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AcousticsShockVibrationSignalProcessingMarch2004Newsletter

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Aloha

IrecentlyacquiredaMarantzcassette recorder,whichIamusingtotakesomefield recordings. Beginningwiththisissue,Iwillbe presentingsomeofthisdata.

Theimageontherightisawindchimeinmy backyard. Itconsistsoffivehollowtubesthat behaveasfree-freebeamsintheengineering sense. Thewindchimesproduceadelightful melodyintheEscale,althoughthepresence ofadditionalfrequenciesrenderstheresulting soundassomewhatatonal.Thefirstarticle providesasoundandvibrationanalysisofthe chimes.

Thesecondarticlegivesasoundanalysisofa thunderstormthatoccurredovermyhometown earlierthismonth. Thestormwaswelcomed given that Arizona has had a drought for severalyears.

Ihopeyouenjoythearticles.Asalways,Iappreciateyourfeedback.

Sincerely,

FeatureArticles

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WindChimeSoundVibration page2

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TomIrvine

Email:

ThunderstormSounds page9

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WindChimeSoundVibration

byTom Irvine

History

Anumberofculturesthroughout history haveenjoyedthepleasingsoundsofwind bellsandwindchimes. Widespreaduseof windchimescanbetracedtoancientChina.

TheChinesebecameexcellentmetal workers,particularlyinrefiningiron,around theyear1000B.C. Theybeganproducing windbells atthistimeforritualceremonies.

TheuseofwindchimesspreadtoJapan around400B.C. TheJapaneseusedthese chimesinBuddhisttemples aswellasin homegardens.

TheJapaneseproducedabronzewindbell calleddotaku.Theylaterdevelopeda smallerandlighterwindchimecalledthe furin,whichweremadefromglass,metalor ceramics. Thefurinchimeswereoften handpainted.

Thewindchimesenjoyedbywestern culturestodayaretypicallymadefromrods ofvaryinglengthssuspendedfromarack. Thisdesignbecamepopularinthe19thcentury. Thisdesignispartlyduetoa musicianwhosoughttoimprovethetoneofthe bells he played in an orchestra. EntrepreneurialVictorians,rememberingthe Japanesefurin,popularizedthisdesign.

Author’sWindChime

Thewindchimemodelis“Cavernous Echoes”byMajestyBells,asshownonthe coverpage. The vendor’s brochure states that this is a five note wind chime hand- tuned to the scale of E. Thematerialis anodizedaluminum. Theouterdiameteris1.25inch. Thechimesarehollow,withawallthicknessof3/32inch. Theboundaryconditionisessentiallyfree-freeforvibrationcalculations. Theconditionisopen-openforacousticfrequency.

Thechimeshavethreewoodenparts,which arefromtoptobottom:thehead,thestriker, andthewindcatcher.

Experiment

Assume that the wind chimes have three types of possible responses as shown in Table1.Furthermore,eachtypehashigher modes. One of the objectives is to determine which modes type or types producethechimespleasingsound.The natural frequencies are calculated using textbookformulas.

Inaddition,thechimesalsohavearing frequency corresponding to a breathing mode. Thisfrequencyis50,540Hzforeach chime,sincethechimeshaveacommon diameter. Thisfrequencyiswellabovethe upperfrequencylimitof humanhearing, however.

Thewindchimeswereexcitedseparately usingthestriker.Theresultingresponses wereduetothebendingmodesineach case. Note that the bending mode is the only type in Table 1 that has non-integer harmonics, however. Inthis sense, wind chimesareatonal.

FrequencyResponse Data

TheresponsedataissummarizedinTable

2. Themusicalnoteisthenearestnoteto themeasuredfrequency.

Thesequence:E,F#,G#,A,B,represents thefirstfivetonesoftheEmajorscale. The complete E major scale contains this sequenceplusC#andD#.

The second natural frequency of each chimerepresentsanoteintheEscale,as showninTable2.

