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{"created":"2022-01-31T15:19:50.061157+00:00","id":"lit28773","links":{},"metadata":{"alternative":"Studies from the Yale Psychological Laboratory","contributors":[{"name":"Scripture, Edward W.","role":"author"},{"name":"Howard F. Smith","role":"author"}],"detailsRefDisplay":"Studies from the Yale Psychological Laboratory 2: 105-113","fulltext":[{"file":"p0105.txt","language":"en","ocr_en":"EXPERIMENTS ON THE HIGHEST AUDIBLE TONE,\nBY\nE. W. Scripture and Howard F. Smith.\nThe highest audible tone, or the upper limit of pitch, is that tone at the extremity of the series of tones arranged according to pitch beyond which any rise in frequency of vibration fails to produce a sensation of tone. The highest audible tone is defined psychophysically by the frequency of the physical vibrations corresponding to it. The term \u201c vibration \u201d is understood to mean one complete pendular oscillation including both phases. The highest audible tone has been differently determined by various observers : Sauveur, 6 400 r Chladni, 8 192 ; Wollaston, 25 000 ; Savart, 24 000 ; Despretz, 36 864 ; Blake, 40 000 to 60 000.\nThe great discrepancy in the results is usually said to have been due to the imperfections of the apparatus employed. There is no need, however, of this assumption, as there is a source of variation quite sufficient to explain the discrepancy ; it is unquestionable that these men worked with tones of different intensities.\nEven in the very latest experiments the factor of intensity has been generally overlooked. Savart was the first to observe that the-highest audible tone was different for different intensities. Rayleigh1 took care to keep his tones of approximately the same intensity. Blake, who used a succession of steel bars of varying length, produced the tone by a pendulum-hammer swinging over a graduated scale, thus insuring a nearly uniform stroke and correspondingly uniform intensity of tone. These experiments, however, went no-farther than to secure a constant intensity.\nThe highest audible tone requires in each case a measurement of intensity as well as of pitch in order to complete its determination. It thus becomes important to inquire how the pitch of this tone depends on the intensity, or, in other words, to determine what the highest audible tone is for each intensity.\nApparatus.\nThe first step in solving this problem was the selection of an apparatus giving tones of the required pitch, but so arranged that the\n'Rayleigh, Acoustical observations; Very high notes, Phil. Mag., 1882 (5). XIII 344.","page":105},{"file":"p0106.txt","language":"en","ocr_en":"106\tE. W. Scripture and Howard F. Smith,\nintensity could be kept constant at any desired point and could be readily and accurately varied. Tuning forks were not used because the range for the highest audible tone is so wide that a very large number of forks would be required, and also because they do not admit any accurate regulation of intensity. The rods of K\u00f6nig with pendulum-hammer are in some respects better than the forks but are not very easy to manipulate in rapidly conducted tests, such as are necessary in order not to fatigue the observer ; moreover, the sound of the impact of the hammer cannot fail to 'be a disturbing element in the experiment. Neither the forks nor the rods give a sustained tone, but one of rapidly decreasing intensity.\nThe Galton-Koenig whistle was selected as the most reliable and readily manipulated instrument for the tests proposed. It gives a sustained tone as long as the blast of air continues ; the pitch of the tone is readily and accurately varied. The whistle consists of a brass tube, about 7cm in length with a cap screwing over one end. To this cap there is attached an accurately fitting piston, which moves inside the tube as the cap is screwed upward or downward. The outside of the tube is marked with a longitudinal'scale the unit of which is lmm, the length of the scale being 12mm. The screw is so arranged that one complete turn of the cap carries the piston a distance of lmm. The upper rim of the cap is divided into ten divisions, each