text:
History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1946 01

P.01 - Front Cover
The Australasian Radio World

Registered at the G.P.O., Sydney, for transmission by post as a periodical.

Price, 1/-

Vol. 10 - No. 8; Jan.-Feb., 1946

P.03 - Contents Banner
THE AUSTRALASIAN RADIO WORLD

Devoted entirely to Technical Radio

and incorporating

ALL-WAVE ALL-WORLD DX NEWS

VOL. 10 - JANUARY, 1946 - No. 8

P.03 - Publication Notes
PROPRIETOR — A. G. HULL

Manager - DUDLEY L. WALTER

Secretary - Miss E. M. VINCENT

Short-wave Editor — L. J. KEAST

For all Correspondence: City Office — 243 Elizabeth St., Sydney, Phone: MA2325

Office Hours — Weekdays: 10 a.m.-5 p.m. Saturdays: 10 a.m.-12 noon

Victorian Advertising Representative — W. J. LEWIS, 20 Queen St., Melbourne, C1, 'Phone MU5154

Subscription Rates: 6 issues - 5/3; 12 issues - 10/6; 24 issues - £1; Post free to any address.

Service Departments — Back Numbers, 1 /- ea. post free; Reply-by-mail Queries, 1/- each

Printed by Bridge Printery Pty. Ltd., 117 Reservoir Street, Sydney, N.S.W., for the proprietor of the "Australasian Radio World," Elizabeth St., Sydney (Footnote P.36)

P.03 - Contents
CONSTRUCTIONAL —

The Champion Amplifier. . . . 5

Simple Service Oscillator. . . . 7

Home Made Filter Chokes. . . . 17

TECHNICAL —

Cathode Follower Tests. . . . 13

Trends in Set Design. . . . 21

U.S. Radio Newsletter. . . . 22

Principles of Radar. . . . 23

Duplex Speakers for Fidelity. . . . 25

Ham Notes — Calling CQ. . . . 27

SHORTWAVE REVIEW —

Notes From My Diary. . . . 30

New Stations. . . . 33

THE SERVICE PAGES —

Answers. . . . 34

P.03 - Editorial
EDITORIAL

I laughed at a comic drawing in the local paper recently. In the first picture a man was struggling on to the step of an overcrowded bus, m uttering to himself, "There’s lots of room if the people on board would just move up a bit." In the second picture the bus has reached the next stop and this time our hero is muttering, "Surely these silly fools don’t think they can get on this bus; they ought to be able to see that it is overcrowded already." The radio trade is like that, too. You find that many people with a handy knowledge of the radio game change over from amateur to professional status, set themselves up in business and, when firmly established, they take on a high and mighty air of superiority and mutter, "The Government ought to stop people starting up in the radio business unless they are fully qualified." Few people in the radio trade are able to boast that they can pass examinations in every phase of radio theory, but this does not mean that they need be unable to give the public service or make profits. On the contrary, they may be endowed with more commonsense, business acumen and general knowledge than those who have spent the best years of their lives in the cloistered halls of a University. A reasonable amount of healthy competition is likely to be a far better safeguard to the public than any government regulations or examinations. A. G. HULL.

P.27 - Technical - Ham Notes — Calling CQ
HAM NOTES

CALLING CQ!

By Don Knock

P re ss new s fro m G -lan d sa y s th a t it w as d ecid ed, on 2 7 th N o v em b er to re la x D efen ce R e g u la tio n s to allow B ritish su b je cts in E n g la n d to p u rc h ase a n d hold ra d io tr a n s m ittin g eq u ip m en t, an d th a t th e b an on a m a te u r tran sm issio n w ould be lifte d sh o rtly. So by th e tim e these w ords reach “A .R .W .’s” p ress, th e G ’s m ay be on again. A s an y b o d y m ay h e a r fo r th e m  selves, U .S.A ., C an ad a, S o u th A m e ric an s a n d o th e rs are in full o ccu p an cy o f 28-29.7 M c/s. 4th D ecem ber, 194S.— M ost m o rn  in g s ju s t now th e “ 10-m etre b a n d ” is alive w ith W ’s an d m ixed up w ith th ese a re a few of th e W /J boys, A m erican s in th e arm ies of o ccu p atio n. F ra n k ly, I d o n ’t blam e th ese H a m s fo r seek in g such “ occ u p a tio n a l th e ra p y ,” alth o u g h th e m ode o f o p e ra tio n is defin itely p irac y. I am in trig u e d to n o te th a t q u ite a b it of cro ss-b an d w o rk in g is go in g on betw een W ’s (in U .S.A . on te n ) a n d W ’s (in th e Ja p a n e se a re a on 2 0 ). N o d o u b t all w ill go m e rrily u n til F.C .C. ta k e s a hand. T h e ed ict by W T A, w a rn in g “ th e g a n g ” off 14 M c /s, has n o t ta k e n co m p lete effect, fo r one o r tw o ir  rep ressib les a re still to be h e a rd on p h o n e a n d C .W ., w edged in betw een th e irr ita tin g din fro m tele p le x sta  tio n s. B o th 14 an d 7 M c /s a re im  possible to recognise as p re -w a r a m a te u r ch annels— fo r stra n g e rs are th e re galore. N e w R e g u la tio n s G a z e tte d O n th e 28th N o v em b er, 1945, th e new A u s tra lia n a m a te u r (e x p erim e n ta l) ra d io re g u la tio n s w ere g a z e tte d on th e lines a lre a d y re  fe rre d to in th is section of “A .R .W. ” T h ere w ill be few obje c to rs to th e p o w e r ra tin g s of 50 a n d 100 w a tts fo r th e tw o g rad es of licences, b u t th e ra isin g of th e m in im u m age to 18 y e a rs fro m th e p rev io u s fix tu re o f 16 y e a rs is likely to be th e su b je c t o f m uch a rg u

m ent. T h ere are p o in ts fo r, b u t m ore a g a in st th e new lim it, a n d it seem s o if-h an d to im ply th a t a y o u n g ste r w ith b ra in s eno u g h to sit fo r a n d p ass th e A .O .C .P. is n e v e rth eless irresp o n sib le to a d eg ree th a t he c a n n o t o p e rate ex p erim e n tal g e a r u n til he tu rn s 18. H e m ay p ass his exam s b rillia n tly p e rh a p s; and th e n is e x p ected to k ick his heels u n til tw o y ears am ble by. In th a t tw o y e a rs he m ay tu r n to o th er fields a n d a p o te n tia lly good m an m ay be lo st to ra d io ’s fu tu re, or, as is m o re likely, he m ay be im pelled to b re a k th e law a n d to o p e rate eq u ip m e n t illicitly. B o th p o ssibilitie s a re d ista s te fu l an d n o t calcu  la te d to en co u rag e th e class of s tu  dious y o u th th is c o u n try needs fo r h e r f u tu re m anhood. K een y o u th — a m a te u r ra d io — a n d w o rld p eace— can be synonym ous.