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Table1. WindChimeFundamentalFrequencies
Chime / Length
(inch) / Vibration
Bending
(Hz) / Vibration
Longitudinal
(Hz) / Acoustical
Longitudinal
(Hz)
1 / 34.69 / 238 / 2832 / 194
2 / 32.56 / 271 / 3017 / 207
3 / 30.69 / 305 / 3201 / 219
4 / 29.94 / 320 / 3281 / 225
5 / 28.19 / 361 / 3485 / 238
Table2. MeasuredFrequenciesandNearestMusicalNotes
Chime1 / Chime2 / Chime3 / Chime4 / Chime5
Freq
(Hz) / Note / Freq(Hz) / Note / Freq(Hz) / Note / Freq(Hz) / Note / Freq(Hz) / Note
244 / B / 278 / C / 312 / D / 330 / E / 371 / F#
663 / E / 753 / F# / 850 / G# / 890 / A / 1000 / B
1272 / D# / 1441 / F# / 1625 / G# / 1700 / G# / 3031 / F#
2050 / C / 2314 / D / 2600 / E / 2712 / D# / 4351 / C#

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Waterfallplotsforeachofthefivechimes aregiveninFigures1through5,respectively.

TheverticalaxisistheFouriertransform magnitude, which has an arbitrary scale factor. Eachaxisscaleislinear.

The corresponding frequencies for each chimearegivenintheaccompanyingtables. The calculated frequency is the bending frequency. Themeasuredfrequencieshave reasonably good agreement for the calculatedfrequencyforeachchime.

Thewaterfallplotsshowtherelative differenceinamplitudebetweenthevarious naturalfrequencieswithineachchime.

Theextenttowhicheachmodeisexcited dependsinpartontheimpactlocationofthe strikeragainstthechime.

Whetherthemanufacturerconsideredthecomplexityofnodallineswhendesigningthe strikerpositionisunclear.

Thewaterfallplotsalsoshowhowthe reverberationtimevariesbetweenthenatural frequencies. Thefundamentalfrequencyis thefrequencywiththelongestreverberation timeforeachchime.

Thepeakamplituderesponse,however,may occuratthesecondorthirdnaturalfrequency foragivenchime.

BendingMode Shapes

Ageometrymodelofchime1isshowninFigure6.

Thefirstthroughthirdbendingmodeshapes areshowninFigures7through9,respectively. Themodeshapesaregreatly exaggerated,withanarbitraryscalefactor.

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Figure1. Chime1SoundPressureWaterfallPlot

Table3. Chime1 NaturalFrequencies
Mode / Calculated
(Hz) / Measured
(Hz) / MusicalNote
1 / 238 / 244 / B
2 / 657 / 663 / E
3 / 1288 / 1272 / D#
4 / 2127 / 2050 / C

Thepeakamplituderesponseoccursatthethirdnaturalfrequency. Thefundamentalfrequencyhasamuchlongerreverberationtime,however.

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Figure2. Chime2SoundPressureWaterfallPlot

Table4. Chime2 NaturalFrequencies
Mode / Calculated
(Hz) / Measured
(Hz) / MusicalNote
1 / 271 / 278 / C
2 / 746 / 753 / F#
3 / 1462 / 1441 / F#
4 / 2414 / 2314 / D

Thefirstandsecondnaturalfrequenciesdominatetheresponse.

Figure3. Chime3SoundPressureWaterfallPlot

Table5. Chime3NaturalFrequencies
Mode / Calculated
(Hz) / Measured
(Hz) / MusicalNote
1 / 305 / 312 / D
2 / 840 / 850 / G#
3 / 1646 / 1625 / G#
4 / 2718 / 2600 / E

Thesecondnaturalfrequencyclearlyhasthehighestamplituderesponse.

Figure4. Chime4SoundPressureWaterfallPlot

Table6. Chime4NaturalFrequencies
Mode / Calculated
(Hz) / Measured
(Hz) / MusicalNote
1 / 320 / 330 / E
2 / 882 / 890 / A
3 / 1729 / 1700 / G#
4 / 2855 / 2712 / D#

Thesecondnaturalfrequencyclearlyhasthehighestamplituderesponse.