one representing a movement of the piston through 0.1mm. These divisions being very large, the sub-divisions of 0.01mm can be obtained by the eye without error. The maker\u2019s graduation was verified to 0.01mm. The whistle is blown by a current of air forced into the bottom of the tube ; near the bottom there is a narrow slot extending across one-half of the circumference. The whistle is thus a closed labial pipe and the tone produced will be determined by\nv\nn being the number of vibrations, v the velocity of sound and l the length of the pipe. The velocity of sound in dry air at 0\u00b0 C. is generally given as 330.7m; for the temperature of t\u00b0 it will be\n330.7^/1 + 0.00367 t.\nThe average temperature of the room used can be taken as 20\u00b0 C. ; as the temperature was not recorded we can assume \u00b1 1\u00b0 C. as the limit of fluctuation during a set of experiments. This gives v = 342.525'\" with a mean error of 5 per cent, (estimated). As the actual '","page":106},{"file":"p0107.txt","language":"en","ocr_en":"Meper\u00eements on the highest audible tone.\n107\nmean variation for a set of results seldom exceeded 5 per cent, it may well be supposed that the constant of precision of the measurements was in this case determined by technical errors and not by psychological variations. In future experiments it will be necessary to maintain the room at an even temperature during each set of experiments ; and to calculate the pitch with the appropriate value of v for each change, possibly also to be on guard against sudden barometric changes.\nIt may seem remarkable that we should have neglected to record the temperature of the room. We give the following as reasons : 1. we did not expect after the elimination of the error of air-pressure to find the psychological sources of error smaller than the technical ones ; 2. the temperature of the air has not been regarded in previous experiments ; 3. it is not the custom of psychological laboratories to pay attention to the psychological and instrumental errors due to changes in temperature.\nSeveral means of blowing the whistle have been employed. Galton1 used a single rubber bulb. Zwaardemaker2 used a funnel with a rubber membrane stretched across the large opening, the smaller end being connected with the whistle by a rubber tube ; the funnel was depressed through a constant distance. These methods are none of them strictly reliable. The pressure is intermittent and cannot be accurately regulated. The only possible method of obtaining a current of air of constant intensity, seems to be by use of a rotary-fan blower. This method has been previously described and tested.3 The source of power used by us was an electric motor run by the city-current ; there were no perceptible fluctuations in speed. The fan-wheel of the blower made from 13 000 to 15 000 revolutions a minute. The blast was carried by a rubber hose into a room in another part of the laboratory ; thus all noise from the machinery was avoided. The hose led to a rubber tube, in which was a stop-cock. The rubber tube ended in a glass T-coupling with a rubber tube on each end of the cross-arm. One of these led to the whistle, the other to a water-manometer. The manometer scale was graduated to millimeters ; the height of the column of water gave the\n1\tG Alton, Whistles for audibility of shrill notes; Inquiries into Human Faculty, 38, New York 1883.\n2\tZwaardemaker, Der Umfang des Geh\u00f6rs in den verschiedenen Lebensjahren, Zt. f. Psych, u. Phys. Sinn., 1894 VII10.\n8 Scripture, A constant blast for acoustical purposes, Am. Jour. Psych., 1892 IV 582.","page":107},{"file":"p0108.txt","language":"en","ocr_en":"108\tE. W. Scripture and Howard F. Smith,\npressure of the blast of air supplied to the whistle. The pressure was regulated by the stopcock. In this manner a constant blast of air could be maintained for any given time and the intensity could be varied at will. The fluctuations of pressure as indicated by the manometer did not exceed 1 per cent. Experiments were made with five different pressures, 50mm, 100mm, I50mm, 200mm and 250mra. Within the limits of accuracy of 5 per cent, with which the experiments were conducted, the intensity of the vibratory movement could be considered as varying in direct proportion to the pressure of the blast.