Ham, L. B.

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Journal of the Arkansas Academy of ScienceVolume 3 Article 181950Loudness Measurements and Their Bearing on theNon-Linearity of the Hearing FunctionL. B. HamUniversity of Arkansas, FayettevilleFollow this and additional works at: http://scholarworks.uark.edu/jaasPart of the Sense Organs CommonsThis article is available for use under the Creative Commons license: Attribution-NoDerivatives 4.0 International (CC BY-ND 4.0). Users are able toread, download, copy, print, distribute, search, link to the full texts of these articles, or use them for any other lawful purpose, without asking priorpermission from the publisher or the author.This Article is brought to you for free and open access by ScholarWorks@UARK. It has been accepted for inclusion in Journal of the Arkansas Academyof Science by an authorized editor of ScholarWorks@UARK. For more information, please contact scholar@uark.edu, ccmiddle@uark.edu.Recommended CitationHam, L. B. (1950) "Loudness Measurements and Their Bearing on the Non-Linearity of the Hearing Function," Journal of the ArkansasAcademy of Science: Vol. 3 , Article 18.Available at: http://scholarworks.uark.edu/jaas/vol3/iss1/1875LOUDNESS MEASUREMENTS AND THEIR BEARING ON THENON-LINEARITY OF THE HEARING FUNCTIONL.B. Ham, University of ArkansasIn an article by Mr. Parkinson of the Johns Manville Cor-poration and the writer1, a series of experiments were described,showing judgments by certain Individuals on the change In loud-ness of a sound with a given decrease or Increase In the soundIntensity.There appeared certain variations In the results that couldnot be accounted for at the time. Itwas found, however, thatthe results were fairly well represented by the logarithmic formof equationL = e^N (i)where L represents the change In loudness as judged by thetypical observer and N is the change in sound Intensity In deci-bels corresponding to the expressed change in loudness. Thevalue of the constant m was found to be 0.076. There was someevidence at the time that the value of the constant (m) might belarger for low Initial loudness levels.At the time of publication of the results, a few men,prominent In the acoustical field, doubted the possibility of ob-taining reliable results by this direct approach. Soon afterthese experiments were published experiments along similar lineswere reported by Fletcher and Munson 2, Geiger and Firestone 3,Churcher 4 , and others.Experiments by the above mentioned people and continued ex-periments by the present author soon showed that the loudnessIncrement function depends upon the intensity level of the sound,the frequency, noise, psychological conditions and whether theIntensity Increments are positive or negative. The object of thepresent paper is to describe a series of experiments which Illus-trate some of the psycho-physical phenomena just mentioned. Atentative explanation for the smaller difference In Intensitychanges to give equal reduction In loudness compared to equalIncrements in loudness will be given. The data were obtainedwith about 400 students cooperating, accumulating nearly 5000measurements.EXPERIMENTAL PROCEDUREThe type of apparatus used In the present series, slightlymodified over that at New York University is listed as follows:an oscillator, two attenuators, an amplifier, loud speaker, fil-ter, and calibrated voltmeter (Fig. 1). The wave forms wereoften checked with an oscillograph. Allbut a negligible numberof experiments have been done with groups of students, numberingabout 15 to 30.. Data tabulated for this number or less wereusually obtained from a single class. Because of varyingla Loudness and Intensity Relations by L.B. Ham and J.S. Parkinson. Jr. Acous.Soo. 3, 511, 1932.2. Loudness, Its Definition, Measurement and Calculation by H. Fletcher and W.A.Munson. Jr. Aoous. Soo. 5, 82, 1933.3. The Estimation of Fractional Loudness by P.H. Geigar and F.A. Firestone. Jr.Acous. Soc. 5, 25, 1933.4. A loudness Scale for Industrial Noise Measurements by B.G. Churcher. Jr. Acous.Soo. 6, 216, 1935.75Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18Published by Arkansas Academy of Science, 195076pschologlcal conditions, data for a single class were lessreliable for a given number of observations than for two classeswith the same total of observers.In the experiments asking for Judgments on fractional loud-ness, a series of six energy levels Is sounded all reduced ex-cept one. Thus for Judgments on a reduction to one-half theoriginal loudness of a tone, the Intensities In decibels aregiven usually In the following reduced order: 0, 18, 6, 15, 8,11. There has been some variation In the decibel Intensitymagnitudes to study the effects of these variations. In themultiple loudness Judgments, the procedure Is the same exceptthat the Intensities are Increased In the same order as above.The observer merely Indicates In the data form presented whetheithe fractional or