O. E. Wagner, Wagner ResearchLaboralory,2645 SykesCreek Road, Bogue Biver,Oregon 97537
W-Waves and Plant Spacings
Abstract
W-waveshave charact€risticfrequenciesin plants. To se€ if branch patlerns mighl corelate with thes€ frequenciesbranch, twig, stem, and leaf spacings{er€ analyzedin a nunber of plants. The distributions of frequeneies (Hz) associated {irh spacings wer€ found to correlarecloseiywith a speclrum anallsis of actual frequenciesenitted b) planls. The distriburions appear to be frequency spectra of plant utilized W,saves.
Introduction
Earlier I reportedthe discovery W-waves of in plants(Wagnerl988a,b;l9B9).Evidence the for existence W-waves of consisted measured of elec, trical patterns, recorded oscillations, excitation behavior, and reflectionphenomena. Measured electricalpatterns appearedto indicate that present plantsand standing waves always are in may play a part in their physiology. Recorded oscillations are another feature that demon' stratedthe presence waves. of Evidenceindicated that the obsprved !raves werenot eleclromagnetil' (Wagner l9BBb; l9B9) but as they interacted weakly with charge it was possible to observe some of their effects with ordinary electrical measurement equipment. disturbed apparI the ent standing wave pattern in a tree at different l o c a t i o na n dd e t e r . t e d c i l l a t o rb e h a v i oc o m s os l r ing from two probesin the tree; a typical response upon disrurbingany standingwavepattern. The velocityof the wavesin the tree was found to be 90 + 6 cm/sec using pulsereflection (Wagner1988b). the evidence All pointed to the existence wavesin plants. of The presence standing of waves plantsled in (or to the ideathat nodes antinodes) may be likely places the growthof branches otherplant for or structures.To test this hypothesisseveralthousandbranchand other spacings plantswere on measured seeif the frequencydistributionsof to plant growth spacings would demonstrate discrete groups. Observation suchdiscrete of spacings would suggest that the growthspacings relatedto are the standingwavesalreadyobserved plants. in A s s u c hd i s c r e t e r o u p i n g s f s p a c i n g s e r e g o w f o u n dI a t t e m p t e do c o r r e l a t eh e f r e q u e n c i e s t t from a low frequency spectrum analyzer conn e c t e d o p r o b e sn p l a n l sw i t h t h e f r " q u e n c i e s t i 28 Northwest Science, Vol. 64, No. l, 1990
(Hz) calculated from observed plant growth spacings. Methods and Materials Measurement Spacings of Details the methodology electrical of of signal
measurements on trees and other plants were described earlier (Wagner l9BBa,b; 1989). The plants used in this study grew at an altitude near 460 m. Measurementsof plant growth spacings (i.e. distancesbetweenbranches,twigs, srens, or leaves) were taken with a rule calibrated in rnillineters and estimated to the nearest 0.1 mm. It is difficult to measure the spacings between branches, twigs, and leaves on branches accurately without good reference points. A few plants, such as big leaf maple (Acer macrophylln) with its bands at branch locations, syringa (Philadelphus sp.) or sweet corn (Zea mays saccarata), have distinct features which do provide good reference points. For consistency,appropriate rel-erencepoints were chosen in every case. Spacings between needles on conifers were omitted from these measurementsbpi"ausethe spacings are so small. While an attempt was made to take c a r e p r e s e n t a t i v r a n d o m s a m p l eo f s p a c i n g s o s that a distribution would be typical of the spacings from a particular speciesof plant, the spacings of branches on tree trunks were ignored because there were relatively few branches per tree. The data recordedwere spacingsbetween: (l) twigs and small brancheson one young (approx. 5 m) white fir (l6ies concolor); (2) lower branches of three (approx. 30 m) white fir trees; (3) leaves and stems on several prickly lettuce (,Lactzco serriola) plants; (4) twigs, mostly from lower branches,on two young Douglas"fir trees (Rezdotsuga menziesii) (9 m) growing in the open
