Theory of Tuning, Wave Lengths and Harmonics - Electrical Experimenter May 1918

32

May, 19 18

ELECTRICAL EXPERIMENTER

Theory of Tuning, Wave Lengths and Harmonics* By Prof. F. E. AUSTIN Ins t-ructor of E lectrical E ngineering, Thayer School of C i vil Engineering, Da rtmou th College

O-CALLED

rcso1um.-c is o f very great impo rt conncctcd in ' eric>

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Diagra ms Showing Effect of Resonance on E. M. F .'s in Different P arts of A. C. C i rc uit ; Also Simple Radio Circuits Used for Comparative Study.

I f a conden ser having a delin ite fixt v:tlt''! o f capacity C be connected, as shown in ligur e 2. in series with a coi l so arr anged as to allow a differen t num ber of t urns o f w inding to be introduced in to the circuit a s d esired, t he n the physical appar atus wilt fulfill all of t he variable cond itio n s possible. with a fox t frequency f. Look ing at t he proposition f ro m a sl igh tly different s tandpoint. s\oppose t h e con denser in figure 2. has an unchangeable ,·a lue o[ capacity and suppose the contact point P is so a rr;m gcd as to inc lude in the circui t mo r e and m o r e turn s of the coil a s t h e contact moves toward the right. With a ny defoni te va lue of the frequency of t he applied p o·essure, some position o f the contact P will be found su ch that the ind ication o[ the ammeter will be a IIW.rimtwt. I f t he contac t be m oved towa rd t he left from the position g iving a m axim um,

100,000

\\ith a coil ha ving an inductance oi 0.703 hen ry, then resonance obtains in the circuit f or a frequency o f 60 cycles, and th e current in the circuit is a m ax·imum. The numerica l value of the maxim um current

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(377)' 2915 vo lts; co ndition of affa irs 1t does not Jook expressure between the

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( l.'ffj L) 0 which is numer ically

equal to 11 10' ver v nearly. T his SCCnllS a bit' Ull\:31ln)'. actly logical that t h e

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m ately). T he pressu re drop between t he terminals of the coi l m ay be stated by ;

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If, therefo r e, a condct!';cr lta,·ing a capa c-

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obtai n, in a c ircuit is exprcst bv I ( - - ) . 2r.f c w hic h in the case under d ision i' equal I to: 11 X - -?.91.'> volts (appro xo-

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Graphic lllustratlo, of "Resultant" A. C. Curve Made U p of Th ree S ompte Sine Curves, or the 1st , 3rd, and 5th ;• H armonics."

:59

ELECTRICAL EXPERIMENTER

May, 19 18 o rder to ope:rate the valve efficiently the filame nt must burn bright ly and should be fed at about 20% above the specified voltage, t he exact amount varying with cha nging conditio ns. An accurate low voltage rheostat is essential for the prope r handling o f a ny hot fi lament rectifier, and espe· cially so in the case of our instrument. T he regu lation of the high voltage battery, however , presents the g reatest variation from common practise, and therefore affords much o pportun ity for research work. A 'phone circuit battery of about 60 volts is generally consider ed q uite sufficient for the majority o f present-day valve detectors, but in t he case of t he bulbs un?er consideration it is best to command a h1gh potential of up to 70 volts, altho very good results can be obtained with as little as SO volts. The c urrent from the cells which form this battery must be con trolled by a potentiometer of very high resistance o r, better st ill, several pairs of high resistance 'phones can be substituted therefor.. The autho r has found during his tests that a potent ial of about 75 volts, subjected to the re ta rding effect encountered by using the skin of the hand or fingers as a rheostat, gave unusua lly good results. T he idea of using part of one's body as a current regulat or is, of course, impractical, but the r esulta nt effect is so str iking that it leads the author to believe t hat a new instrument . may be developed to take the place of t he present potentiometer , which is known to be a very wasteful instrument. An adj ustable bank of receivers of di fferent resis ta nce but simila r pitch , connected w ith a common sound chamber or horn, should entir ely eliminate the need of a potent iomete r. There is also a chance of employing a variable condenser in this connection to a ppro x ima te the capacity effect obt ained in using the body as a resista nce. D uring the war it will naturally be impossible to test out a ny form of wireless instruments, except 'in the laboratory, where some type of non-radiating circuits must be utilized, and e ven there a buzzer practise set woul d constitute the limit of sending power available now. No aerial or ground connections a re permitted under the recent Radio Act. For the real electrical experimenter and research worker there still remains a wide field in which to work with any type of valve-amplifier that is not too highly valued to experiment w ith. T wo of the many possible uses to which electronic relays can be put outside the radio field are considered separately in the following paragraphs. Hot filamem valves are slowly coming into use as r ectifiers of electric current in commercial stations, but are still considered in the c hrysalis, or unfin ished state. The great draw-back in using bulbs for this purpose lies in the excessive waste of filament which takes place, making the rectifier very short lived. I t would be folly to use an expensive instrument for experiments along this line, but one of our lamps, which cost only about 60c to replace, may be used without one's being considered extravagant. By using the filaments interchangea bly at intervals of a few hours each it may be possible, under the r ight conditions, to greatly increase the active life of these bulbs when u sed as model rectifiers. T he most wonderful prope rty of the vacuum valve, and the one which holds the most in store for the inventor, is doubtless its ability to act as a n amplifier. For increasing, ind irectly, electrical energy and mechanical motion the electronic valve presents a very desirable medium. Many systems o f automatic sound control are being de\·eloped with the aid of the amplifier valve. There is no limit to the possi-