the Incremental loudness Is more or less thanthe loudness Judgment desired by using plus (+) and negative (-)signs.Careful explanations of the procedure to be followed Inmaking the Judgments have been found necessary to avoid psycho-logical disturbances. The detailed method of taking all data Isas follows: first, produce the reference tone; then, the com-parison tone level; finally, repeat both tones In the same orderas In the first Instance. A generous amount of time Is given tosee that all observers understand what Is to be done and muchtime Is used In the first one or two measurements to see that allunfamiliar Initial directions are made clear. A brief Introduc-tion to the nature of the work and apparatus Is usually given tohelp remove fear reactions. No one, who makes the observation,has any idea In which way the apparatus is to work to get thevarious energy levels. Students usually feel that some kind ofan examination must be coming when the data forms are passedaround, so that careful preparation Is urgent. The maximum num-ber of loudness Judgments taken by any one person Is about 18,representing about 216 tones to which he must give attention.EXPERIMENTAL DATAThe complete data for all frequencies and intensity levelsare given in Table I. The object in setting the table up thisway Is to determine the possible trend In loudness estimateseither with variations of frequency or of intensity level. Thereis a fairly defined tendency for a decrease in decibel level togive 1/2, 1/3, and l/5 the loudness In the 60 cycle tone withdecreasing intensity level of the reference tone which does notappear in the remaining data. Geiger and Firestone's data, usinga telephone receiver, shows rather marked incremental decibeldecreases with low level Intensities both in the 1000 cycle andthe 60 cycle tone. A wider range In Intensity levels of thereference tone In the present series would be necessary to com-pare results closely In the two papers. One can go to lowerlevels when a single person Is experimenting In a room. Compar-ing these experiments with the Geiger and Firestone experiments,there appears to be a rather important difference whether theroom Is bathed in the sound or the sound comes directly from atelephone receiver. There are background noises incident to agroup of people that may alter the apparent loudness. Most ex-periments with telephone receivers up to the present Indicatethat the change in decibel level for a multiple change in loud-ness (or a fractional change of the same amount) is approximate-ly the same for any given frequency for tones In excess of 40 dbabove threshold. The present series Is in keeping with thisgeneral conclusion In the fractional series in that the 60 cycletone has its low intensity reference tone below 25 db, which Iswell below 40 db.76Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18http://scholarworks.uark.edu/jaas/vol3/iss1/1877There Is a small tendency for increased energy changes forequal fractional and multiple changes In loudness for Increasingfrequencies up to 1000 cycles.The more accurate method of taking data In the presentseries Indicated one significant result over that obtained In theearlier series; namely, that multiple Intensity Increases are alittle greater than fractional Intensity decreases for equalchanges in loudness. Table IIIs set up to show this effectbetter. Alldata for any one frequency are tabulated in a singlerow. The effect Is well seen for all frequencies except for theone-half loudness versus the two-times loudness experiments with1000, 5000, and 10,000 cycles. The fluctuation error of loud-ness judgment is not sufficiently small to show the probable trueeffect at this change in loudness compared to the larger changesIn loudness. Part of the difference between the fractional andthe multiple series could be attributed to the masking effect ofbackground noises. The major assumed cause of the differencewill be discussed later.The results of the present series compares very favorablywith the former series at New York University. At that time, theexperiments were more with the middle range frequencies. Whenthe change In decibels required to give corresponding changes infractional and multiple loudnesses are tabulated for 500, 1000,and 5000 cycles, a value of 0.073 Is obtained for the constant mof equation 1used In the experiments at New York University.This compares well with the value of 0.076 obtained at that time.Table IIIwas constructed to see if any significance couldbe obtained by comparing the fractional loudness series with themultiple loudness series when the fixed (or reference) tone wasmore nearly at the same level in both series. There seemed tobe but little, If any, added significance.From the best possible weighting of all data given in thepresent article, two curves (Fig. 2) have been drawn. One repre-sents the fractional loudness data while the other represents themultiple loudness data. The fractional loudness curve