(emphasizing nelv but completed growth); (5) twigs on another young Douglas-fir(B m) grow(6) ing in semishade; lower branchesof 5 approximately l5 m ponderosa pines(Pinusponderosa) growing in a clump with other trees; (?) leaves and brancheson one bigleaf maple,cut down for (8) easyaccess; leavesand brancheson one small (approx.4 m) Oregot ash(Fraxinus LatifoLia); (9) leaves and branches one syringashrub;(10) on joints on many stalksof sreet corn;(l l) leaves and branches some lower branchesof two on deliciousapple trees(Pyrus Malus sp-);ar'd(12) leaves and branchesfrom four different Concord grape (Yitus labrusca) vlnes. No attempt was made to obtain all the spacingsfrom any particular tree or other plant exceptin the caseof prickly lettuce. The plant growth spacingswere analyzedto seeif rhey clusteredinto discrete groupings by taking the frequency distributions of the measured spacings using I mm intervals. Spacing mostly appearedto be discrete(Figure l). Each spacingin the twelvesetsof dala abovewasthen convertedto a frequencyin Hz by dividing a W(see wavespeed 96 cm/sec twice the spacing of by (96 data analysis), cm/sec waswithin the previously rneasured wave speed of 90 + 6 cm/sec (Wagnerl988a.b)). The number of spacings in each0.1 Hz interval (bin) wasplotted againstfrequency in Hz for each set of data to make the l2 graphs Figures of 2-5.By converting spacings to frequency(Hz) and taking the distribution I couldcompare frequencies derivedfrom growth spacingsdirectly with frequencies found from Any correlationbetween spectrumanalysis. these frequencies would tend to indicate the W-waves with their wavepatternswere involvedin setting plant growth spacings. did not attemptto verify I if an existing branch spacingpattern correlated with the iz sir& standing wavepattern in a particular plant as I assumed that the standingwave pattern slowly changesas the plant grows (see Wagner 1988b). Measurementof W-wave Frequencies Direcl measurements the frequencyspectrum of of electrical signals(Figures6 and 7) were recorded on a frequency spectrum analyzer (Schlumberger l20l) by placing probesin the plants(Wagnerl9BBa,b; l9B9).Concernfor possible 60 Hz interferenceled to testingthe analyzer far away from 60 Hz sourcesbut the same ap-
Figxre I . Spacing distributions o{ (A) 536 branch and leaf spacingsfron the lo{er branchesof two delicious apple trees, (B) 429 spacings from the lower branche! of five ponderosapine rrees(approx. l5 m hish), and (C)s02leafand branchspacinssfrom Concord grape rines. The interyal used in taking the distribuiions was 0.1 cm.
parent W-wavepeaks(harmonics) usually appearedwhena 4B.8Hz supplywasused.Carewas taken to assure that any peak considered a Was wavepeakfrom the spectrumanalyzer wasfound only in association plants. with Peaks suchas60 Hz harmonics {rom ac powerare common(60 Hz also appearsto be a common W-wavefrequen' cy)and numerous electronicdevices radiateother spurioussignalsso spectra were taken approximately 1500 times to validate the various W-Waresand Plant Spacings 29
l
5 20 40 60 FREOU€NCY (r|2)
0
?
4
6 3 1 0 FREOIIENCY (HZ)
1 2
1 4
Figure 2. Frequencyof occurrenceof spacings (convenedto frequency in Hz by using f = 4aA where f is rhe frequency and s is ihe spacing. See the rexl) ver, sus frequency(Hz) ofbranch, rwig, sren, and teaf spacinesfor (A) 489 spacinsson a youns white fir (5 m), (B) 863 spacingson the lower branches of thre€ 30 n vhire fir", and (C)720spacinss priclon ly lettuce.The bin (inlervalsused in obraining rhe disrdbutions) &ese ftequencydisributions is 0.t in Hz. The frequenciesabove peaks in Figures 2-S were raken from rhe Lorus 1,2,3 *orksheets used for dats analysis. +Nunber in parenthesis after a frequency refers to the number of spacingsfor thar peak.
