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
S
employed itt the g iven equatio n it may be no ted ft r t tha t the llltt11CratoJ· E denotes 1·he applied a lt ernating-pressur e, having a f requen cy denoted hy f (f means th e num be r of complete cycle, per secoml). R denotes the resistance of th e coil. exprest in ohms. C the capacity of th e cond ense r in
D I
E
INDUCTIVE
271'/ C
RESISl'A:'>ICE
-v~·-~~·~N-+1-------------
Wllen such nnmerical relationship dbtains in any ca e, then rPsoumtce is said to exist. T h e va lue of 7i' is, o ( course, a constant a t all times and the value o f f is definitely fixt fo r any gi vcn circuit. It is, therefore, appa rent that with a given ftxt value for . 1 27r'j L, a s imilar numerical value for - - -
K
27TfC
CO N OF. NSER
Fig. 1.-The Fundamen ta l Theory of Wire less May be Better Understood by Studying Th is Elementary Alternating Current Circuit, Comprising an Induct ive Re sista nce and Capa city Con n ected in Series. advanta"c. wi th a know ledg-e o f the f unda menta l law a nd its careful application, in maki ng and ope rati ng- luning- coil< :md s im ila r dc\'iccs. When a · coi l. cons ist ing o r a number of turns of insulated wire is co nnected in series with a condense r, and an a lternating pressure applied to the terminals of the a rrangement. as ind icated diagrama tically in figure l. the a lternati ng current in the arrangement indicated by an ammeter conmTted as sh o wn may h<· cxprc, t hy · E 1 -
1 )' ( 2rrfL - !.7
amo unt of energy. The symbol 1r denotes the va lue of 3. 1416. It is instructive to note th a t if the condenser be removed from the circuit and a direct-pressure be applied to the terminals of the coil, th e direct current may be exE prest by l = - : that is, according to Ohm's R law. :Now. h~· looking a t the fi rst equation it is evideut that the la st equ a tion may be obtained from the fir st when the numerical 1 val ue o f 2'iif L is made equal to - - - .
f arads, while L den otes the "o-ca lled coefficiem or ind uctance oi the coil, c:xp rest in '" ' "'') s. L depend, upon the square o£ the number •Jf turn, o f wire of wh ich the
may be found by varying th e v a lue o f C. T he value o£ C for a ny condenser depends upon the number of sheet s of dielectric used in making th e condenser. upon th e lli1rd of materia./ the dielectric consists of, upon the si=c of the dielectric sheets, and upo n a numerical conslw11 which is dependent upon the k ind of units employed in expressing size o r area, attd thickness.
D I
I
I
E
INDUCTIYE
RESISTA\'CE
N
K
•
CONDE N SER
F ig. 2.-This Alternating Current Circuit Shou td Be Carefully Studied by All Radio Students. a s It Contains Similar E lements to Rad io Circuits, I. e., a Variable Induct ive Resistance and a Capacity or Condenser.
coil is composed ; that is, of uwo coils o f the arne genera l sh ape. the one haYi~g twice as many turns as the other wtll have four times the inductance. A lso a coil h aving an iron cor e \\'ill • This nrliC'le rspeciall y prepared f or 1he uElcc· have very much g reater inductance than trlc:~.l Expl'rimf'nti"l'.'' the same o r a simi la r co il with ~---------------- lR----------------, o ut th e core. When, as in wireless work, it is desi r ed to employ v ery high frequencies, co i I s, hav ing no iron co res are used. s ince they may be mag netized and demagnet i zed very quickly and Diagram Representing the Genera tion of the "Sine Curve"-the Form without absorbof the Average Alternating Current Wave. ing an excessive
T h e capacity of ordinary condensers made up of sheets of dielectric and metal plates, may be exprest by:
c = .000,000,000.224
An k
fa~·ads.
ln the equation A denotes the area o f each dielectric sheet in square inches, n the number of sh eets used. k the so-ca.Jied specific inductive capacity o f the dielectric, and t the thickness of each dielectric sheet in thousandths o f a n inch ; that is, in mils. T he coefficient o f inductance of a coil having an iron core may be approximately exprest by:
471' n, A
L
= ---
b X DO'
he~trys.