T h e N ew F re q u e n c ie s A s th is is w ritte n (D ec. 2nd, 1945), w o rd is o u t a b o u t th e fre  q u en cy ch an n els to be a llo tte d to A u s tra lia n a m a teu rs. T h ey a re :—

28-29 50-54 166-170 1345-1525 M c/s. T h ere w ill be sa tis fa c tio n a t least th a t so m e c h an n els a re m ad e av ailable by th o se who h old a u th o rity , b u t also a m easu re o f p e rp le x ity as to th e choice of tw o o f th em. It w as e x p ected in th e first p lace th a t, fo llo w in g decisions by U .S.A .’s F.C .C ., th e p re -w a r 10-m etre band w ould be slig h tly d e h y d ra te d — a t th e H .F. end— 28-29 M c /s as ag ain st th e W ’s 29— 29.7 M c/s, is p e rh ap s no serio u s bone o f co n ten tio n. N ev erth eless, it is a d efinite lo ss to th e A u s tra lia n a m a te u r. T h e new “fiv e-m etre” b a n d fro m 50-54 M c /s c o n fo rm s to A m erican decisions, an d, a lth o u g h it is n o t h arm o n ically re la te d to 28-29 M c /s, it is a b an d w hich m ay pro v e to be v ery u sefu l indeed. T h ere is a p o ssib ility o f in  fre q u e n t D X here. N o b o d y sh o u ld g e t th e id ea th a t m o d u la ted oscilla to rs a n d “ sq u eg g er” receiv ers will be a p p ro p ria te. T h is b a n d calls fo r (Continued on next page)

One of the neatest Ham stations we have seen is th is — pre-war G8LP, operated by Geoff Hanley, of Wolverhampton, England. Power was 50 watts and his 20 m. phone reached Australia in fine style. G8LP survived the war and will be looking for VK's again soon.

fu ll C.C. a n d su p erh et. C.W. te c h  niq u e as did 56-60 M c /s— th e p r e  w a r ban d. U nless sta b le Y F O w ith m u ltip lic atio n is used, c ry stals o u tside th e u su a l ru n o f th in g s w ill be n eeded, fro m 6 to 6.6 M c/s. T he b a n d 166 to 170 M c /s is a puzzle re g a rd in g choice o f allo catio n, fo r th e A m erican a rra n g e m e n t gives th e a m a te u r 140 to 145 M c /s in lieu o f th e p re -w a r “ 2 J-m e tre b a n d .” 166-170 is in clu d ed in a g o v ern  m en tal block o f freq u en cies. T h ere m ay be a re aso n fo r th e A u s tra lia n choice, b u t c e rta in it is th a t th is new b a n d w ill com e in fo r p le n ty of use w ith local n etw o rk s.

T ech n iq u e calls fo r ap p lic atio n o f n o n -sta n d a rd valves b u t fo rtu n  a te ly “ a co rn s” a n d valves of the 800 a n d 815 ty p e s w ill be av ailable. A e rial d im ensions a re o f co m p actly u se fu l size— a m ere 33 inches, giving a h alf-w av e of 166 M c /s. T h e last b an d, 1345 to 1425 M c /s, w as p ro b  ab ly n o t in te n d e d as a jo k e o r an in su rm o u n ta b le o b stacle— b u t th e av erag e a m a te u r can fo rg e t it— u n  less he has liv ed w ith R a d a r th ro u g h th e w a r y e a r, a n d has acq u ired R a d a r tech n iq u e ( a n d g e a r). T he sto ry goes th a t 3.5 M c /s (80m ). m a y be re sto re d a b o u t M arch, 1946. A s fo r 7 an d 14 M c //s — th e re is no in d ic a tio n as to th e fu tu re. M ean  w hile, licences w ill be issu ed fo r o p e ra tio n on th e new ban d s, a n d we know th a t th re e of th em will com e in fo r p le n ty o f occupancy. ■—D .B .K

P.28 - Technical - New Amateur Regulations
In fo rm a tio n released to th e W ire  less In s titu te by th e S u p e rin te n d e n t, W ireless (P .M .G .’s D e p t.), N .S.W ., o u tlin es th e fo llo w in g sa lie n t p o in ts: (1) T h ere will be tw o classes of licences— “ A ” a n d “B ,” w ith th e la tte r e q u iv a len t to th e p re -w a r licence. (2) F ee fo r e ith e r is 2 0 /- p er y e a r a n d does n o t in clu d e re ce p tio n o f b ro a d c a st p ro g ram m es. A n o th e r licence is n eed ed fo r th e la tte r. (3) M inim um age is ra ise d from 16 to 18 y ears. (4 ) A ll p rev io u s licen ce-h o ld ers w ill be eligible fo r a C lass “ B ” licence— an ap p lic atio n fo rm is to be co m p leted — also a “ S ta tu to ry D e cla ratio n of S ecrecy” ! (3) T h e p re se n t A .O .C .P. becom es th e 2nd class g ra d e an d m orse code speed re q u ire m e n t goes fro m 12 to 14 w ords p e r m inute. (6 ) T he first-class A .O .C .P. calls fo r h ig h er know ledge of ra d io and e le ctrica l th e o ry an d m o rse code sp eed is 18 W .P.M. (7 ) A n y p erso n u n d e r 18 y ears o f age w ho has a lre a d y q u alified fo r 2nd class A .O .C .P. w ill be issued w ith th is— b u t w ill n o t b e lic e n s e d u n til r e a c h in g 18 y e a rs ! (8 ) A .O .C .P. exam s (fro m J a n u  a ry, 1946) w ill be held on th e sec

ond T u esd ay o f J a n u a ry, A p ril, J u ly a n d O cto b er, b u t it is likely, ow ing to sh o rtn ess of tim e in w hich to m ake a rra n g e m e n ts th a t th e first 1946 exam will be held on 5th F e b  ru a ry. E x am fees a re : F irst-c la ss, 1 0 /-; second-class, 7 /6. (9) P o w er ra tin g s: C lass “ B ” m axim um I N P U T to fin a l a n o n e is 5 0 w a tts. C lass “A ” m axim um o u tp u t to final an ode is 100 w atts. (10 T h ere is y e t n o d e c is io n a b o u t frequencies. (11) A ll new licencees m u st serve a p ro b a tio n a ry p e rio d o f 6 m onths, d u rin g w hich th ey are n o t p e rm itte d to use telep h o n y . (12) N o tran sm issio n o f reco rd ed m usic o r e n te rta in m e n t is p e rm itted . (13) H o ld e r o f a first o r secondclass co m m ercial or a ir c r a f t o p e ra  t o r ’s tic k e t is e n title d to th e exp e rim e n ta l tic k e t (w h a t g ra d e is no t s ta te d ) . (14) H o ld e r of a b ro a d c a st s ta  tio n o p e ra to r’s tic k e t is n o t ene n title d to th e A .O .C .P. w ith o u t ex am in atio n . (15) A n “ A d v iso ry C o m m ittee” w ill o p e ra te in all S ta te s in th e sam e m a n n e r as th e V ig ilan ce C om  m ittee fu n c tio n ed prev io u sly.