Fig re 3. Irequency o{ occurrence spacings of versus frequency (Hz) for (A) 633 spacinssfrom rwo Douslas-fir (9 m) srowing in rhe open, (B) 314 spacingsfron a youns (8 m) Douglas fir growins in semishade, and (C) 429 spacingsfron th€ lower b.ancbes of f i r p a p p r o r i m a r p l y5 m p o n d F r o s p i n . g r o h i n g l a in a clunp wirh several other rrees.
plants on the spectrumanalyzer.Thc specrrum analyzer data were taken from I July to 8 0ctober 1988. The spectrawere also confirmed,checked, and analyzedin the following ways (l) A battery operated instrumentatton amplifierin a rnetalbox (a 90 cm aluminumcube) wasconnected a pottedplant in the samemetal to bor vith appropriate probes. pair of coaxial A cables took the signal to the differentially
apparent W-rave frequencies.Common mode cancellationand coaxial cable with appropriate grounding was used to minimize undesirable signals.No attempt wasmadeto compareamplirudes of the same frequency peak in different 30 Wagner
",I
6
I
I 'itl irll rrl,lrll
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aREOUENCY(rir) Figur€ 4. Irequency of occurrence rersus f.equency(Hz) {or (A) 865 branch and leaf spacinss from a big lea{ naple (approx. l0 m), (B) 622 branch and leaf spacingsfron a snall (4 m) oregon ash, and (c) 642 bran.h and t"at .ta.ing" fron a .yringa Ghrub). Figure 5. Frequencyofoccunence versusfrequency(Hz) for (A)392joint spacinss swe€tcorn,(B)s36 branch on and Ieafspacingsfron rhe lover branchesof two deliciousapple rrees,and (C) 502leafand branch spacingsf.on Concord grape vines.
connected spectrumanalyzer outsidethe metal box (Figure8). The amplifier increased signal the amplitudefeeding into the spectrumanalyzerto rhe millivolt range with the typical peaks(usually harmonics 0.16Hz with certainharmonics of that usually are of higher amplitude) I have associatedwith plants still appearing, but at much higher amplitudes. This confirmedthat the obsewed frequencies werecomingfrom the plant and not the spectrum analyzer.All appropriate measures weretaken for commonmodecancellation of unwanted signals.
(2) The apparentplanr frequencies we.e also confirrnedon a Schlumberger1220low frequency spectrum aralyze4 a considerablydifferenr analyzerwhich is more sensitiveand better designed reducespurious to responses than the 120t. (3) Probesin a control dead dry log did not give plant spectra,but they were observed, however,from salt solution filled logs. (4) Almost all observed peaksappeared to represent harmonics subharmonics this or and fact was used to check peak validity. If the W-Waves and Plant Spacings 3l
-20
dB AVG 11.2
t6
itu *ln,,,h'1,1,-il1,i,,n'il-f l,n*,l,r
-1
(HZ) PowER(dB)/ FREO
20
Fieure 6. Specrrun (0-20 Hz) f.on conracrsspacedabout 3 cm on a willow (Sdk sp). Notice the peaksspacedat 0.32 Hz and the t.6 Hz harnonic peals wbich ofren have great€r amplitude than lhe ordinary 0.32 Hz spacedpeaks.This spectrum ras chosen as rarher typical o{ spectra frorn plants. Severalof the 1.6 Hz harmonic peaks have been marked ro indicare rhe frequency of the peak. This is essentiallythe same as the spectrun of Figure 7 excepl that only a derailed porlion of th€ spectrum(bas€band20 Hz) is shown atlo{ing $e structure berwe€nthe 1.6 Hz spacedpeaks to be seen. The arrows indicate 0.32 Hz spaced peaks The scalesare linear.
