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Theproblemofmeasuringdistancesinairissomewhatdifferentfromotherproblemsinthea-pplicationofultrasound.Althoughthepossibilityofusingacousticrangingforthispurposehasbeenknownforalongtime,andatfirstglanceappearsverysimple,neverthelessatthepresenttimethereareonlyasmallnumberofdevelopmentsusingthismethodthataresuitableforpracticalpurposes.Themaindifficultyhereisinprovidingareliableacousticthree-dimensionalcontactwiththetestobjectduringseverechangesintheair'

scharacteristic.

Practicallyallacousticarrangementspresentlyknownforcheckingdistancesuseamethodofmeasuringthepropagationtimeforcertaininformationsamplesfromtheradiatortothereflectingmemberandback.

Theunmodulatedacoustic(ultrasonic)vibrationsradiatedbyatransducerarenotinthemselvesasourceofinformation.Inordertotransmitsomeinformationalcommunicationthatcanthenbeselectedatthereceivingendafterreflectionfromthetestmember,theradiatedvibrationsmustbemodulated.Inthiscasetheultrasonicvibrationsarethecarrieroftheinformationwhichliesinthemodulationsignal,i.e.,theyarethemeansforestablishingthespatialcontactbetweenthemeasuringinstrumentandtheobjectbeingmeasured.

Thisconclusion,however,doesnotmeanthattheanalysisandselectionofparametersforthecarriervibrationsisofminorimportance.Onthecontrary,thefrequencyofthecarriervibrationsislinkedinaveryclosemannerwiththecodingmethodfortheinformationalcommunication,withthepassbandofthereceivingandradiatingelementsintheapparatus,withthespatialcharacteristicsoftheultrasoniccommunicationchannel,andwiththemeasuringaccuracy.

Letusdwellonthequestionsofgeneralimportanceforultrasonicranginginair,namely:

onthechoiceofacarrierfrequencyandtheamountofacousticpowerreceived.

Ananalysisshowsthatwithconicaldirectivitydiagramsfortheradiatorandreceiver,andassumingthatthedistancebetweenradiatorandreceiverissubstantiallysmallerthanthedistancetotheobstacle,theamountofacousticpowerarrivingatthereceivingareaPrforthecaseofreflectionfromanidealplanesurfacelocatedatrightanglestotheacousticaxisofthetransducercomesto

 

wherePradistheamountofacousticpowerradiated,Bistheabsorptioncoefficientforaplanewaveinthemedium,Listhedistancebetweentheelectroacoustictransducerandthetestme-mber,disthediameteroftheradiator(receiver),assumingtheyareequal,andc~istheangleofthedirectivitydiagramfortheelectroacoustictransducerintheradiator.

BothinEq.

(1)andbelow,theabsorptioncoefficientisdependentontheamplitudeandnotontheintensityasinsomeworks[1],andthereforewethinkitnecessarytostressthisdifference.

Inthevariousproblemsofsoundrangingonthetestmembersofmachinesandstructures,therelationshipbetweenthesignalattenuationsduetotheabsorptionofaplanewaveandduetothegeometricalpropertiesofthesoundbeamare,asarule,quitedifferent.Itmustbepointedoutthatthechoiceofthegeometricalparametersforthebeaminspecificpracticalcasesisdictatedbytheshapeofthereflectingsurfaceanditsspatialdistortionrelativetosomeaverageposition.

Letusconsiderinmoredetailtherelationshipbetweenthegeometricandthepowerparametersofacousticbeamsforthemostcommoncasesofrangingonplaneandcylindricalstructuralmembers.

ItiswellknownthatthedirectionalcharacteristicWofacircularpistonvibratinginaninfinitebaffleisafunctionoftheratioofthepiston'

sdiametertothewavelengthd/λasfoundfromthefollowingexpression:

(2)

whereJlisaBesselfunctionofthefirstorderandαistheanglebetweenanormaltothepistonandalineprojectedfromthecenterofthepistontothepointofobservation(radiation).

FromEq.

(2)itisreadilyfoundthatatwo-to-onereductioninthesensitivityofaradiatorwithrespecttosoundpressurewilloccurattheangle

(3)

Foranglesα≤20.Eq.(3)canbesimplifiedto

(4)

wherecisthevelocityofsoundinthemedimaaandfisthefrequencyoftheradiatedvibrations.

ItfollowsfromEq.(4)thatwhenradiatingintoairwherec=330m/sec,thenecessarydiameteroftheradiatorforaspedfiedangleofthedirectivitydiagramatthe0.5levelofpressuretakenwithrespecttotheaxiscanbefoundtobe

(5)

wheredisincm,fisinkHz,andαisindegreesofangle.

CurvesareshowninFig.1plottedfromEq.(5)forsixanglesofaradiator'

sdirectivitydiagram.