P.33 - Shortwave Review - New Stations
NEW STATIONS

m in u te s’ P ress R o u n d u p in E n g  lish. K C B A, S a n F ra n c is c o , 6.1 7 m c, 4 8 .6 2 m : T his is a new freq u en cy fo r th is o u tle t o f th e C olum bia B ro a d m a stin g S y stem an d carries th e U .S. G o v ern m en t I n te r  n a tio n a l In fo rm a tio n S erv ice to J a p a n, K o re a an d S o u th -e ast A sia fro m 7 p.m. till 1 a.m. I t is in p a ra lle l w ith K C B F (9.75m c), K N B A (7.8m c) a n d K R H O (6.12 m e) a n d fo r th e b en efits of th e b ro a d ca st-b an d chasers w ith K S A I, lOlOkc, fro m 7.30-11 p.m. — L .J.K. K G E I, S a n F ra n c is c o : P ro b a b ly b e  fo re th is ed itio n reach es read ers, K G E I in tran sm issio n to G uam an d th e P h ilip p in es fro m 7 p.m .- 1 a.m. w ill m ove fro m 9.55mc, 31.41m, to 9.53m c, 31.48m. T his w ill only be lO kc fro m V L W -7, P e rth, an d m ay cause in te rfe re n c e in som e p a r ts o f A u s tra lia , b u t th e m ove aw ay fro m S in g ap o re (9.55m c) w ould be w elcom e.— L .J.K. J I E - 3, T a ih o k u , 9.'395m c, 3 0 .9 4 m : T his s ta tio n in F o rm o sa, once a re g u la r, has been h e a rd again a f te r a lo n g spell. N o t su re of schedule b u t it can be h e a rd m ost n ig h ts if m orse p erm its. W L W S, C in c in n a ti, 15.13m c, 19.83 m : A rth u r C ushen re p o rts : “ W L W S, on 15,130kc, is a new freq u e n c y w ith ‘V oice o f A m erica’ b ro a d ca sts. H e a rd till 6 a.m. T h en signs re -o p en in g a t 6.13 at even b e tte r s tre n g th .” H C IV T, A m b a to , E c u a d o r, 7.00m c, 4 2 .8 6 m : T h is one is re p o rte d by M r. R o g e r L egge, J r ., a n d d o u b tless A rth u r C ushen o r D r. G aden w ill la n d it b e fo re long. I t closes a t 1 p.m. H C 5 E H, C u e n c a , E c u a d o r, 3.9 4 m c, 7 5 .8 8 m : H e re is a n o th e r being h e a rd re g u la rly by M r. L egge, b u t w ill be a “ to u g h y ” in th is co u n  try, I th in k. A nyhow, it is on till 2 p.m. a n d som etim es la te r. R a d io B IS S A U, B is sa u , P o rtu g u e s e G u in e a , 7 .0 9 5 m c, 4 2 .2 8 m : H e re is a good catch b y R oger. L egge and th is W est C oast A fric a n should be au d ib le in A u stra lia. L an g u a g e used is P o rtu g u e se a n d schedule is 8-8.30 a.m. T his is ju s t a little la te p e rh a p s fo r th a t c o u n try and th a t freq u en cy, b u t th e tim e sh o u ld su it A rth u r C ushen. R A D IO M A C E IO, A la g o a s , B ra z il, 9 .3 0 m c, 3 2 .2 5 m : R o g e r L egge, J r., also re p o rts th is one. H e a rd in P o rtu g u e se fro m 9-10 a.m. Y N E T, M a sa y a , 7 .1 0 2 m c, 4 2 .2 4 m : T his N ic a ra g u a n sta tio n w ith slogan, “ R ad io M asay a, E m isso ra del P u eb lo ,” acco rd in g to R o g er L egge, o p e ra te s fro m 10.30 a.m. till 1 p.m. Y N B H, M a n a g u a , 7 .0 1 m c, 4 2 .8 0 m : A n o th e r in N ic a ra g u a re p o rte d by R o g e r Legge. “ R ad io P a n - am e ric a ” is h e a rd till 1 p.m. R A D IO M A C A S S A R, M a c a ss a r, 9 .3 7 m c, 3 2 .0 2 m : T his chief to w n a n d p o rt o f Celebes, N e th erlan d s In d ies, is h e ard n ig h tly fro m 7.30. S ig n al stre n g th is f a ir b u t m o d u  la tio n is p oor. T he a n n o u n ce r sta te s th e b ro a d c a st is to A u str a lia a n d th a t re p o rts w ould be w elcom ed. F ro m 9 p.m. n ativ e lan g u a g e is used. I am g ra te fu l to E rn Suffolk, o f L o b eth al, S o u th A u s tra lia, fo r first advice of th is sta tio n. I h ad h e a rd th e m several n ig h ts b u t could n o t catch call. M r. Suffolk him self say s it to o k an h o u r o f c o n c e n tra te d lis te n  in g to id e n tify it. R A D IO H A N O I, H a n o i, 1 2.135m c, 2 ^ .7 2 m : “ L a V oix de V e tn a n ,” H a n o i, In d o -C h in a, is re p o rte d by M r. L eo E d el as b ein g h eard ’n ig h tly a t fa ir stre n g th, b u t b ad ly d isto rte d. F re n c h a t 10 o’clock a n d new s in E n g lish a t 11. S logan, w av elen g th an d freq u en cy given a t 11, p re ce d in g th e new s. K N B X, S a n F ra n c is c o , 6.06m c, 4 9 .5 0 m : T his freq u e n c y used fo r som e tim e a little w hile ago by K N B I is now h e a rd n ig h tly fro m 8 o’clock as K N B X d ire c te d to th e P h ilip p in es a n d C hina. L a n  g u ag es used a re : E n g lish, T ag a - log, M an d a rin an d C antonese. Closes a t m id n ig h t a f te r a 10 R A D IO K U A L A L U M P U R, M a la y P e n in ., 6.0 9 m c, 4 9 .2 1 m : M r. Leo E d el is th e first to re p o rt th is one. H e a rd n ig h tly fro m aro u n d 8.30, b u t o ften sp o ilt by noise. “ T H E V O IC E O F F R E E I N D O  N E S I A ” ( L o c a tio n ? ), 15.22m c, 19 .7 1 m : A n o th e r re p o rte d by M r. E d el. H e a rd ev ery n ig h t fro m 9 till 11. V L C -1 0, S h e p p a rto n , 21.6 7 m c, 1 3 .8 4 m : E rn Suffolk re p o rts this new A u s tra lia n tr a n s m itte r as h e a rd on 24th D ecem b er in p a ra lle l w ith V L G -3 in p ro  g ram m e to B rita in. H e says sign als of V L C -10 w ere fa ir a t closin g a t 5.25 p.m ., b u t a t 5 o’clock th e y w ere inclin ed to be w eak and flu tte ry. D r. G ad en has since re  p o rte d th is one a t sam e tim e one a fte rn o o n.


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Planet Earth/2b. Solar Energy

A Fallen Scientist
On a cold late November day in 1997, Fred Hoyle found himself injured, with his body smashed against tomb-like granitic rocks at the base of a large cliff near Shipley Glen in central England. His shoulder bones were broken, his kidneys malfunctioning, and blood dripped from his head. He could not move, on the edge of death. He had no notion how long he had been laying at the base of the cliff, as it was dark, the moss-covered stones and cragged tree branches hovered over him in the dim light. But then it came. The sun. It illuminated the sky, burning bright, and he remembered who he was. Fred Hoyle was a physicist of the sun. Fifty years before, he wrote his greatest works, a series of scientific papers published between 1946 and 1957, and in the process discovered how the sun generates its energy through the generation of mass, in particular the generation of new forms of atoms of differing masses. He had founded a new field of science called stellar nucleosynthesis. In the early years of the twentieth century, scientists had discovered that enormous amounts of energy could be released with the spontaneous decay of radioactive atoms. This loss of atomic mass, is called nuclear fission, and by the 1940s, this power was harnessed in the development of atomic weapons and nuclear power. The sun, however, emits its energy due to nuclear fusion, the generation of atoms with increasing atomic mass. Fred Hoyle was at the forefront of this research, as he suggested that all atoms of the universe, are formed initially in stars, such as the sun.

Above him, the injured Fred Hoyle observed the sun. Its bright light illuminating the morning sky, glowing a yellowish white. It is a giant of the solar system, 1.3 million planets the size of Earth could fit inside the volume of the sun. It has a mass 333,000 times larger than the Earth. It is beyond the imagination of large, and while stars elsewhere in the universe dwarf the sun, its enormous size is nearly incomprehensible.