wasset at 30000Hz peaks spectrumbaseband were usuallyobservedspacedat 800 Hz (not shown)vith the last one at 29600 Hz due to the resolution characteristicsof the spectrum If and the natureof the spectrum. the analyzer peaks baseband setat 2000Hz the observed was at wereusuallyspaced 80 Hz with rhe lOth peak representingthe first 800 Hz peak obsened on the analyzerwith a 30000 Hz baseband.If the peaks was baseband set at 500 Hz the observed at wereoften spaced 16 Hz intervalswith the fifth was 100 Hz, peak at B0 Hz or, if the baseband were on apparentplant frequencles the observed (Figure7). If the baseband was 1.6Hz intervals interval was set at 20 Hz the comnonly observed 0.32 Hz, with larger peaksat 1.6 Hz intervals (Figure 6). For basebands I Hz peakswere of found at 0.16. 0.08. 0.04. and 0.02 Hz. often appear certainharmonics Characteristically the to be larger than others,for example, 7th and of l0th harmonics 1.6Hz (l1.2 and 16 Hz) using 32 Wagner
(note also the larger peaksof a 20 Hz baseband Figure 7). There appearsto be a regular re' pattern in the relative peating characteristic but amplitudeof harmonics it hasnot yet been The above harmonics completelydetermined. seemto appearonly whenprobesin plantsor salt are solutionfilled woodsamples usedor from cerin tain other typesof sensom the vicinity of plants (Wagner l9B9). (5) Another techniquewhich appearsto confrequencies involves of firm the presence W-wave running a small ac electric current through a plant using one probe near the top and the other the near the bottom of the plant. Connecting spectrumanalyzerto two probesin the plant set betweenthe current supplyprobesindicatesthat beatswith W-wave the smallac current frequency (Wagner l9B9).When the spectrum frequencies analyzerrevealsa peak at an ac sourcefrequency S, other peaksare alsooften seensymmetrically placed about this peak. Theseother peaks
dB AVG
16
32
48
80
96
-1
(dB) FREa (Hz) PowER /
100
Fisu.e 7. Spectrum(0-100Hz) fron probeson madrore(Aiutus nenziest,. The 1.6 Hz spacedpeaksshow clearly. The targe peak is the 60 Hz power peak which i! difficult to etininate near 60 Hz power lines. This spectrun was raken at 0543 brs 2 August 1988 at a tenperature of 10.6' C. Again this was a typical spectrum from probes in a plant. The scalesare linear.
appearat frequencies S+g" or S-g. wherethe g. appearlo be commonW-wavefrequencies. Many apparent W-wavefrequencieshave been observed whichmatchthose commonly observed on the spectrumanalyzerusing the first method (two probeswithout a specialac sourceto producebeats). This beat (or heterodyne) four probe techniqueappears providean additionalcheck to on the validity of the obsened W-wavefrequencies.Amplitudes are often orders of magnitude larger than those observed by the sirnple two probe method first used. The beat method is more tediousthan the direct approachsinceonly a few frequencies usually appearr ith a givenapplied frequency it appears sho* peaksof but to important W'wavefrequencies outsidethe 1.6Hz harmonicseriesof the two probe method(e.g. 4, 10, ard 12 Hz)(6) The given spectra(e.g.Figures6 and 7) result from at leasteight averages the l20l on spectrum analyzer minimizenoise.Exponento tial averagingwasused(usuallywith a Hanning window) wirh a time constant several of seconds
to seveial minutes(depending the baseband on used).The slowrise and fall of someof the peaks could be seenasthe spectrumanalyzeraveraged. (7) In initial phaseteststi{o begoniaplants (Begoniasp,)were displacedvertically from one another by approximately one meter. Pairs of probes wereplacedin eachplant and the probe outputsrun through high input impedance bandpass filters with center frequencies of 80 Hz (usuallya large amplitudeW-wavefrequency). A phasemeter indicated that the 80 Hz signals obtained were relatedby a constant phaseangle. This apparentlyindicatedthat the tv.oB0 Hz Wwavesignals werenot only real but that they were causally linked (e.g.perhaps the 80 Hz signals came from a spacial(and vertical) standing Wwave pattern common to both plants).
DataAnalysisand Results
If standingwaves are responsible the spacfor ings between plant structures then both a wavelength and a frequency can apparently be W-Wavesand Plant Spacings 33
Iignre 8. A diagram ofone €xperimental setup used 10 sho{ thal W'l{aves app€ar in metal shields.Tbe amplifier uied vas batte.y poweredso that eve{.thing haying to do with the anplifier was in the shield (aluminum box) except for the two grounded coaxial cables,going through small holes in one side of the box, taking the anplifi€d signal to the spectnm analyzer.(See !h€ t€xt.)