May, 19 18 in which 7i has its usua l value, 11 deno tes t he number of I II YIIS o f w ire wound on the coil, 1\ de notes t he area o f the ho lt t hru t he center of the co il, exprest in sqmzre reHiimetrrs, a nd b deno tes the length of t he coi l (not o f t he wire), cxprc't in centi-
ELECTRICAL EXPERIMENTER
33
the ammete r indication decreases, and if the (On tact be m oved lo wanl the right fro m thi~ po,itio n, the amm etc •· ind icatio n
d cp,·nd, upon the nume r ica l value in \ Olt ' of lhe applied pressure, ;111d upon the n ·sista ncc in CJiom s o f the coil o r part of llt l
meters. Rewrning to the con>idcration o f the initial equation . a nd rc~tating the condition
f--
1
I I i,/
for resonance as when 27i/ L = - - - it i' ].7if
c
evident that the t'IJ ila t ion m ay b~ cha11gcd to: I 2:r.fC 27i/L T h e reason fo r tlte la tter a rrangement of the C£tuation is because it is muc h ea s ier to con struct o coil to produce a ' '" riablc inductance t han it is to cons I ruct a condenser to g ive a variable capacity. Con sidering the last equation, it is evident t hat i [ 271'[ C has a ny g iven nume rical value, with a definite value o i frequency ( valu e o f f) then some va lu e may he given L, so that t he numerical value oi I - -- ·ha ll be equal to the nume rical value 2r.f L o f 2'ffj C.
~
=- - .
II'
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69 8
Every True Alterna t i ng Current, of Any Sh ape Wh a tever, I s M ade Up of a C e rtain Number of Simple Sine Curves Added Together. The Heavy Line Represents the " Resulta nt" W ave F orm, P roduced by the Addition of the Th ree Sine W aves Indicated i1n Light L ines. Th ese Componen t Curves are Called the "Harmonic s."
a lso dracuses. Tu make the matter clearer and m or e concrete, it will be well to assign definite a nd p ractica l numer ica l values to the \'ar ious sym bols in the last equation. Let u' s uppose t he frequency f o f the a pplied a lternat ing pressure io; 60 cycles per second ; theu 2r.j is equal to very nea rly 3i7. S upp ose f ttrt her t hat the capacit y C of the I lixt condcm er is 10 microiarads o r - - -
'
lndf/tI we res
1/IJ~.
coi l that is connected in the ci rcuit. S uppose t he pr essuo·e is 110 volts ami the ohm ic res istance o f the wire on the coil is ]0 ohm s, then unde r t he condit ion s of r esonance me nt ioned, the curr ent " ill be LlO ...;- 10 = I I a mpe res. A ver y s t riking and importan t phenomenon ~hou ld IJe noted at this poim, name ly. the nume r ical va lnc of the drop in pressure between t he te rmina ls o f the coil and a lso between t he termina ls of th e con d·en ser. The d rop in pres ure between the te rm inals of a couckn~cr when rc>onan cc
100,000
( .(J()(J()I fu rctd ).
One million m icro fa rads arc equ:al to on e farad. According to this assumpti on l,r.f C hccom cs e<] urtl to 377 X
1
1 I - - -. :\ext ;, uppo'r that - - - = .00377.
100.000
=
T h en, s ince 2r.1 lndf/cl!vo res
= 0 .703
"~"
c
!.'Hf
377. L -
.00377
377 X .00377
l it\' of - - - far:od i> conncctcd in ' eric>
.
"
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
1"1
,,
\ 1R' +
I
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q
--
+
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(Co 11tilllll!d
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pagl! 59)
0 11
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•.nl It").,
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=
(377)' 2915 vo lts; co ndition of affa irs 1t does not Jook expressure between the
I
ormo 1c
~,
'
rttw··· '
( 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
.. .... \ - ......... ......v ·.,.. \ II/ . ..· ·~~ ~ v ' ~,\ ·~;;
=
m ately). T he pressu re drop between t he terminals of the coi l m ay be stated by ;
ltcttr\'.
If, therefo r e, a condct!';cr lta,·ing a capa c-
~mf er/,a
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.
~~...~~· ~.~:
th,.~c
pdc:c even Lhe
=
2'TrFC
= 754 X
I
-
-
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)
whol~3.le
) e welcr m u at p ay.