Figure5. Chime5SoundPressureWaterfallPlot

Table7. Chime5NaturalFrequencies
Mode / Calculated
(Hz) / Measured
(Hz) / MusicalNote
1 / 361 / 371 / F#
2 / 995 / 1000 / B
3 / 1950 / 3031 / F#
4 / 3221 / 4351 / C#

Thesecondnaturalfrequencyclearlyhasthehighestamplituderesponse,aswasthecasefortheprevioustwochimes.

Figure6. Chime1,UndeformedModel

Figure7. Chime1,FirstBendingMode

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Figure8. Chime1,SecondBendingMode

Figure9. Chime1,ThirdBendingMode

ThunderstormSounds

Figure1. HailontheAuthor’sFrontPorch

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Introduction

Lightningisadischargeofelectronsfrom cloudtocloud,orfromcloudtoground. Theelectrons strike adjacent air molecules. These violent collisions produceheatwhichrapidlyexpandsthe surroundingair. Theairtemperature maybenear50,000degreesFahrenheit

Furthermore, the air molecule expansion rate is greater than the speed of sound. The air molecules expand and then contract. This action produces shock waves, which are heard as a loud thunderingnoise. Theshockwavesmay beconsideredasasonicboomeffect.

Nearbylightningstrikesproducesthunder withaloudbutshortcrackingnoise.

Distantstrikesprovokealong,low rumble.For these strikes, the sound wavesreflectofftheground,tallbuildings,mountains,andclouds.Thisseriesofreflectionscausesarumblingsound.

Additionalrumblingnoiseoccursbecause soundisgeneratedfromallpointsalonga lightningbolt,whichmaybeaslongas1 mile, or 1.6 km. The sound waves originatingfromvariouspointsmayreach the observer at different times. The resultingdelaysdependinpartonthe geometryofthebolt. Thesoundfieldis furthercomplicatedbyanyforksinthe lightning.

Alllightningstrikesgeneratesound. The strikemaybesofaraway,however,that thesoundisattenuatedtoaninaudible levelbeforeitreachesanobserver.

Thunder Data

AbriefthunderandhailstormoccurredinMesa,Arizona,at6:30pm,onMarch4,2004.AwaterfallplotofarumblingthunderburstfromthisstormisshowninFigure2. Theamplitudeislinear,butthe scalefactorisarbitrary.

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Figure2. ThunderRumbling,SoundPressureWaterfallPlot

The waterfall plot shows that energy at lower frequencies tends to have a longer reverberationtimethantheenergyathigherfrequencies.

SOUNDPRESSURESPECTRALMAGNITUDE THUNDERRUMBLING

0.08

0.06

0.04

0.02

0

101001000

FREQUENCY(Hz)

Figure3. ThunderSoundPressure

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ThespectralfunctioninFigure3coversthecompletedurationofthethunder rumbling.Notethattherecordingsystemhadsomeroll-offbelow50Hz. Asignificantamountofthesoundoutputmayhavebeeninfrasound,below20Hz

which is the lowerfrequencylimit ofhuman hearing.Thehighestpeak occursat76Hz. Thesignificanceofthefrequencyremainsanareaforfuture investigation.

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SOUNDPRESSURESPECTRALMAGNITUDE-HAIL

250

200

150

100

50

0

1010010002000

FREQUENCY(Hz)

Figure4. HailSoundSpectra

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HailData

Thethunderandlightningwerefollowed byabriefhailstorm,showninFigure1. Thehailstoneswereaboutthesizeof marbles. Asoundspectralfunctionof thehailstormisshowninFigure4. The amplitudeisagainlinear,butthescale factorisarbitrary.

Thespectralpeaksbetween100Hzand300HzinFigure4maybelargelydueto theeffectofthehailstrikingthesheetmetalsurfacesoftheauthor’s1993Ford Taurus,which wasparkedinthe driveway.

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