Is drawnwith 8.4, 14.3 and 20.8 decibel reductions representing reduc-tions of 1/2, 1/3 and 1/5 in loudness. The multiple loudnesscurve is drawn with 8,6, 17.7 and 24.8 db increases representingincreases of 2, 3 and 5 times the former loudness.In the experiments published in 1932 In which it was con-cluded that the results could be fitted reasonably well on acurve for which m = 0.076, the results are 9.1 db for a loudnesschange of 1/2 or 2, 14.4 db for a loudness change of 1/3 (or 3)and 21.1 db for a loudness change of 1/5 (or 5).Since 20.8 db and 24.8 db represent intensity ratios of 120and 300 approximately a practical accounting of the fractional-multiple loudness curves of Fig. 2 for a loudness change of 5 maybe Illustrated In the following way: If 2 pigs produce equalsqueals, 600 equally Intense squealing pigs willproduce an in-crease of five times In loudness. To reduce the loudness of 600pigs to 1/5 this loudness, the number of pigs would have to bereduced to 5 in number, instead of 2.PSYCHOLOGICAL CONSIDERATIONSObservers are influenced by many factors, some of which havebeen discovered gradually as the experiments hava progressed.That unsuspected distractions do occur Is found In the type ofdata sometimes recorded. Some of the conditions influencing the77Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18Published by Arkansas Academy of Science, 195078results are listed In the numbered paragraphs to follow.1. Distractions are observed when unknown noises exist dueto outside activities and when there are Incidental mishaps. Oneoerson In a group tripped over a lamp cord upon entering theroom. The resulting data proved to have but little value. Themethod used to record the data will show Inconsistencies.2. Deafness will lead to erroneous results. The dampingfactors in the ear are different for deafened people. The mask-Ing effects In a room subject to noise Is also different forpeople with normal hearing.3. The magnitude of the difference In intensities used formaking loudness Judgments is a factor especially if the differ-ences are less than 2 db. This factor has been minimized by useof wide ranges in sequential intensity levels in the tests.4. The method of illustrating how the experiments are to beperformed appears to be Important. To Illustrate how the com-parison tone is to be sounded, the switches are thrown to a com-parison sound of equal intensity so as to not start with a bias-ing intensity difference in two tones. You will note that thefirst comparison is to be made with no difference in intensities.Further directions are given at this time.5. Fatigue factors are Important. The experiments oncestarted should take but a short time before interest wanes andfatigue sets in. There should be no mistake in tone sounded andfaulty transients should not be allowed because of the distract-ing effect.6. Observing estimates by others offers some difficulty.This is minimized by the recording of a plus ( +) or a minus (-)sign for each new tone intensity by everybody.DISCUSSION OF RESULTSThe observer apparently has no language vocabulary to des-cribe adequately his method of arriving at the loudness judg-ments of the type described In this paper. The accuracy is ofthe same order as asking a person to Judge the length of a roomIn terms of the multiple lengths of some arbitrary standard.This has been tried with a room about five times the length of anarbitrary standard. Many try to describe how their judgmentswere made by using comparisons such as: distance units on alinear scale, piles of equal masses, feeling on the ear drum,addition of sounds, frequency range on a piano scale, speed, andsound cut into parts. The Judgments prove to be surprisinglyclose and wide deviation may be traced usually to some psycho-logical factor. The better experimental setting in the soundabsorbing room at the University of Arkansas has led to much moreconsistent data than that obtained formerly at New York Univer-sity or that obtained at the University of Arkansas before thesound absorbing room was available. In fact, there appeared tobe some small effect discernable from the external noise when theexperiments were performed in ordinary rooms. The effect was notsufficient however to be identified definitely by Itself. Noisesfrom any origin tend to mask a tone so that the threshold In-tensity level is raised. One may anticipate, therefore, in thepresence of a noise that a tone which is decreased In Intensityto sound half as loud need not be reduced so much, since thethreshold Intensity is raised. Likewise a sound In the pressureof a noise need not be raised as much as In a sound absorbingroom to appear twice as loud.78Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18http://scholarworks.uark.edu/jaas/vol3/iss1/1879That positive Increments In Intensity to produce a fixedmultiple Increment In loudness are greater than the reductionsIn Intensity to produce equivalent fractional decreases In loud-ness (Fig. 