bilities of experimentation in this dir ection. Loud-speakng megaphones, phonographs, telephones, horns, ad infinitum, all await development. Submarine destroying de· vices, aerial torpedoes, locating apparatus of all kinds, can be invented which w ill prove to be the undoing of things out of sight. but not out of the hear ing of the delicate ear of the microphone, augmented and sensitized by the addition of an amplifier bulb. It is the author 's hope that the foregoing ideas may prove of real interest to a very large class of readers.

Important Notice to Subscribers Due to the congestion existing at the pre:sent tim e in aJI railroad move me nts, aJso on account of the fact that many train clerka have gone t o war, the:re is a con. gestion of mails all over the U nited States. It may ha ppen that your maga zine will be slow in reaching you, and this delay may be from a few days up to several wee ks. Kindly bear this in mind before sending in a complaint, as the magazine will aurely reach you in due time. Only after no t having received a cer tain co py for a period of three weeks should a complaint be sent in. You will confer a favor upon the publishers not to write until this time has ela p sed, t hereby saving them a vast amount of clerical labor.

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pdc:c even Lhe

=

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= 754 X

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100,000

= .00754 and L =

----1 - =0.17 henry.

.00754 X 754 It is thus evident that with a given condenser having an unchanging capacity, if the frequency is doubled, the value of the inductance must be decreased four times in o rder to produce a condition of complete resonance in the seri es circuit. T he current in the circuit under the new condition of doubled frequency will be the same as with the original frequency of 60 cycles, provided the ohmic resistance has no t been changed, and likewise the pressures between the terminals of the condenser and of the coil will be 2,915 volts as before. In order to decrease the inductance four times, the number of turns in the coil, or included in the circuit by the contact P will need to be only one-half as many as were originally included. If the number of turns were decreased th reefold the inductance would be reduced ninefold. ( Coutimted 011 page 62)

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T H EORY OF TUNI NG, WAVE LENGT HS AND HARMONICS. ( C ontin1ted from page 33) terminals o f the parts of a circuit can be more than that which is applied to the w ho le circuit. The relation of the different pressures may perhaps best be represented by such a diagram as shown in figure 3, in which the two pressures of 2,915 volts are shown at such an angle with each other as to form a resultau t pressure equal to 110 volts. The two large pressures are very greatly out of phase with each othe r, so that their geometric resultant on this composite mu t ual effect is really only llO volts. T he next step in the development of our discussion should be to consider what will happen in the circuit, and the numerical effect on the equations given, if the frequeucy of the applied pressure is doubled; that is, f is to become 120 cycles. I n this case 2'Trf 754, very nearly. Supposing the condenser is the same as used when the frequency was 60 cycles ; tlhe value of

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Mrs. Potts' Sad Iron netled onr SSOO.· ooo In royalties. Ball and soc 1c e t G 1 o v e Fastener b a a patb8t of t he applied pressure, causing a maximum current in the receiving ci rcuit having a frequen cy j ust three tim es that of the fwzdamental o r resultant pressure and cu rrent. T he predominating tone in the receiver has a pitch o r frequency three times that of the f undamental or resultant curve. By still f urth er adjustment of the var iable induetance, the fifth ha rmonic may be made predominant. If an imprest pressure is made up of , say, fifteen harmonics and the tun ing coil has sufficient range in adjustment, the Fifteenth harmonic might be made the predominant one. As the frequency goes up the wave length inversely becomes lower. Thus the third harmonic has a frequency three times the fundamental, and a corresponding wave length of one-third that of the fundamental, etc. A n other interesting h ct in connection with the matter of ''tuning" may be alluded to h ere, t hat has a very important relation to music and musical instruments. Nearly every person can distinguish the musical tones given out by a violin f rom those given out by a cornet or a piano. That is, a tone having a definite pitch or frequency given out by a violin has a very different qua fity from the same tone or note (same frequency) given out by a piano or by a cornet. W hen a ll these instruments are tuned to, say, middle C, they each produce a note having the same frequency or the same pitch, but the shape of the sound waves sent out by each instrument is very diffe rent. T h is may be illustrated diagramatically b fi 7 d fi 8 Y gure an gure · The resultant curve in figure 8 is made up of the sum of three sine waves as indicated, but has a very diffe rent shape f rom the r esu ltant curve in fi gure 7. T h e two res11ltant curves might have exactly the same wave length (distance f rom 0 to X ) , that is the same frequency, yet" they will never be mistaken for one another. Two wireless wa ves having exactly the same frequency may readily be distingu ished by an expert oper ator simply because of the characteristic of quality. It may be valuable to have devices that will tune not only for pitch but also for quality.

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