associated with a particular spacing.As is well i h n o n n f o r w a v e si n g e n e r a lt.h e f r e q u e n c ys given as the quotient of the wave velocity and the wavelength.The in situ wave velocity was beThis velocity waschosen takenas96 cm/sec. causea preliminary study suggestedthat more plant frequencies found on the spectrumanalyzer matched frequencies(Hz) determined from whenthis velocity wasused.96 branchspacings cm/seccomparesfavorably with the velocity of previously obtainedfrom direct 90 t 6 cm/sec (Wagner impulse and responsemeasurements l988a,b).The frequency(f") of a particular spacis ing (using 96 cm/sec) defined here by the following formula: f"=9612s"=481s" The 2 in the wheres, is a particularspacing. is because spacingmight the denominator chosen correlate to antinode or node spacing which is The aboveformula wasused l/2 the wavelength. to convert all the spacingsto frequencies(Hz). Figures are distributions the spacings 2-5 of con34 Wagner
in the verted to frequencies Hz. I measured power spectrumof electricalsignalsfrom the sameplants but all plants testedseemedto give the samebasicspectrum. peaks not A cornplete of the spectral set does alwaysappear on the spectrum analyzer.Some peaks appear rvhile the spectrum analyzer is averaging,then disappear and again reappear (e.g. Hz usually 2.4 seemed showon hot afterto noons). However,just by placing probes in a branch of any plant one can often obtain an plant frequenset almostcomplete of apparent used(e.g.Figures ciesfor the particularbaseband 6 and 7). All of the peakssholrn are harmonics (integralmultiples) 0.16 Hz (or 0.02 or 0.04 of or 0.08Hz).Noricein Figure6 that most of the peaks spaced 0.32Hz, whichis typicalfor are at a 20 Hz baseband.Larger amplitude peaksappear at multiplesof 1.6Hz. Even if the smaller peaks(e.g. Figure 6) fail to shorr in a spectrum, at least some of the 1.6 Hz seriesare almost alwayspresent.
it After much experimentation was decided that the most important criteria for real plant peaks on the spectrum analyzer was that they of shouldbe harmonics 0.02,0.04,0.08,or 0.16 Hz, sinceharmonicsof theseparticular frequento with ciesalmost always seemed be associated plantsin m1 latcslstudips. Theseharmonics inwhich often cludethe 1.6Hz seriesof harmonics, have higher amplitudes and appear more often (againseeFigures6 and 7). than other harmonics In Figure ? the peaks are spacedmostly at 100 1.6Hz (baseband Hz). There are enoughfrequencies available,however,as indicated by the (e.g.Figures6 and ? and specspectrum analyzer tra not shown),that the distribution of branch but some spacings couldbe nearlya continuum appearto be more dominant of the harmonics than others.The 1.6 Hz serieswith their large seemto showup in a large number amplitudes plant spacings. There probably of corresponding which frequenare selection rules that deterrnine (it ciesare dominantin settingplant spacings is inrecognized thereare manyother factors that such as envolvedin setting branch spacings vironment and genetics). are Although I believethat plant spacings set not by Wwave noise but by definite, numerous, harmonically related W-wave frequencies,it is useful to consider a criterion for peak validity t w h e nn o i s ei s p r e s e n i n c a s eo u r a s s u m p l i o n s with are incorect. The statisticalerror associated is a countingprocess of the order of 1TI, where N is the number of counts in a particular spacing bin (interval).So in determining the validity of a plant peak,a peak which is 20 countshigh of wouldhavean uncertaint) the orderof ]2O20 x 100percent.If a peakis still far abovethe peaks in adjacentbins after $l is subtractedfrom the in numberof spacings that peakit canbe called to a real peak.This criterion not only appears demonstratethe validity of many W-wave fre(Hz) is plottedversus quencies whenfrequency but are fiequencyof occurrence, if spacings plotfrequency occurrence, becomes of it ted versus clear that many more of the peaks in all the d i s t r i b u t i o n s p e a r o b e r e a lb 1 t h i s , " r i t e r i o n ap t (e.g. erFigurel). I estimated that the maximum ror in the frequency(Hz) in the frequencyof occudenceversusfrequency(Hz) plots is +0.1 Hz. however. seemto indicatethat the The results. lessthan t0.l Hz and probably enor is generally