Thedirectivitydiagrmneededforaradiatorisdictatedbythemaximumdistancetobemeasuredandbythespatialdispositionofthetestmemberrelativetotheotherstructuralmembers.Inordertoavoidtheincidenceofsignalsreflectedfromadjacentmembersontotheacousticreceiver,itisnecessarytoprovideasmallangleofdivergenceforthesoundbeamand,asfaraspossible,asmall-diameterradiator.Thesetworequirementsaremutuallyinconsistentsinceforagivenradiationfrequencyareductionofthebeam'

sdivergenceanglerequiresanincreasedradiatordiameter.

Infact,thediameterofthe"

sonicated"

spotiscontrolledbytwovariables,namely:

thediameteroftheradiatorandthedivergenceangleofthesoundbeam.Inthegeneralcasetheminimumdiameterofthe"

spotDminonaplanesurfacenormallydisposedtotheradiator'

saxisisgivenby

(6)

whereListheleastdistancetothetestsurface.

ThespecifiedvalueofDmincorrespondstoaradiatorwithadiameter

(7)

AsseenfromEqs.(,6)and(7),theminimumdiameterofthe"

sonieated"

spotatthemaximumrequireddistancecannotbelessthantworadiatordiameters.Naturally,withshorterdistancestotheobstaclethesizeofthe"

surfaceisless.

LetusconsiderthecaseofsoundrangingonacylindricallyshapedobjectofradiusR.TheproblemistomeasurethedistancefromtheelectroacoustictransducertothesidesurfaceofthecylinderwithitsvariouspossibledisplacementsalongtheXandYaxes.Thenecessaryangleαoftheradiator'

sdirectivitydiagramisgiveninthiscasebytheexpression

(8)

whereαisthevalueoftheangleforthedirectivitydiagram,Ymaxisthemaximumdisplacementofthecylinder'

scenterfromtheacousticaxis,andLministheminimumdistancefromthecenteroftheelectroacoustictransducertothereflectingsurfacemeasuredalongthestraightlineconnectingthecenterofthememberwiththecenterofthetransducer.

Itisclearthatwhenmeasuringdistance,the"

running"

timeoftheinformationsignaliscontrolledbythelengthofthepathinadirectionnormaltothecylinder'

ssurface,orinotherwords,themeasuredistanceisalwaystheshortestone.Thisstatementiscorrectforallcasesofspecularreflectionofthevibrationsfromthetestsurface.ThesimultaneoussolutionofEqs.

(2)and(8)whenW=0.5leadstothefollowingexpression:

(9)

Intheparticularcasewherethesoundrangingtakesplaceinairhavingc=330m/sec,andontheasstunptionthatLmin<

<

R,thenecessarydiameterofaunidirectionalpistonradiatordcanbefoundfromthefomula

(10)

wheredisincmandfisinkHz.

CurvesareshowninFig.2fordeterminingthenecessarydiameteroftheradiatorasafunctionoftheratioofthecylinder'

sradiustothemaximumdisplacementfromtheaxisforfourradiationfrequencies.AlsoshowninthisfigureisthedirectivitydiagramangleasafunctionofRandYrnaxforfourratiosofminimumdistancetoradius.

Theultrasonicabsorptioninairisthesecondfactorindeterminingtheresolutionofultrasonicrangingdevicesandtheirrangeofaction.Theresultsofphysicalinvestigationsconcerningthemeasurementofultrasonicvibrationsairaregivenin[1-3].Upuntilnowtherehasbeennounambiguousexplanationofthediscrepancybetweenthetheoreticalandexpe-rimentalabsorptionresultsforultrasonicvibrationsinair.Thus,forfrequenciesintheorderof50to60kHzatatemperatureof+25oCandarelativehumidityof37%theenergyabsorptioncoefficientforaplanewaveisabout2.5dB/mwhilethetheoreticalvalueis0.3dB/m.TheabsorptioncoefficientBasafunctionoffrequencyforatemperatureof+25oCandahumidityof37%accordingtothedatain[2]canbedescribedbyTable1.

Theabsorptioncoefficientdependsontherelativehumidity.Thus,forfrequenciesintheorderof10to20kHzthehighestvalueoftheabsorptioncoefficientoccursat20%humidity[3],andat40%humiditytheabsorptionisreducedbyabouttwotoone.Forfrequenciesintheorderof60kHzthemaximumabsorptionoccursat30.7ohumidity,droppingwhenitisincreasedto98%orloweredto10%byafactorofapproximatelyfourtoone.

Theairtemperaturealsohasanappreciableeffectontheultrasonicabsorption[1].Whenthetemperatureofthemediumisincreasedfrom+10to+30,theabsorptionforfrequenciesbetween

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