2) Is quite new, except that Itwas anticipated fromthe Gelger -Fire stone experiments mentioned earlier. In theirseries of experiments, however, the results obtained from thedifferent frequencies depended upon the Intensity level of thereference tone. Although the effect Is negligible or Inconclu-sive In Isolated Instances, the results as a whole show a con-sistent set of results In respect to the Increments of Intensityrequired for equal Increases In loudness versus equal decreasesIn loudness. An explanation of this effect on the non-linearresponse basis appears reasonable.If the ear, for example, responds In a n on-symmetricalmanner to a sine wave In accordance with the equation E, = ap +bpwhere p = P sine wt, one may show that one of the resulting termss a steady pressure on the ear. In some experiments onmasking 5 performed by Dr. Guttman and the present author, therewas assumed the presence In the ear of a sensitive mechanism fordamping, masking or Impeding the transmission of a strong, un-)leasant sounds. The object of this mechanism may be the protec-;lon of the sensitive perceptive apparatus, Cortls organ. Thisapparatus does not function to as great a degree In a deafenedperson.The theoretical problem then Is to see If some algebraicequation of any degree In Instantaneous excess pressure p may beset up properly to fit the loudness curves for Increasing and'or decreasing loudnesses. The problem may be complicated In;hat the middle ear may have as a part of Its function the regu-lation of the lntralabyrlnthlne pressure by action of the lntra-aurlcular 6 muscles.5. Masking Effects of an Interfering Tone on a Deafened Ear by John Guttman andL.B. Ham. Archives of Otolaryngology, 12, 425, 1930.6. Zimmerman, C. Arch, of Physiol. 144, 30, 1912.79Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18Published by Arkansas Academy of Science, 195080CAPTIONSFig. 1 ApparatusFig. 2 Graphs showing the relationship between(aO fractional loudness versus decreases inintensity (thinner curve), and(b) multiple loudness versus increases inIntensity.Table 1 Left half gives the reduction in Intensitylevel for a reduction to 1/2, 1/3, and 1/5of the original loudness at stated intensitylevels. The right half gives correspondingdata for multiple loudnesses of 2, 3, and 5times the original loudness at intensitylevels indicated at the far right.80Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18http://scholarworks.uark.edu/jaas/vol3/iss1/1881Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18Published by Arkansas Academy of Science, 195082IntensitymtotommmIntensityCyclesLevel,/o££,,,£.5n/c_££„o£„o5<-oSLevelSec.(db)1/2.•§1/3.%1/5.^2.-g3.55.3(db)fractionalo©o©o©©o©o©Multipleabove456.055810.084815.27456.483710.401814.1518above356025-456.24477.993511.21145.868316.632615-35below254.85435.26437.09455.818811.988023.7226below15above505.20668.974718.81256.57498.7019above4020030-505.704012.772519.88157.6510514.7410023.195520-40below306.943512.382418.43256.634012.893721.8740below20above706.644415.384721.56457.9212614.685922.6220above5050045-708.144411.984217.892310.505617.204425.302325-50below457.594114.462620.20258.785015.733722.9238below25above807.076413.35139.087018.705727.1023above55100050-809.418814.438219.39447.542617.162725.82730-55below508.425014.705118.90247.938817.347324.040below30above608.797413.212823.38348.833915.003724.3040above40500035-6010.416316.345022.95457.142215.552226.072320-40below358.421213.181020.8998.583718.292126.5122below20above455.562011.342015.19226.8849above3010000.35^158.6511015.11121.20108.3510718.5825.4915-30below358.355514.814221.00427.6158below1582Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18http://scholarworks.uark.edu/jaas/vol3/iss1/1883TARIiFTTCOCOCOCQCOCOCyclesIntensity.*5.v,5k,Svh-SIntensitySec.svi???^n1/2°"S1/S°^1/5°^2°^3°^5°^fractional•©.a?»<d•©«(d•©Mult1DieOhOfnOf-,OhOf-,Of-,-"^60All5.761487.8512611.181045.9320812.6912419.8044All200All6.2114110.819618.92657.2019413.5115623.9095All500All7.4512913.9111519.80938.7423215.7614023.5281All1000All8.4820214.4314619.22688.3118417.8015725.359GAll5000All9.4414914.998822.90888.469816.028025.3685All10000All8.2218513.897319.29747.8121418.5825.49AllTABLEIIICOCOCOCOCOCO[~,,,,,¦,.„Intensity"n^<n^<mt-i<mth*ht-ivithIntensitySecLevel1/2O>S1/3°31/5°32°33°35°3LevelY*Frart"1final•©•©•©*©•©*<Dm,,ih-i.pidLLiunaiooo^O?HO?Hohnuitipie500,Medium9.4519514.3917420.501128.4223516.2615324.6483High1000&5000Low8.0610314.478719.76589.0410416.789325.7573Medium83Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18Published by Arkansas Academy of Science, 195084Journal of the Arkansas Academy of Science, Vol. 3 [1950], Art. 18http://scholarworks.uark.edu/jaas/vol3/iss1/18

Loudness Measurements and Their Bearing on the Non-Linearity of the Hearing Function

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Loudness Measurements and Their Bearing on the Non-Linearity of the Hearing Function

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