bin within the possible error of t 0.05Hz since so many peaksseem to fit the 1.6 Hz series (Figures 2-5). As an introduction to plant spacingdistributions Figure I showsthree distributions where are to the spacings not converted frequency(Hz). distribuFirst noticeFigure lA wherethe spacing tion is plotted for data from two apple trees. revealthat most of the larger peaks Calculations when using frefit commonW-wavefrequencies 9 quency quals 6 cm/sec ivided y two limes e d b (e.g.for a samplecalculation take the the spacing 2 cm spacingfrom Figure lA and use it as s, in the formula f" = 48ls" given above.This gives W-wave frequency revealed as 24 Hz, a common on the spectrum analyzer),Similarly, in Figure lB I have a plot of spacingsversusfrequencyof a o c c u r r e n cfe r d a l a l r o m f i r e p o n d e r o sp i n e s . o The largest peak is very apparent with a spacforing of 15 cm, or 3.2 Hz usingthe frequency mula. In Figure lC wherethe numberof spacings is plotted versusspacingfor concordgrape, more real peaksby the above/N/N criterion are shownthan later when frequencyof occunence (Hz) in Figure 5C. is plotted versusfrequency Where growth spacingsare convertedto frequency it can be seen that many of the peaks repeat from plant to plant, Figure 2A, for exam( p l e .s h o n sr e a lp e a k s u s i n g h e n o i s e r i l e r i o n t c above) frequencies 2.2,6, 6.9,8, 9.6, 12,13.8, at at the 15,16,t9.2, and24 Hz and others. Consider validityof the 6 Hz peak.Thereare 15 spacings in this peak.The squareroot of 15 is near4. Subtracting 4 still leavesthe peak considerably higher than the adjacentpeaks.The validity of the 6, 6.9, 8,9.6, 12, 13.8,15, 16, 19.2,ard 24 Hz peaksis obviousby my criterion.Someof these peaksfit inro the 1.6 seriesof harmonics (Figures and 6 observed the spectrumanalyzer on into the 0.04,0.08, 0.16 or 7)and the remainder series harmonics. appears of It that possible bin (t.05 Hz) and measurement errorscan take care of rnostvariationsfrom exactfit on the spectrum peaks. Figure28, someof the peaks analyzer In matchthose figure2A, In Figure2C the main of peaksare: 21.9, 30, 32, 37, 40, 48,60, and 68.6 Hz. The graphsrevealthat many peaksare in thp real categor),as determined our noise by crileria. cspeciall)at the higher frequencie.. it that, for most of the Characteristically, appears W-Wavesand Plant Spacings 35
distributions shown in Figures 2-5, those peaks at lower frequencies suggest a possible continuum of larger spacings, if a spacingrather but (Hz)distributionis analyzed than a frequency this may not be the case(Figure l). A careful study o f i n d i v i d u ap e a k s u g g e s tts a t n o s p a r " i nig l s h s random, especially at the higher frequencies, e s i n c e v e r y e a ke r e n w i t h o n l yo n e s p a c i n gn p i it seems match a 0.02,0.04,0.08,or a 0.16 to Hz harmonicor oneof the apparentlyrnoredominant harmonics 1.6 Hz. For example. of notice in figure2C the two spacings B0 Hz which is at usually a very dominant peak on the spectrum analyzer and noticethe peaksat 48 Hz in Figures 4A and 58. The prominence particularpeaksapparentof ly varies not only from speciesto speciesbut within the same species.Cornparing spacrngs from plantsof the samespecies growingin the shadeand the sun it appears that shadegrown plants would have larger spacingsas growth is longerin the shade. This seems be borneout to by the two set6 of Douglas-fir data (Figure 3A and B). Someof the main peaksof the shaded ft are at longer wavelengths lower frequen(or cies:. 