Stars are classified by their color (which is related to temperature), and luminosity (or brightness), which is related to the size of the star. The sun sits in the center of a large pack of stars called the Main Sequence, in a diagram plotting color and luminosity called the Hertzsprung–Russell diagram. The sun’s yellowish-white light spectrum indicates an average surface temperature of 5,778 Kelvin, and luminosity of 1 solar unit. Along the main sequence of stars, each star can be grouped by their color.

Annie Jump Cannon developed what is called the Harvard system, which uses letters to denote different colors, which relates to temperature. Using this system, the sun is a class G-star. The hottest blue stars are class O, with the cooler red stars class M. The series was used to map the night sky, denoting stars following a sequence from hottest to coolest (O, B, A, F, G, K, and M). O and B stars tend to be blueish in color, while A and F stars tend to be white in color, G are more yellow, while K and M are pink to red in color. 90% of stars fit on this Main Sequence of stars, however some odd-balls lay outside of this Main Sequence, including, the highly luminous Giant Stars (Supergiants, Bright Giants, Giants and Subgiants), and lower luminous White Dwarfs.

The Anatomy of the Sun
The outer crown of the sun is its atmosphere, composed of a gaseous halo seen when the Sun is obscured by the Moon during a solar eclipse. As a highly dynamic layer, giant flares erupt from this region of the Sun. The Corona is an aura of plasma (composed of highly charged free electrons) much like lightning bolts, which reach far into the space around the Sun. Solar Prominences are loop-like features that rise 800,000 kilometers above the Sun, and Solar Flares, arise from the margins of dark Sun Spots. Sun Spots are cooler regions of the Sun’s Photosphere, which are a few thousand Kelvin cooler than the surrounding gas. These Sun Spots have been observed for hundreds of years, and follow an 11-year cycle, related to the Sun’s magnetic orbit around its core. Sun spots appear just above and below the Sun’s equator in a clear 11-year burst of activity. Sun flares during this enhanced Sun Spot activity result in charge particles hitting the outer most atmosphere of Earth, resulting in a colorful Aurora in the night sky near the Earth’s magnetic poles during these events. Sun spot activity is closely monitored, since it can affect Earth orbiting satellites. (see http://www.solarham.net/). Measurements of solar irradiance hitting the upper atmosphere, measured by NASA satellites Nimbus 7 (launched in 1978) and Solar Maximum Mission (launched in 1980), among others since then, show slight increases of total solar irradiance striking the upper atmosphere during periods of sun spot activity. This is due to faculae, which are brighter regions that accompany sun spot activity, giving an overall increase of solar irradiance, however when darker sun spots dominate over the brighter faculae regions there has also been brief downward swings of lower solar irradiance during sun spot activity as well. Measured solar irradiance of the upper atmosphere since these satellites were launched in 1978 has shown that the sun’s energy striking the Earth’s upper atmosphere only varies between 1369 and 1364 watts/meter2 during these events (Willson & Mordvinov, 2003: Geophyscial Research Letters).

Temperatures are highest in the upper atmosphere of the sun, since these blasts of plasma excite the free particles producing temperatures above 1 million Kelvin. The lowest level of the Sun’s atmosphere is the Transition Zone, which can bulge upward through convection. Convection is the movement of energy along with matter which can effectively transport energy from the inner portion of the Sun upward. Below the Transition Zone is the much thicker Chromosphere, where the temperature is around 5,778 Kelvin. The Chromosphere is the red color seen only during Solar eclipses. Below the Chromosphere is the Photosphere, which unlike the upper atmospheric layers of the Sun is held by Sun’s gravity and represents more dense matter. Although the Sun does not have a clearly defined surface, the top of the denser Photosphere can be viewed as the “surface” of the sun, since it is made of more dense matter. Below the Photosphere are two zones which transport energy outward from the Core of the Sun. The upper zone is the Convection Zone, in which Energy is transferred by the motion of matter (Convection), while the lower zone is the Radiative Zone, in which Energy is transferred without the motion of matter, called Conduction. Between these two zones is the Tachocline. The inner Core of the Sun, representing about 25% of the Sun’s inner radius, is under intense gravitational force, enough to result in nuclear fusion.

The Sun’s Nuclear Fusion Reactor
The Sun’s energy is generated from the intense gravity crushing particles called protons into neutrons. When two protons are crushed together in the core of the sun, overcoming the electro-magnetic force that normally repels them, one proton will release sub-atomic particles and convert to a neutron. The result of this change from proton to neutron releases energy, as well as a positron and neutrino. The Earth is bombarded every second with billions of these solar neutrinos, which pass through matter unimpeded and often undetected, since they are neutrally changed and have an insufficient amount of mass to interact with other particles. Released positrons make their way upward from the core of the sun and interact with electrons which encircle the sun, and are annihilated when each positron comes in contact with an electron. Electrons, which are abundant as negatively charged plasma of the extremely hot outer layers of the sun, prevent positrons from reaching the Earth.

In chemistry, the simplest atom is just a single negatively charged electron surrounded by a single positively charged proton, what chemist’s call hydrogen. With an addition of a neutron, the atom turns from being hydrogen, to something called deuterium, which is an isotope of hydrogen. Deuterium carries double the atomic mass of hydrogen, since each proton and neutron carries an atomic mass of 1, so deuterium has a mass of 2. While electrons, neutrinos and positrons have an insignificant amount of mass, or a mass close to zero. The incredible gravitational force of the sun, breaks apart atoms, with electrons pushed upward away from the core of the sun, forming a plasma of free electrons in outer layers of the sun, while leaving protons within the center of the sun. Electrons, which carry a negative charge are attracted to Protons, which carry a positive charge. Outside of the gravity of the sun, the free Protons and Electrons would attract each other to form the simplest atom, the element Hydrogen. Inside the core of the sun, however, the Protons are crushed together forming Neutrons. This process is called the Proton–Proton chain reaction. There is some debate on how protons in the core of the Sun are crushed together, recent experiments suggest that protons are brought so close together they form diprotons, where two protons come together forming a highly unstable isotope of Helium. Elements are named based on the number of protons they contain, for example Hydrogen contains 1 proton, while Helium contains 2 protons. During this process protons are also converted to Neutrons. The addition of Neutrons helps destabilize atoms of Helium, that contain 2 protons. The Proton–Proton chain reaction within the sun takes free Protons, and converts them through a process of steps into atoms of Helium, which contain 2 Protons and 2 Neutrons. Elements with differing numbers of Neutrons are called Isotopes, hence, inside the core of the sun are the following types of atoms:

 * 1 proton + 0 neutrons (Hydrogen)
 * 2 protons + 0 neutrons (Helium‑2 isotope)
 * 1 proton + 1 neutron (Hydrogen‑2 isotope, Deuterium)
 * 2 protons + 1 neutron (Helium‑3 isotope)
 * 2 protons + 2 neutrons (Helium‑4 isotope)

Through this process, Hydrogen with a single Proton is converted to Helium‑4 with two Protons and two Neutrons, resulting in larger atoms inside the core of the Sun over time.