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~--~(1 just the book o n H ERE'S Electricity that you need to answer your many qucs· t ions-to solve your knotty proble ms. to teach you new k inks, to be your memory fortnblcs. rul es. formulas and other Eleclrical and Mechanical facts th't some people try to carry in the ir h cnds-nnd f3il.
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
Burlington
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;:~r td~a wort~?t Is Geo11:e P. Kimmel. tbe well-known PaJcnt Attorney or Was bloJrt,on 0 c .. (8~·£ Orlenlnl Building. WashlogWo. 0. C.)· · Sen d fo r Free Booklet !r It will be well worlh your while to 3end for Mr Kim· mel's free booklet. It will toMh you !loucb · about patent prncllce And procedure nnd will show you how 1mportnnt It Is to select tho right pntenl attorney to get 1011r nntcnt nnd to old you In solllnc or promot· log lt. Erperlenccd Inventors as wcU u the loe;rpcrlcneed should read ~lr. l(hnmel's "Patent Know!· edge for lnventort." It Is dltrereot from tbe mual stu!!' sent oul by potent concerns. Tbe booklet wtU ~=rdc~~ f!~~~:~d postpaid oo r equest. Address posl· obtained tree by wrtllng
AU T OMAT IC SPARK ADVANCE F O R MAGNE TOS. (223) John M. O'Brien, West Winfield, N. Y., submits an idea of an automatic spark advance for magnetos, and wishes to have our advice. A. This idea looks quite good to us, and seems to have several features that no doubt would be of interest to some of the automobile builders. \Ve think a patent may be obtained on this idea, but would advise a search made by a reputable patent attorney before finally applying for patent. This correspondent also submits a tank gage remote from the dash of the car. It is an electrical contrivance, and the amount of gasoline in the tank is indicated on an electrical meter. A. This is a very good scheme, and quite novel we are sure. Vl/e think a patent can be obtained upon it. It is one of these little ideas that appeal greatly to the average motorist. Another idea in the form o f a ball bearing is also suggested by our correspondent. He desires to know if it is of any value. !"-·. There is nothin g new contained in th1s 1dea as far as we c:~n see. It simply seems to be a variation of some of the ball bearings now on the market.
sold for $50,000.
Wooden Shoe Pep
0
~~~: GEORG~I ~MEL
PATENTS
May, 1918
ELECTRICAL EXPERIMENTER
LIGHTING OUTF IT. Willard St. John, Hawley, Minn., ~ubmits an idea of a lighting outfit which os to take the place of the unit lighting schemes using gasoline engines for motive power, especially where there is a windmill already in operation. A detailed description of the entire scheme is given and our advice is asked. A. To our mind the device is too lm•practkal and expensive, and we do not think it would replace the outfit.s on the market now. Also, inasmuch as no new princi-ple is involved, there would, of course. be no chance for patent protection. (224)
COMBINATION AUTOMATIC H E ATER. (225) Robert Bostwick, Jr., Seattle, \\'asl1., has hit upon an idea to combine a heating coil with a fan, all automatically operated. The automatic part is that a certain electric controller is contained in the device, so that when the temperature rises above a certain degree the fan will start running, thereby cooli1;g the atmosphere. Conv_ersely, if the temperature drops to a ce rtam level the heating coil is connected into the circuit, which in turn throws hot air into the room, thereby heating it. A. A capital idea ; very good and very simple. We are quite sure that our correspondent will find little trouble in securing a patent, which we arc also certain should pr ove valuable. He should get in touch with a patent attorney at once. AUT O GAS T A NK. 22 .< 6) L. B. Wilcox, flint, Mich., submas an idea for an automobile gas tank which is supposed to keep a reserve supply of gasoline. The arrangement is such that the tank automatically acts as a reminder to the driver. In other words, he would not be caught without gasoline far from a supply depot. A. The idea is good, but it is not of practical value, and we cannot see wherein an ordinary indicating tank gage would not be cheaper and simpler.