\nIn some of the earlier experiments we used a foot-blower as a bellows. Even the best bellows cannot be accurately regulated ; a foot-blower still less so. The following mean variations are from experiments on trustworthy observers. With the foot-blower we find, for example, mean variations of 10$, 14$, 5$, 9$, 8$, 13$ ; with the rotarv-fan blower, 5$, 9$, 2$, 7$, 4$, 2$. The records are not on the same observers in the two cases but the difference is sufficient to indicate quite a gain in accuracy by using the rotary blower.\nThe whistle was started near 0, i. e. above the upper limit of pitch, and the cap was gradually unscrewed until the observer deteoted a tone. The reading of the scale was observed at this point. The cap was unscrewed a little further to make sure that a good musical tone was heard ; then it was screwed up again, stopping at the instant the observer lost the tone. The two readings were noted down in separate sets, D and A. This was repeated five times, making 10 records with the given intensity. Sets of records were made in succession with the five pressures, beginning at 50mm. After a rest of about 3 minutes another series of 50 records was made but the pressures were used in the reverse order. This reversal of the order of the pressures eliminated the error of fatigue, if there was any.\nft will be noticed that the method differed from that used by previous observers, being the method of regular variation.1\nThe execution of the experiments was in charge of H. F. Smith who is responsible for the care exercised. The setting up of the blower, shafting and belting was done by the laboratory mechanic, J. H. Hogan, who controlled the running of the machinery during the experiments. Rubber belting was used, but owing to its inferior flexibility it should in future be avoided for small pulleys like that\n1 Scripture, On the method of regular variation, Am. Jour. Psych., 1891 IV 577.\nScripture, Ueber die Aenderungsempfindlichkeit, Zt. Psych. Phys. Sinn., 1894 VI 472.","page":108},{"file":"p0109.txt","language":"en","ocr_en":"Experiments on the highest audible tone. \u25a0\t109\non the blower ; with the high speed used it has been ignited by the slipping. The whole arrangement of apparatus was supervised and inspected by E. W. Scripture.\nComputation.\nThe median value was taken for each single set of five of the same kind. For the result descending or for the result ascending the two medians were weighted in the usual way inversely as the square root of the mean variations and were then averaged. For the final result the four medians were weighted and averaged.\nAs the use of the median is new, all the results were calculated also in the usual way to obtain the arithmetical mean. The components were weighted in the regular way.\nThe computation was done by E. W. Scripture with the aid of Crelle\u2019s, Rechentafeln. There were in all 120 sets of 5 results each. The median of each set was first recorded, then the error of each result from its median was written underneath it. The average of each set and the error of each result were likewise computed and were written beside the median and its errors. It was soon noticed that the average seldom differed much from the median ; this was used as a check on the computation of the average, the whole computation being repeated in case of much divergence. It was also noticed that, given the median and the average, the errors from the average could be calculated from the column of errors from the median ; for the latter half of the work this was done by the amanuensis while the computer calculated the errors directly. As a credential for the reliability of the computation, it can be said that only one mistake in the calculation of the errors was found in the results verified in this way. The mean errors of each of the 240 sets of five errors were computed according to the formula on pp. 18,24, the division by 4.5 being performed from th\u00e7 multiplication table for 45. The square root of each mean error was taken from a table of square roots. The reciprocals for weights were written as decimals to two places.