2-6,3.0,and 3.4 Hz compared 8.7, 2.3, to 24,32, a ,48 Hz for exarnple) than the trees grown in the sun. The main peaksseenin the ponderosa pine data(Figure3C)at 1.6,2.1,2.4,2.6,3.2,3.8, 4-8, 6.3 and 9.5 Hz (6.3and 9.5 Hz are within 0.1 Hz of 6.4 and 9.6 Hz) showan almostperfectfit with the 1.6Hz seriesftom the spectrumanalyzerand to other peaksthat most commonlyappearon the spectrum analyzer. The 2p (3.2 Hz) spacing discussed the early data(Wagner l988a,b)proin videsby far the most prominentpeak here. In Figure 4A the big leaf maple providesthe largestpeakat 8.8 Hz. Maple branches provide visiblecluesto a possible correlationbetween structureand wavebehaviorwith groupsof closely spacedbands often appearingjust above branchrhorls. Thesebandsappearto be analogousto the standingwavesthat appearin small water pools connected larger pools wherea to largewavehasbeengenerated. The branchwhorl produces disturbance the larger apparently a in wavepattern and the results appear on the upper side of the whorl. In Figure 48 the dominant peaksare 6 and 8.8 Hz with a lessdominantpeak at 9.6 Hz. In Figure4C somclargepeaksai. at 6 . 4 ,l l , 1 5 ,1 6 . 6 , 7 . 2 ,r 7 . 8 , 1 9 . 2 , 2 1 . 9 , 2 4 , 3 2 t Hz 36 Wasner
and so on. Theseeither fit the 1.6 seriesor fit the other seriesto probably within the possible bin error. The "signature" of syringa seemsto be more complexthan the signatures from other plantsstudied. In sweet corn (Figure5A)the major peaksare at 2,4 Hz and a minor peakat about2,6 Hz which may not be real. The closest0.32 Hz seriesfrequency(multiple of 0.32 Hz) is 2.56 Hz and 2.4 Hz fits a 0.16 Hz seriespeak.Minor peakswhich may not be significant are also at 3.2,8, and 9.6 Hz which are multiples of 1.6 Hz, Figure 58 yieldspeaks 9.6, 12,13.8,16, 19.2,24,and32 at Hz. These peaks with the 1.6series fit and other available frequencies.In Figure 5C the major peak is at 6 Hz (with 22 spacings)and some of the other peaksdo not appearto be real. Complicatedgrowthpatternsmay makeit appearthat spacings lessdiscrete. are Possible variations in the in situ W-wavevelocity during the growing season could also be a possiblecausefor scatter (Wagner l98Bb). When I rake into account that plant frequenciescan be quite small (0.04 Hz and less), and that plant frequencies can appearlo be harmonics of any of the low frequenciesobserved on the spectrum analyzer,then all of the plant peaks from spacingsfit W-nave frequencies within experimentalerror. A statistical correlation would appear to be meaninglessfor this r e a s o nI. h a v en o t i c e d h a t , . e r t a i nr e q u e n c i e s t f seem to be dominant, particularly those which are multiples of 1.6 Hz. Considering,for example, the number of spacingfrequencies the in peaksthat are labelledin Figures2-5(usuallythe peakswith the largestamplirudes) percentof 42 these spacing frequenciesrepresentharmonics (integral multiples) 1.6Hz; 9.5 percent of represent harmonics 0.16 Hz (but not of 1.6 Hz); of 11.7percentrepresent harmonics 0.08Hz ftut of not of 1.6 Hz and 0.16 Hz);21.1percentrepresentharmonics of0.04Hz, and l6 percent representharmonics 0.02 Hz (Note:(l) There are of 2300 spacings converted to frequency in the labelled peakswith about 7000 spacrlgs represented all the graphdara;(2)Harmonics 0.02 in of and 0.04 Hz are not distinguishable because the bin (interval) width used accommodates +0,05 Hz from the centerfrequency.) The largepercentage of 1.6Hz harmonics reinforcesthe idea that these harmonicsare dominant, as suggested by the spectrum analyzer data (Figures 6 and 7).