T HEORY OF TUNING, WAVE LENGTHS AND HARMONICS. (Contimud from pagt 59) If the· frequency of the applied pressure were increased three-fold-that is, to 180 cycles per second-the necessary inductance to be employed with the given condenser to produce resonance would be
L=
1
= .078 henry;
1131 X .01131
or one-ninth the amount required or iginally. If the applied pressure E and the resistance R of the coil is the same as originally, the current in the circuit will be 11 amperes as before. It is now a simple process to comprehend the application of the for egoing to a wi reless receiving circuit, with low resistance telephone receiver s connected as indicated in figure 4. or with high resistance receivers connected between the terminals of the condensers as indicated in Fig. 5. T he applied pressure E may be produced by wireless waves acting on the aerial. This pressure E may, of course, be of a ny value depending upon the energy available at the r eceiving device due to the distant sending <\pparatus. There may be three differ en: wave frequencies from these di fferent sending stations operating thru space at the same time, one having twice the frequency and a third having three times the frequency of the first. By slowly moving the contact P along the turns of the so-called tuning coil the value of the inductance L is so varied as to produce resonance and a maximum current in the t elephone receivers for one of the fr equencies. The pressures due to the other two fr equencies may produce a certain small current in the receiving circuit, and weak sounds in the receiver. By moving the contact from the position giving a maximum for one frequency, to another position, a certain position is found such that resonance and a maximum current is produced for another frequency. The maximum current for this frequency produces a much louder note in the telephone receivers than the currents due to the other two frequencies, which are now said to be "tuned out." The higher the frequency of the wireless waves producing the pressure and resulti ng cu rrent in the receiving circuit, the higher the pitch of the note in the receivers. Jt may be well to call to mind the relation of frequency and wave length. The high er the frequency the shorter the wave length, as indicated by the equation V =fA in '~hich V denotes the velocity of prop~ga uon or speed of a wave, f denotes its f r equency in cycles per second, and A (Greek letter lambda) denotes the wave length. The velocity V of propagation is the same for all wave lengths. That is. V is a constant; so if f is decreased, then A must be correspond ingly increased. The importance of th e numerical value of the r esistance R of the circuit needs consideration. Consulting the original equation 1
it may be seen that when 2?TfL =--that 2wFC fH AT PRO T EC T A ND PAY E E the current is exprest by I = - - = - ; 1 R '1/ R• ~:U~~ ~~~JM~! rl~~r,.:ri'·~·~:;~~· JMs'¥ ~~"t1ti!'l which shows that at perfect resonance with WAT SON E. COLEMAN, Patent Lawyer a given value of applied pressure E, the WaehJnctea. D. c. 624 F. Street, N. W. smaller the numerical value of the resistAn electrically operated machine has been ance of the c~il or of the complete circuit, EVERY INVENTOR invented for picking the feathers off a the $'reater w11l be the current in the coil ahould b&Yo lhla booi 'TA-rmm, ANl> chicken, which can pluck all the feathers off or c1rcuit, or in a telephone r eceiver when i.fu~7:,!.:;! connected as in figure 4. ;.~·~o::'r ~~'r.:t~. •~>;fh~'"ii. Write wi thin five minutes, In such an arrangement it is evident that lo:..~J~:Or:;?u~t'11tr/:d..."~'-:'! ~Pg~ nOOUIJn~ 10 1 0 t~e smaller the resistan ce of the r eceivers when solutions electrolytic and Carbon ~ ~ , "~tho domllld 1 greater will be the current in them. the while lowered resistance their have heated ' ""'.. '' •••••••••'· .,..,P, .......,••, 11 their resistance increased when H owever, the sensitivEJiess of a telephone o•!,.!~·::.::~::~:~f:~i.. -~~!~t ~~8!t.8!.~~ •m· metals have d h H.S.IIILL,IOl Mclachloo Bids. Washio..oa, D.C. r ~d~e~pe::n~d~s:_v~ery largely upon the _:.:....:...:.::.::..:.:..:...::.:.:.=::.::..~::;::;::·:;:·-7,~~~1~le~y~a~r_::e.;:.~ea~t~e;_·---:-""7""::---:--~--:---~~r::ec~e=i~v_:e~