\nInfluence of intensity.\nThe results are given in table I. Although the results were calculated into vibrations, they were allowed to stand in the table as hundredths of a millimeter in order to avoid the impression of a false degree of accuracy which arises when 0.01mm is turned into a whole number with zeros at the end. In the curve (fig. 33) the frequencies are given for the sake of comparison.","page":109},{"file":"p0110.txt","language":"en","ocr_en":"no\nE, W. Scripture arid Howard F. Smith,\nto 000\n55000\n50000\n35000\n30000\n20000\n15000\n10000\n5000\nFig. 33.\nTable I.\nUnit of measurement, 0.01mm.\n\t50ram.\tlOO\"1\u201c1.\t150mm.\t200\u201cm.\t250mm,\nComstock\t\t( 932\t541\t361\t247\t\n\t1 228\t543\t348\t245\t\nBishop.\t\t( 916\t464\t368\t276\t280\n\tj 924\t462\t364\t277\t279\nWaters\t\t\t524\t381\t335\t287\n\tj 943\t514\t377\t828\t291\nPersons\t\t938\t566\t365\t2\u00a35\t242\n\tj 938\t561\t360\t268\t249\nGosling\t\tj 923\t527\t364\t339\t342\n\t1\t917\t527\t366\t337\t340\nFurbish\t\t(907\t424\t317\t207\t* 163\n\tj 905\t425\t320\t202\t174\nLarge figures, computation with medians. Small figures, computation with averages.","page":110},{"file":"p0111.txt","language":"en","ocr_en":"Experiments on the highest audible tone.\nIll\n1.\tThe general result for all observers indicates that the pitch of the highest audible tone varies directly and almost proportionately with the intensity. The deviation from exact proportionality does not exceed the mean variation of the separate observers from the final averages. The curves of results agree very closely for all observers except for the pressure 250mm. This disagreement may be due to the very great and almost painful intensity of the tone.\n2.\tThe lowest results reach almost to Chladni\u2019s and the highest almost to Blake\u2019s, suggesting differences in intensity as the possible sources of discrepancy of previous results.\n3.\tHow far the upper limit can be pushed with still greater intensity, it is impossible to say. With a pressure of 250mm of water the tone of the whistle is already very painful and fatiguing.\nInfluence of dibection.\t'\nExperiments descending from 0 of the scale, i. e. from high to low pitch, or from silence to sound, alternated with those from low to high, or from tone to silence. The differences between tbe two are shown in table II. In order to detect any influence of fatigue the separate pairs for a given pressure were not united.\nTable II.\nUnit of measurement, 0.01mm.\n\t50mni.\t100mm.\t150\u201c\"\".\t200\u00bb\"\u201c.\t250mm.\t250mm.\t200\u201c\"\u201c.\t150mm.\tlOO\u201c\u201d1.\t50mm.\tE.\nComstock _\t! 2\t+ 23 + 37\t+ 20 + 58\t+ 29 + 43\t\t\t\t+ 23 + 50\t+ 39 + 80\t+ 38 + 68\t+ 23\nBishop\t\t( +42 ( + 43\t+ 55 + 57\t+ 21 + 28\t+ 65 + 53\t+ 55 + 53\t+ 75 + 83\t+ 50 + 47\t+45 + 36\t+ 41 + 26\t+ 46 + 46\t+ 50\nWaters\t\tj +11 | + 25\t+ 46 + 16\t0 - 14\t+ 2 + 25\t+ 5 + 3\t- 2 + u\t+ 35 + 28\t+ 28 + 2\t+ 7 + 15\t+ 24 + 17\t+ 9\nPersons...\tf +40 ( + 43\t+ 25 + 14\t+ 26 + 23\t+ 17 + 16\t+ 10 + 11\t-\t3 -\t6\t+ 43 + 80\t+ 23 + 34\t+ 36 + 13\t+ 18 + 19\t+ 24\nGosling...\tj +37 j + 16\t+ 25 + 13\t+ 21 + 19\t+ 2 + 13\t+ +\t+ 26 + 13\t+ 5 + 9\t+ 32 + 34\t+ 31 + 28\t+ 24 + 17\t+ 26\nFurbish ..\t] +20 j + 22\t-14 + 7\t-43 - 41\t+ 28 +-S0\t+ 32 + 19\t- 6 - 6\t+ 14 + 84\t+ 36 + 30\t+ 16 + 8\t+ 36 + 22\t+ 18\nThe figures give the differences between results descending and ascending, D\u2014A. Larger figures, differences between medians.\nSmaller figures, differences between averages.\nThe figures prove conclusively that the highest audible tone when proceeding from silence to tone is much higher than the highest audible tone from tone to silence. The column R gives the median difference for each person for the various pressures. The average","page":111},{"file":"p0112.txt","language":"en","ocr_en":"112\t25 W. Scripture and Howard F. Smith,\n-difference was not calculated. An inspection of the table shows that the averages run along closely with the medians ; the calculation of the averages would require considerable labor and would add nothing to our knowledge.