How the Sun Made the Larger Elements
The proposed idea for this proton-proton chain reaction within the sun’s core was first theorized by a group of physicists in 1938, working together to solve the question of how the sun generates its energy. While attending the annual meeting of the Washington Conference of Theoretical Physics, the participants worked out the possible path of reactions. One of the members of this group, was a Jewish German immigrant named Hans Bethe, who was a professor at Cornell University in New York. Upon returning from the conference, Hans Bethe and Charles Critchfield began their study of larger elements, and their possible generation within the sun, and larger stars. They discovered something remarkable when fused atoms within a sun’s core gained 6 or more protons: They could act like a Catalytic cycle to enhance the production of Helium‑4 from Hydrogen. A catalyst is a substance that does not get used up in a reaction and will continue to act repeatedly over and over again in a reaction. Bethe and Critchfield discovered that in the presence of atoms with 6, 7 and 8 protons, these atoms can facilitate the fusion of Hydrogen into Helium at a faster rate, working as a catalyst. This process is called the CNO-Cycle, since it requires larger atoms, the elements Carbon-Nitrogen-Oxygen to be present within a sun’s core. Our own Sun is a rather smaller Star, and as such contains a smaller amount of energy generated through the CNO-Cycle. It is estimated that only about 1.7% of the Sun’s energy is generated by the CNO-Cycle, however, in larger Stars the CNO-Cycle is an important process in the generation of energy, especially in stars of higher temperatures.

The discovery of the CNO-Cycle in the Sun and other Stars by Bethe, was marred by the rise of Adolf Hitler in Germany in the late 1930s. Hans Bethe, still a citizen of Germany, but of Jewish heritage, worked during this time to get his mother and family out of Germany. In fact, the paper describing the CNO-Cycle won a cash prize from the journal, which helped fund his mother’s emigration to the United States. Hans Bethe’s talent for understanding the physics of how nuclear fusion and fission worked was recognized by the United States military, who appointed him to lead the theoretical division for the top-secret Los Alamos Laboratories in the design and construction of the first nuclear weapons during World War II.

Even with the design and implementation of fission nuclear bombs in the 1940s, scientists were racing to figure out how larger atoms could form naturally within the heart of stars by the fusion of atoms.

Supernovas
All this was spinning in Fred Hoyle’s mind as he lay at the base of the cliff. He knew all this. He had felt left out of nuclear research having served during World War II only in the capacity of a specialist in radar research. It was only after the war that he became passionately interested in the Sun’s nuclear fusion. How larger and larger atoms could form inside larger stars. Inspired by the research conducted in the United States during the war, Fred Hoyle developed the concept of nucleosynthesis in stars to explain the existence of elements larger than Helium‑4. Our own Sun generates its energy mostly by the Proton-Proton chain reaction, in other words, burning Hydrogen to form Helium‑4. With the occurrence of Carbon-Nitrogen-Oxygen, this process could be accelerated, but, Fred Hoyle pondered how elements larger than Helium‑4 could exist and be formed through the same process. He called this secondary process Helium-burning, a process of fusion of atoms together to produce even larger atoms, the numerous elements named on a periodic table of elements. Fred Hoyle, William Fowler and the wife and husband team of Margaret and Geoffrey Burbidge drafted a famous paper in 1957, which demonstrated that larger atoms could in fact be generated in very large stars, and that the natural abundances of those elements within surrounding planets led to greater knowledge of the steps taken to produce them in a star’s lifetime. These steps lead upward to the production of atoms with 26 protons, through a process of fusion of smaller atoms to make bigger atoms, but atoms with more than 26 protons required a special case: They formed nearly instantaneously in a gigantic explosion called a Supernova.

Thus, it was theorized that the basic distribution of elements within our solar system was formed through a stepwise process of fusion in a gigantic star that eventually went critical and exploded in a supernova event, injecting atoms of various sizes across a Nebula, a cloud of gas and dust blasted into outer space. This gas and dust, the Nebula, formed slowly over thousands of years into a protostellar-protoplanetary disk, that eventually led to the formation of our Solar System, and every atom within it. Carl Sagan often quoted this strange fact with the adage, “We are all made of stardust!”

Will the Sun Die?
The fact that our Solar System formed from an exploding giant star, raises the question of what will happen to our Sun over time? The fuel of the sun is atoms of Hydrogen, in other words single Protons which over time are converted to Neutrons, or more specifically Helium‑4 atoms that contain 2 protons and 2 neutrons. Eventually, there will remain no more Hydrogen within the core of the Sun, as this fuel will have been replaced by Helium‑4. At this point, the Sun will contract, and compress inward and become more and more dense. At some point the increasing gravity will cause the Helium‑4 to fuse into larger atoms, and the Sun will begin a process of burning Helium‑4 as a fuel source, which will result in an expansion of the sun outward, well beyond its current size, forming a Red Giant. During this stage in its evolution, the Sun will engulf Mercury, Venus, and even Earth, despite burning at a cooler temperature. The Earth is ultimately doomed, but so is the Sun.

Eventually the Helium‑4 will be exhausted, and the Sun will contract for its final time, reducing its energy output drastically, until it forms a faint Planetary Nebulae, composed of larger atoms of burnt out embers of carbon, nitrogen, oxygen, and the remaining atoms of this former furnace of energy, until it is crushed to about the size of Earth. Scientists estimate that this process will take 6 billion years to play out, and that Earth, with an age today of 4.6 billion years, has about that many years remaining until our planet is destroyed during the Red Giant stage of our Sun’s coming future.

The Big Bang
When Fred Hoyle tried to rise himself up from his splayed position below the cliff, he winced in pain, bringing back the memory of his most noteworthy quote, a phase he mentioned during a radio interview in 1949. A phase that suggested that not only that the Solar System had its beginning with a violent explosion, but that a much older explosion birthed the entire universe. Hoyle rejected an origin of the universe vehemently, favoring an idea that the universe has always existed, and that it lacked any beginning. During the 1949 radio interview, Hoyle explained his steady state hypothesis, by contrasting his ideas to the notion of a “Big Bang”, an explosive birth of the universe. A new idea that was proving interesting to other scientists but Hoyle rejected it. During the 1960s, Hoyle begin rejecting any idea that seemed to contradict his own, and became noteworthy for his contrarian scientific views. In 1962, a young student named Steven Hawking applied to study with Fred Hoyle at Cambridge, but was picked up by another professor to serve as his advisor. This was a good thing, as Hoyle became entrenched in his idea that the universe had no beginning, so much so, that in 1972 after a heated argument with his colleagues over hiring practices, Hoyle quit his teaching position at the university and retired to the countryside. That same year he had received a knighthood, and he struck out on his own.

However, the memory of that period likely brought a painful sensation to his heart. Outside of the academic halls, Fred Hoyle became a burr toward the established scientists of the day, drafting more and more controversial and strange ideas and finding some success in publishing science fiction novels with his son. In 1983, he was excluded by the Nobel prize committee, which awarded the prize to his co-author William Fowler and Subrahmanyan Chandrasekhar for their work on stellar nucleosynthesis. Snubbed, Fred Hoyle fell into obscurity. However, the concept of a “Big Bang” would come to define the future exploration of theoretical physics, and make Steven Hawking a household name.

Although Fred Hoyle was rescued from his fall from the cliff and transported to the hospital, he never recovered from his fall from science. A fall that could have been averted if he had observed the growing number of breakthroughs regarding the nature of light, and startling discoveries that proved the universe did indeed have a beginning.

license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Planet Earth/2b. Solar Energy


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History of wireless telegraphy and broadcasting in Australia/Topical/Publications/Australasian Radio World/Issues/1947 01

P.01 - Front Cover
The Australasian Radio World

Registered at the G.P.O., Sydney, for transmission by post as a periodical.