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May, 19 18 ampere-tun zs. When arranged as in figure 5, the receiver would naturally have a much greater resistance than when arranged as in figure 4, since when connected across the condenser they are subjected to very high pressures. T h c greater resistance does not imply, however . that they should be wound with wire having a high resistance. In fact, such should no t be the case, since a la rge value of ampe re-turns is desirable. If copper wire is used in wi nding the electromagnets of th e 'phones, a given resistance will of course mean many more turns and therefore more ampere-turns, than if wire hav ing a higher specific resistance is employed. Coils wound with insu lated w ire so arranged with a var iai.Jie contact d cvicc as to have t heir ind uctance var ied at will thruout a consider able range, arc ca lled hmiug coils when used in connection with wireless receiving appa ratus, and it is interesting to note that as th e con tact P shown in figure 2 is moved so as to reduce the m unber of turns, that is to decrease the imluctance, a t the same time the resistauce of the circuit has also .been decreased. That is, the decrease in inductance and o f resis tance must occur simultaneously in such a d evice. Reclueing the number of turns reduces the actual length o f wire in circuit. The tuning m ight be effected by drawing an iron core in and out o f a coil, which would give a very wide variation, but which would be sluggish in action, and of course would not vary the olzmic resistance connected in circuit . Another method of varying the inductance might be effected by copstructing th e coil of two portions, arranged to move with reference to each other . I n such a case the var iation is said to be effected by 11m tual iuductio11, and the ohmic r isistance o f such appa ra tus is constant. Harmo11ics.-A very interesting and instructive use of the tuning coil is in tuning the receiving circuit to respond loudly to the var ious harmonics of any single fundamental wave t hat is being sent out from a sending station. This may perhaps be best explained by considering t he shape and composition of a lternating-current waves or curv~, and it is advisable to define just what is meant by an "alternating-current curve or wave." A t rue alternating pressure, current, or magnetic field is one w hich has exactly the same wave shape during each successive second, and one t hat is produced in acco rdance with a definite law: T he very simplest alternating curve is the so-called sine curve, shown in figure 6. Such a curve is constmcted by first d rawing a circle, as shown at the left, and laying off on a horizo ntal straight line, the length of the circumference of the given circle. The length is shown as 0 X in the figure. Op is therefo re one-half a circumference, Og one-fourth o f a circumference. The sine curve may be constructed by first erecting at point g a vertical line equa l in length to the radius of the ci rcle, then at point n a vert ical line equal to th e line A' B, which is. called the sine of the angle A ' 0 A. I n shor t, all the verticals erected on the horizontal base line represent the sines of corresponding angles about the cent er of the given ci rcle. The dotted horizontal lines · fi 6 ., · d m 1gure wu l g1vc an i ea as to the construction of the sine curve. Now every t rue alternating wave of any shape whatever is made up of a certain number of these simple sine cur ves added together. T he so-designated resultant curve in figure 7 is a true alter11ating curve, which is made up of three simple sine curves all starting at the zero point 0 , and all increasing in the vertical or positive direction. I t may be noted that one of the component sine curves has the same frequency or wave l cng~h as the resultant curve. This sine
ELECTRICAL EXPERIMENTER curve may be called the first harmol'ic. Another component sine curve has three times the frequency, hence one-t hird the wave length of the resultant curve. This sine curve is called the third lzarm01~ic. The other component sine curve has five times the frequency and one-fi fth the w ave length o f the resultant curve. The resultant curve is co nstructed by adding together algcbraical/y the vertical heights o f a ll three of the component sine curves a t each point chosen. The small circles on the resultant cur ve indicate the points that were chosen in order to construct the part icular curve. By algebraical addition is mean t that at any given point on t he horizontal all vertical d istances of the component sine cu rves extending below the horizontal must be subtracted from the vertical or the sum of the verticals extending above the horizontal at the same point. At points where all the component curves pass thru the horizontal datum line, there of course the resu/ta1Jt nrrve also passes thru the horizontal. It is evident that a great variety of rcsultant curves could be constructed from three simple sine curves by simply varying the heights or am plitudes of these cu rves: o r o f only one of them. E very alternatin g wave of pressure if applied to any circuit will produce in the circuit an alternating cur ve of current that is also made up o f component sine curves. It may, for exam· pte, be supposed that figure 7 denotes an alternating pressure E imprest on a circuit as shown in figure 5. By properly adjusting the movable contact P, resonance may be produced in the circuit with reference to the third hannollic compone~>t 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.
63
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