,theotherisgeneratinganegativepressure. surface,definedbytheplaneθ =π/2,exactlymid-
Becausethetwosourcesareslightlyseparated,how- waybetweenthetwosourcesandperpendicularto
ever,thefieldswillnotexactlycancel.Ifθisdefined thelinejoiningthem.
astheangleincludedbetweenthedesireddirection Ifthedistancedisnotsignificantlylessthanthe
inspaceandthelinejoiningthecentersofthetwo wavelength λ, then Eq. (20) is not accurate, and
(out-of-phase)sources,anddisthedistancebetween a more complicated expression, Eq. (21), must be
thetwosources,thenatlargedistancesrawayfrom (cid:6) (cid:7)
the pair (Fig. 1a) the total acoustic pressure field p=2 A sin 1 kdcosθ sin(ωt−kr) (21)
r 2
used.Thereisstillanodalsurfaceatθ =π/2,butif
kdislargeenoughtheremaybeadditionalnodalsur-
faces,eachaconeconcentricwiththelinejoining
θ r thesources,indirectionsgivenbyanglesθnsatisfy-
ingkdcosθ =2nπ withn=1,2,... (Fig.1b).
+ n
Generalized source. Generalizing from the above
showsthatthepressurefieldradiatedbyasourceof
arbitraryshapewillhaveanamplitudethatatlarge
d
distance can be written as the product of a func-
tionofrandafunctionofdirection,asinEq.(22).
−
(a) P(r,θ,φ)=Pax(r)H(θ,φ) (22)
Here,P (r)fallsoffas1/r,andH(θ,φ)isafunction
ax
θ onlyofdirectionandhasamaximumvalueof1.At
fixed distance r, the pressure amplitude has maxi-
mum value given by P (r), termed the axial pres-
ax
sureamplitude.ThedirectionforwhichH(θ,φ)has
itsmaximummagnitudeof1definestheacousticaxis
of the source. The acoustic axis may be a plane or
aseriesofsurfacesofconstantθ orφ,butoftenthe
acousticaxisisasingleline.Theratiooftheintensity
foundatdistancerinsomearbitrarydirectiongiven
byθ andφ tothevaluefoundatthesamedistance
on the acoustic axis is simply H2(θ,φ), and the ex-
pressionofthisasanintensitylevel,calledthebeam
patternb(θ,φ),isgivenbyEq.(23).Thedecibelvalue
b(θ,φ)=20logH(θ,φ) (23)
ofthebeampatternisthereductioninintensitylevel
inthatdirectioncomparedtothevalueontheacous-
ticaxis(atthesamedistancefromthesource).
Baffledpistonsource. Aloudspeakeroraholeinapar-
(b) titioncanberepresentedasabaffledpiston.Thisis
Fig.1. Pressurefieldofadipolesource.(a)Coordinatesθ aflat,circularsourceofradiusamountedonalarge,
andrusedtodescribethefield.Thedistancebetweenthe flat,rigidsurface,commonlycalledabaffle.Allpor-
componentsourcesisd.(b)Nodalsurfacesofthefield
tionsofthesourcemovetogetherwithuniformpar-
whenthedistancedissufficientlylargewithrespecttothe
wavelengthλ. ticlevelocitynormaltothebaffle.Itisconvenientto