1/-

Vol. 11 - No. 8; January 15, 1947

P.03 - Contents Banner
THE AUSTRALASIAN RADIO WORLD

Devoted entirely to Technical Radio

and incorporating

ALL-WAVE ALL-WORLD DX NEWS

VOL. 11. - JANUARY, 1947. - No. 8.

P.03 - Publication Notes
Editor, Publisher, Proprietor — A. G. HULL, Balcombe St., Mornington, Vic.

Short-wave Editor — L. J. KEAST, 6 Fitzgerald Road, Ermington, N.S.W. 'Phone: WL1101

Ham Notes By — D. B. KNOCK (VK2NO), 43 Yanko Av., Waverley, N.S.W.

Advertising Representative for Vic. — W. J. LEWIS, 20 Queen St., Melbourne, 'Phone MU5154

Advertising Representative for N.S.W. - Amalgamated Publications Pty. Ltd., 83 Pitt St., Sydney, Phone: B1077

Subscription Rates: 6 issues - 5/3; 12 issues - 10/6; 24 issues - £1; Post free to any address in the world.

Address for all correspondence - Australasian Radio World, Balcombe St., Mornington, Victoria

Printed by Bridge Printery Pty. Ltd., 117 Reservoir Street, Sydney, N.S.W., for the proprietor of the "Australasian Radio World," Balcombe St., Mornington, Vic. (Footnote P.36)

P.03 - Contents
CONTENTS

TECHNICAL —

Designing Battery Receivers. . . . 5

The Control of Tone. . . . 13

The Choice of I.F. Frequencies. . . . 19

Calling CQ. . . . 21

Further Restrictions for Hams. . . . 11

Australian Broadcasting Stations. . . . 26

SHORTWAVE REVIEW —

Notes from My Dairy. . . . 30

THE SERVICE PAGES —

Answers. . . . 34

P.03 - Editorial
EDITORIAL.

This issue and the last one must surely rank as two of the weakest issues we have ever published. We admit it quite frankly. Instead of wasting time explaining the whys and wherefores of the many factors which have conspired to bring about such a sad state of affairs we want to again reassure readers that there are brighter issues "just around the corner." Our postwar plan for improvement is still to open, but it won’t be long now. Already the features of the plan have been brought into alignment, but there are still one or two points to be straightened out. First and foremost, we need an editorial representative in Sydney. For preference the representative should be an enthusiastic young fellow, with at least a fair idea of technical radio and the ability to build up a set or two, who will keep in touch with the Sydney radio trade, find out all the new components that are being prepared for release, and generally make sure that we don’t miss any of the Sydney goings-on because of our decentralisation plan. For a start it might be possible for the job to be part time, or even done by someone who spends lunchtime in town, but it should soon develop into a full-time job with the establishment of a city office when such luxuries again become available. Next thing we want is a larger team of contributors of technical articles. We never seem to get enough of the type which are suitable. If you have any ideas or propositions to help us in these matters or any other suggestions, you will find that we are especially receptive at this moment. — A. G. HULL

P.29 - Technical - Short-Wave Listening
Short-Wave Listening There are SW L’s with a flair for meticulous and careful observation of amateur transmissions, and from whom detailed reports are welcomed by the Ham worth his salt. It’s a safe bet that when an SWL with plenty of experience, like Ted Buchester, Q’ld, puts his pen to paper, something of interest results. O f my remarks recently about V K ’s who scorn SWL reports, he writes at length: "I can recall sending a report to a VK7, a most helpful bit of gen. by the way, and he told me to let it be known he did not QSL to listeners. He was playing recordings (now I am aware how you chaps hated these guys), and the modulation was 100 p.c. and honestly 5 and 9. If I hear a 'Ham’ calling C.Q., and his sig. is, say, R8 or ?■ at this location and he eventually has a contact, and the other man gives him a poor report, and the said ’Ham’ talks of dragging the antenna down or something like that, it annoys me not to be able to give him a buzz. I do the next best thing and drop him a line, not asking for a card, but a reply, and I have not missed on that yet. I am using an ordinary 6-tube Super, 1 -stage R.F., and have tried a few antennas, but am doing quite well with one of those V types as in ARRL Handbook, 1945. Have not concentrated on normal short-wave stations, but like, the 'Hams’ best as yet. I have only two verifications from overseas amateurs, namely W llC Y and XE2FC. These were pre-war. My oldest veris are from KSL and KGU, 1935, and I can recall three very outstanding signals heard here prewar, i.e., W 6CQS, W 5B K Y and K 6BNR. I seem to hear more V K 3’s and 5’s here. V K 3TW puts in a fine signal most consistently. PK6AW comes through here quite well, also a few South Americans, but G ’s are very scarce. I am learning C.W. now, and am definitely going on the air in the near future. Am just out of the R.A.A.F. (served by ''sentence” of 5 years 4 months) and me and quite a few 'Hams’ in same. It appeared the 'Hams’ and the Air Force did not hit it too well re ideas, but the 'Ham’ won in the end. Would like very much to purchase a Call Book.” Mr. Buchester’s log of amateur stations for August last is shown here for the benefit of overseas readers. Re the V K call book: It is understood that 2/6 to the P.M .G.’s Dept., Wireless Branch, Treasury Gardens, Melbourne, will bring the complete list to the present period. — D.B.K.