Discussion
in available the Thereare so many frequencies spectrumthat almostany plant apparentW-wave that cerspacingcould be allowablebut it seems such asrhe multiples of 1.6Hz, tain frequencies, appear moreoflen thanothersin plantspacings. that frequencies appearare 4,6, 0ther common 10,12,60,and manyothersthat are not integral multiplesof 1.6 Hz but appearto be multiples observed the on subharmonics of lowerfrequency (e.g. analyzer 0.16,0.08,0.04,and0.02 spectrum t " H z ) .S i n c e l i s n o tc l e a rr n h ad e l e r m i n ea n i m i portant W-wave frequency, more study is requrrecl. in The most important observation this study is that branch spacingsoften seem to be in groups(noisewouldnot be exspacing discrete pected to produce definite repeating spacings) rather than in smooth distributionsand this discretespacingwould be expectedfrom standMany spacingdistributions. ing wavedetermined ofthe peaksin the plant distributionsrepeatfrom indicates close the plantto planrwhichpossibly of interrelationships plantsand a commonsource for W-waves.Usually the major plant peaks match the major spectrumanalyzerpeaksshown in Figures 6 and 7, or they are harmonically earlier. relatedas observed that someof the datado not fit It is possible W-wavefreexactlyon peakswhich represent quencies because the followinghypotheses: of tend Standingwavepatterns l) End effects. to set the branch spacingsbut with variations stemming frorn growing conditions. There is tend to be longer someevidence that wavelengths data taken on salt near ends(from unpublished solution filled samples)and plants grow from fit their ends.It is not yet clearhow end effects i a b i n t o t h e p i c t u r e u t e n d e f f e c t s r ec o m m o n n wave phenomena(e.g. Strutt 1945:487). The for 2) Errors in measurement. spacings werehard the prickly lettucedata,for example, the alternatedfrom side to obtain because leaves to sidealongthe sralk.Theremay be someunconsciousrounding in measurementespecially point asin white wherethereis no goodreference fir, I tested this hypothesis on a white fir by lines excoveringall numbersand delineating cept for mm marks on the measuringrule before measuringa spacing,The spacing was then markedon the rule and then the rule numbers
were uncoveredto see and record the spacing, wasrepeated unril sufficientdata This procedure for with datataken wereobtained a comparison by the usualmethod.The data were then analyzed and cornparedto data taken $ithout the This experimentindicated coveringprecautions. that there was some rounding error, but not enoughto warrantretakingthe data. 3) Frequency distriburion slot (bin) and one can error.Using the calculus measurement derive an approximate expressionthat ielates in in srnallchanges spacingto small changes frequency.The relation follows: As" = -s3 Af./48 (or As. and Af" representsmall changes errors) For in spacingand frequencyrespectively. example,if an interval(bin)is centered 6 Hz (Bcm on then the approximateallowablespacing spacing) eror to stayrvithin a bin ofwidth 0.1 Hz is t 0.7 mm. If the interval is centeredon 60 Hz (B mm spacing),however,one would have to measure within approrimately ,t 0.007mm to staywithin that different bins should the bin. This suggests be used for different frequency ranges. A error at 60 Hz would millimetermeasurement frequency error of 17.5 meanan approximate Hz whilea millimetererror at 6 Hz wouldmean error of t0.075 Hz. an approximate frequency by The possible error introduced the computer in taking the distributions was considered negligible.
Conclusions Observations and
Thesedata,as reportedearlier(Wagnerl9BBa and 1989),indicate the W-wavesare apparently patassociated someplant growthbehavior with terns.The discrete spacingdata by itself hints ar the likelihood of sometype of standing wave repeatingon individual functionwith frequencies of plantsand from plant to plant,A comparison data, iehere actualfrequencies spectrumanalyzer frequencies calculated with spacing are measured, reinforces the with a vave speedof 96 cm/sec, plant spacidea that W-waves explainthe discrete ings. This invites further investigation into the and function of W-waves. source(s) here,is close The number 1.6,which appears to the goldea ratio (Dixon l9B9). Perhaps Wnumbersas wavesare relatedto the Fibonacci they are manifestedin plants. W-wavesmight W-Wavesand Plant Spacings 37
also be involvedin other natural phenomena, such as in the formation of quasicrystals, where the golden rdrio appears.
Acknowledgments
The author wishesto thank John Salinasof RogueCommuniry College his assistance for in
analyzingdata. I also would like to thank Dr. Alan Streaterof the SouthernOregonStateCollegephysics department his comments this for on paper. I am grateful to my wife Claudia for her assistance taking data. in
Literature Cited
Dixon, R. 1989.Spiral Phyllokxis. CompurersMa!h. Applic. l7:535-538. Sruft, J. W. I945. The Theory of Sound.Dover publicarions, New York.
V/agner, 0. E. 1988a.Sranding wavesin ptant tjssue.Bull. Aner. Phys. Soc. 33:2203. 1988b.Wave behavior in plant rissue.Nor$w. -. Sci. 62: 263.270. 1989. V-{aves and plani connunicarion. N o r t h w .S c i . 6 3 : 1 1 9 - 1 2 8 .
Receioed Octoberl9B8 12 Accepted. publication 13 October i9B9 for
38
Wagner