\nThe table makes evident that, within the limits of accuracy employed, D\u2014A is not a function of the intensity.\nFatigue.\nSingle sets of experiments sometimes showed considerable differences whether taken at the beginning or at the end of the series. To determine the amount of fatigue the difference between the first pair and the last pair for each pressure was computed. Thus a table was formed giving the differences between the 1. and 10. pairs, 2. and 9. pairs, 3. and 8. pairs, 4. and 7. pairs, 5. and 6. pairs. The valu\u00eas showed such irregularity that it can not be said either that fatigue raises the upper limit or lowers it.\nIn similar manner some of the mean variations were compared. The result was the same ; it cannot be said that fatigue influences the regularity of judgment.\nThe attempt was made to fatigue the ear directly. After the complete set of experiments was finished with Bishop, the whistle ivas blown steadily for 45 seconds at 200mm pressure and then 10 records were taken at that pressure. The change of upper limit was not sufficient to warrant any conclusion. This line of experiment lay somewhat aside from the problem and was not extended.\nMiscellaneous observations.\nA phenomenon, closely related to fatigue, appeared in the oscillatory change from sound to silence. If the whistle was kept stationary at the pitch where the tone had just been lost, the tone would alternately he heard and lost again. The experience is similar to the phenomenon of fluctuation of attention with weak sensations. Another fact noticed was that even above where the tone could no longer be heard, an indefinite, somewhat painful sensation was felt in the ear.\nIt may not he uninteresting to note certain questions arising concerning the functions of the middle and internal ear. Helmholtz\u2019s piano-string theory of the function of the cochlea being accepted, does the energy required to arouse the shorter resonating membranes increase as the pitch of the membrane increases ? If so, why should there be the oscillating fluctuation in the hearing of the tone as just","page":112},{"file":"p0113.txt","language":"en","ocr_en":"Experiments on the highest audible tone.\t113\nnoted ? The question of the end-organs being left aside, might not the abilty of accommodation by the tympanum, as determined by the action of the M. tensor tympani be the determining factor for the highest audible tone? The extent of the reflex-action of a muscle depends to some degree on the intensity of the stimulus affecting the sense-organs. The impulse to accommodation proceeding through sensory and motor centers might be weaker for weak sounds, the tympanum would be less tightly stretched and as the pitch increased the limit of accommodation would be reached sooner than with louder sounds. On the other hand loud sounds would produce a much greater tension and therefore a higher accommodation. If this hypothesis is justifiable, the highest audible tone would be a matter of tympanic accommodation. The oscillations mentioned would correspond to the oscillatory fatigue and recovery of the nervous centers regulating muscular effort.\nIn this connection it may be suggested that the gradual falling off in the pitch of the highest audible tone with advancing age1 may be due, 1. to the gradual loss of function of the resonating organs of the cochlea, proceeding from those of higher pitch downward ; 2. to the gradual obtuseness of these organs, rendering them functionless for a given intensity but capable of answering to greater intensities ; or, 3. to a gradual decrease in the power of accommodation. The problem cannot be settled till Z ward ema aker\u2019s experiments are repeated with different intensities.\n1 Zwardemaaker, Der Umfang des Geh\u00f6rs in den verschiedenen Lebensjahren, Zt. Psych. Phys. Sinn., 1894 YII10.\n8","page":113}],"identifier":"lit28773","issued":"1894","language":"en","pages":"105-113","startpages":"105","title":"Experiments on the highest audible tone","type":"Journal Article","volume":"2"},"revision":0,"updated":"2022-01-31T15:19:50.061163+00:00"}