D ate 26/8/4.6 27/8/46 28/8/46 29/8/46 18/8/46 16/8/46 21/8/46 23/8/46 24/8/46 25/8/46 T im e R e c ’d 1730 1742 1810 2110 2112 2114 2119 2130 2140 2146 1510 1645 1700 1725 1729 1800 1807 1835 1852 1856 1859 1904 1910 1917 2010 2014 2017 2020 2025 2015 1713 1718 1720 1735 1530 1700 1940 1600 1605 1900 1912 1510 1512 1540 1543 1548 1610 1705 1716 1835 1850 1854 1857 1900 1912 2105 2110 21-30 1505 1512 1615 S ta tio n J 2 A B B W 6 L Y W 6M O Y V K 7 A B W 3P O Z P K 6 A W V P 9 F W 1C C Z V K 5 B F V K 3 T W W O T Q K W 6 P D B W 6M O V K 8 6 V X V E 7 0 T (called only) W 6 U D F V R 2 J I W 2 A Q K W 8 W H W J 9 L G V R 2 J I W 6A H T 1 2 0 A W 4 F G W W 2Q C P W 9 W JN W 3 H K Y W 3 T H W 2R M W 4G A Q W 9 0 T K K 6 B H L V K 3 Y H O A 4 B E W 6 F G U V E 7 Z M V S 1 B V W 2Q W Q J 9 I .G T 1 2 0 A V K 6 R U X A A P OA 4M D 4 N A X G 2P U W 7 E H Q W 6U N A W 9C A C W 6A N N V E 4 A C J 2 S J B W 7 E L J W 9 0 T K K A 1 A K J 2 S J B P K 6 A W W 1 1 A S P K 6 A W L A I F D 4A N L W 5 P T L Q R A Ja p a n G lend ale, C alif. C a lifo rn ia T asm an ia New Je r s e y B ia k Is ., New G uinea B erm u d a So u th A u stra lia H am ilto n, V ic. M issouri E a g le R o ck S a n Jo s e H aw aiian Islan ds .V an cou ver G uam Is. Su v a, F i ji E lm sfo rd, N .Y. G uam Is. M arsh all Is. (1 4 2 8 0 k c ) S u v a, F iji. C a lifo rn ia C o sta R ica P o rta b le K 2, Ja p a n R o ch ester, N .Y. P h ilad elp h ia H am b u rg, New Y o rk K en tu ck y ( J 9 ), M arsh all Is. H aw aiian Is. M elbou rne -Lim a, P eru S a n D iego B ritish Colum bia Sin g ap o re N eb rask a M arsh all Is. C o sta R ic a W est. A u stra lia A th en s, G reece L im a, P eru G erm an y Cam bridge W ash ington C a lifo rn ia Icelan d S a n P edro W in n ip eg T o k io (1 4 2 9 5 k c ) A leu tia n Is. M arsh all Is. ( P .J 9 ) M an ila T o k io, Ja p a n B ia k Is ., D u tch N .G. ____M Q CC B ia k Is., D u tch N.G. N orw ay F r a n k fu r t, G. San A nton ia M ass. N o rth T ex a s W K D J9 A A R K 6 W 7H O L V K 4 K S J9AAB W 2 B X A G W 5K W M CQ W IC C Z W 7 F P Y V K 2A G M K H 6C C K 6 R V O V K 4 JU W 7 A B Q J 9 L G V R 2 J I W 6 R U L CQ W 6A H J 9 L G W 6A H W 6 B T D P K 6 A W C IS U W 5 R D E V K 4 K W V K 2M G CQ W 3 G K J W 5 S K E T estin g W 6 0 C A •19LG K A 1 A B V K 2 D P K A 6 B X W 6A N N V K 37.L V S 1 B V W O F N 1 W 5 Y F \V4 W 6A N N G 2 P U V K 2 A B D W 1 B C R W 9C A C V K 3 T est, only CQ W 6 U Y V J 2 A A F W 6 U Y V X E 1 A P P K 6 A W W 4.A IT C alled CQ W 8 W 3 L A C W 6 V K 4 JP Q SA 4 5 5 5 4 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 5 4 5 5 5 5 4 5 5 5 5 5 5 4 5 5 4 R 6 6.8 6.7 9 6 8 5.6 8 9 + 9 + R.6 9 FfI 6 8 7 7.8 6-8 7-8 5 -6 7-8 6-8 6-7 6-8 6-7 5 6 6 7 6-8 7 6 7 8 8-9 7 8 9 5-6 7-8 9 6 7 8 5-6 6 5-6 7 8 7 5-6 8 7-8 7 8 6-7 7-8 6 8 7 5 8-9 5-6 8-9
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P.26 - Technical - Australian Broadcasting Stations
AUSTRALIAN BROADCASTING STATIONS (Arranged in order of frequency) The following is the latest complete list of all the Australian broadcasting stations, including all commercial, national and relay stations. 2CR 550 545 Cumnock 6WA 560 536 Wagin 3WV 580 517 Dooen 7ZL 600 500 Hobart 2FC 610 492 Sydney 3AR 620 484 Melbourne 4QN 630 476 Clevedon 5CK 640 469 Crystal Brook 2DU 660 455 Dubbo 7BU 660 455 Burnie 2CO 670 448 Corowa 2HR 680 441 Lochinvar 4AT 680 441 Atherton 7QT 680 441 Queenstown 6WF 690 435 Perth 2NR 700 429 Lawrence 7NT 710 423 Kelso 6GF 720 417 Kalgoorlie 5CL 730 411 Adelaide 2BL 740 405 Sydney 4QS 760 395 Dolby 3LO 770 390 Me’boume 2KA 780 305 Katoomba 4TO 780 305 Townsville 6WN 790 380 Perth 2BH 790 380 Broken Hill 4QG 800 375 Brisbane 5RM 810 370 Renmark 2NA 820 366 Newcastle 6GN 820 366 Geraldton 3GI 830 361 Sale 2CY 850 353 Canberra 4GR 860 349 Toowoomba 7HQ 860 349 Hobart 2GB 870 345 Sydney 3UL 880 341 Warragul 4WK 880 341 Warwick 6PR 880 341 Perth 5AN 890 337 Adelaide 2LM 900 333 Lismore 7AD 900 333 Devonport 4RK 910 330 Rockhampton 2XL 920 326 Cooma 4VL 920 326 Charleville 3UZ 930 323 Melbourne 4QR 940 319 Brisbane 2UE 950 316 Sydney 5DN 960 313 Adelaide 3BO 970 309 Bendigo 4AY 970 309 Ayr 2KM 980 306 Kempsey 6AM 990 306 Northam 2GZ 990 303 Orange 4MB 1000 300 Maryborough 4CA 1000 300 Cairns 7EX 1000 300 Launceston 3HA 1010 297 Hamilton 2KY 1020 294 Sydney 3DB 1030 291 Melbourne 5PI 1040 288 Crystal Brook 2CA 1050 286 Canberra 4SB 1060 283 Kingaroy 2RG 1070 280 Griffiths 6WB 1070 280 Katanning 2LT 1080 278 Lithgow 4RO 1080 278 Rockhampton 7HT 1080 278 Hobart 3LK 1090 275 Lubeck 4LG 1100 273 Longreach 7LA 1100 273 Launceston 6MD 1100 273 Merredin 2UW 1110 270 Sydney 4BC 1120 268 Brisbane 2AD 1130 265 Armidale 3CS 1130 265 Colac 6PM 1130 265 Perth 2HD 1140 263 Newcastle 2WG 1150 261 Wagga 7ZR 1160 259 Hobart 2NZ 1170 256 Inverell 3KZ 1180 254 Melbourne 2CH 1190 252 Sydney 5KA 1200 250 Adelaide 2GF 1210 248 Grafton 3YB 1210 248 Warrnambool 6KG 1210 248 Kalgoorlie 4AK 1220 246 Oakey 2NC 1230 244 Hunter River 3TR 1240 242 Sale 6IX 1240 242 Perth 3SR 1260 238 Shepparton 2SM 1270 236 Sydney 3AW 1280 234 Melbourne 4BK 1290 233 Brisbane 2TM 1300 231 Tamworth 5AD 1310 229 Adelaide 3BA 1320 227 Ballarat 6KY 1320 227 Perth 3SH 1330 226 Swan Hill 4BU 1330 226 Bundaberg 2LF 1340 224 Young 6TZ 1340 224 Dardonup 3GL 1350 222 Geelong 4GY 1350 222 Gympie 3MA 1360 221 Mildura 2MO 1370 219 Gunnedah 5SE 1370 219 Mt. Gambier 6GE 1370 219 Geraldton 4BH 1380 217 Brisbane 2GN 1390 216 Goulburn 4MK 1390 216 Mackay 2PK 1400 214 Parkes 5AU 1400 214 Port Augusta 2KO 1410 213 Newcastle 3XY 1420 211 Melbourne 2WL 1430 210 Wollongong 2QN 1440 208 Deniliquin 4IP 1440 208 Ipswich 2MG 1450 207 Mudgee 7DY 1450 207 Derby 2CK 1460 205 Cessnock 5MU 1460 205 Murray Bge 2MW 1470 204 Murwillumbah 3CV 1470 204 Maryborough 2AY 1480 203 Albury 2BE 1490 201 Bega 4ZR 1490 201 Roma 2BS 1500 200 Bathurst 3AK 1500 200 Melbourne It will be noticed that in several cases the same frequency is shared by two or three stations.

P.30 - Shortwave Review - Notes from My Dairy
Shortwave Review. Conducted by L. J. Keast NOTES FROM MY DIARY 1947 . . . W H A T HAVE YO U? First of all let me say my good wishes for the Festive Season were frozen out of December issue on account of pressure on space, but I hasten now to say "thank you very much" to all those fine reporters who, during the year, have rushed along the results of their loggings, thus enabling those indulging in this great hobby of D Xing to reap the benefit of their finds. And amongst the reporters referred to I include and thank Miss Sanderson for her splendid contributions. This lady has shown that she can "bat" with the rest and her carefully and correctly typed lists are a treat to read. But there must be many readers of these columns who hear changes of frequencies or schedules that may be given at the very time the Gilletts, Cushens, Gadens, Edels, Suffolks, Whitings, Halletts, Legges, Boords, Sandersons and the many other regulars are not on that particular station, and I would like those readers to send in some reports. Please do not hesitate. . . don’t be frightened. . . SEND THEM IN. Let this be one of the things 1947 has for us. What the technical side has I do not know, but I’ll wager our good friends Mr. Hull and Don Knock will be watching. However, even at the risk of being considered "catty,” I must tell our friends in the other states, we have the first television receiving set in Australia on display in Sydney. W ell, here’s wishing all readers of these pages the very best and whatever you hope 1947 may have for you may it happen. W ITH THE BBC TW EN TYFOUR YEARS AGO Yes, it is just over 24 years since the first BBC programme went on the air. On November 14, 1922, British broadcasting under the control of the Broadcasting Committee began— the declaration of the polls in the General Election was the first broadcast-— and the initials BBC began to penetrate the national consciousness. On December 15, the British Broadcasting Company Limited was formally registered with a Board of Directors drawn from the General Electric Company, Marconi’s, the Radio Communication Company, Metropolitan Vickers, British ThomsonHouston, and Western Electric, and the late Lord Gainsford was appointed the first chairman. HERE’S HOPING The Bob Hope family increased 50 per cent recently with the adoption of William Francis (Kelly) Hope and Honora (Nora) Hope, both less than one year old, from the Cradle at Evanston, 111. The Hopes have two other Cradle babies— Linda, age 7, and Anchony, age 6. W ell, that’s a very fine gesture, and we wish them all the best of luck. KEEPING COUNTRY AFOOT Red Skelton says, "It’s the radio comedians that keep the nation on its feet— every time they tell an old joke, thousands of people get up and turn the radio off.” THE SIX PIPS The man who originated that famous feature of the BBC programmes, the six-pip time signal, has received the Gold Medal of the British Horological Institute. The medal is open to world competition. He is Mr. Frank HopeJones, a man who came from the North of England to London five years ago. The signal has been adopted by many foreign countries. The award seems not to have been made with undue haste, for the BBC time signal has been regularly used for over twenty years. It is, of course, an electrical device, but on one occasion years ago the apparatus was mislaid, and an engineer improvised the "pips” with a hammer and a piece of wire. No one noticed anything wrong. — "London Calling” SAYS W HO? Miss Sanderson, of Malvern, Victoria, writes: I have been hearing the AFRS station at Amoy. It was 8.15 p.m. and the programme was very easily copied, the noise level is very high, so together with morse it is very hard to hear what is going on at times. I have heard another Chinese station, XOPD, in the 31m. band, at a very good level, the freq. was 9.55 mcs. and the programme typically Chinese, and the time was 10 p.m. Call sign was given in English. 41 metres is improving in strength and some quite good signals are heard as early as p.m., when Hanoi on 7.26 mcs. or 41.32 m. gives news in English and a commentary, prior to this time the broadcast is in French. VUM and V U B2 are heard in English news and local news on the respective frequencies of 41.25 m. or 7.27 mcs and 41.44 m or 7.24 mcs. With regard to early morning listening, this has been very good. I have heard quite a number of stations from Europe and Allied countries. Captown No. 3 is heard at 6.30 a.m. in a programme of news and music at qu'ite a fair signal for this part of the band. Bulgaria, Brazil, in 31 m. and 30 m. with good signals, and Sweden heard on Sundays at 5 p.m. with its English lesson and later a church service at 8 p.m. I have recently heard from a DX-er in Sweden, and he has sent on two very interesting magazines which contain the broadcast and shortwave schedules. I have sent on some of our magazines (Radio) for his perusal. This young man is a student and writes very good English. I have had a verification from Radio Andorra, and CBFZ and schedules from Burma Broadcasting Service. These are very useful and I am very plased to receive them. I am still finding Universalite very handy, and have sent off a report to Mr. How,e and also to Mr. Boord. I trust that these gentlemen will find them of interest.
 * Jc * *

Arthur Cushen, of Invercargill, sends another most interesting budget: Two interesting veries received yesterday: KOFA, Salzburg, Autria, a station of the Armed Forces Radio Service, uses 750 watts on 7220 kcs., and heard to 8.15 a.m. last May, signed off at that time. They have a new card, shows map of Austria, mats from Salzburg, and is signed by Martin S. Bloom, Station Engineer. The other was a card from XTPA, Canton, China, operated by Canton Broadcasting Station, has nice white card, with green bands, calls in green on big letters in background, with details of veri. information in both Chinese and English, signed by S. S. Lee, Director. X TPA is very good every night on 11650 kcs. I’m at present trying to get some details on a very interesting station, French operated on 6010 kcs., heard as early as 4 p.m., has news in French at 4.30 p.m. sometimes relays Paris, and other times news from own studio, news on German happening) then goes into modem dance numbers, French and German vocal, yodel numbers, etc., gives call at 5 p.m., as "Radio Ruhr’’ in German, no location mentioned, station fades out at 6 p.m. Signal peaks at 4.30 p.m. Berlin or Russian operated station in Germany, terrific signal here, heard at 4 p.m. and later, sometimes relays LEIPZIG (9 7 2 0 ), XEOI, 6018, Mexico City, heard between these two, the latter signs off at 4.30 p.m. with "Sunrise Serenade.” Some other written include EPB, Teheran, 15100 kcs., news 9.30 p.m.; Bandoeng, 9.30 p.m., Eng. announcements, 7995 kcs.; RADIO SOFIA, 7660 kcs., heard poorly at 5.30 a.m. Veri. received two weeks ago from "RADIO RODINA”, Sofia, Bulgaria, using 5000 watts on 9315 kcs., the outlet on 7660 kcs. has 500 watts: sent 7 pages of information and two photos of the station, building, and concert hall. Letter stated mine was first report from New Zealand and expressed the hope that they would not be abusing my kindness by hoping that this would be the beginning of a fruitful collaboration. >;: % :Ji A long and interesting letter from an old D X-er who has just returned to civil life, our friend H. A. Callander, of Tasmania, who at present is in Victoria but expects to be back on the Apple Isle soon after the New Year. With a grand array of aerials and no less than five receivers, it is no wonder Mr. Callander can send in a good log. His report comes from Richmond and he says 10 m. is gradually showing some improvement. 20 m. band is getting up to peak around 4 p.m. The 40 m. is, he says, rather noisy. (His loggings on these bands I have sent to Don Knock.) On 31 m. PCJ was heard at excellent strength last Tuesday in an English programme from 5.30 p.m. until closing with the Dutch National Anthem. At 7.30 p.m. they announced that they would be on three days weekly: Tuesday, Wednesday and Thursday. Another good station on this band is KNBI (Voice of America) on 9.49 mcs. — heard in evening at 11.25 when giving the Hits programme. I have been mostly concentrating on 10 and 20 m. bands, but will put in the next couple of weeks on the Commercials D X side, so will forward you a more detailed programme next report. Jj« ^ ❖ Dr. Gaden has left the "Hams" for a while apparently, as I have from him some notes as follows: RNB 17.77 me. 16.88 m. heard around 7.30 a.m. at good strength; not heard at night lately. SEAC, Ceylon, 15.12 mcs. 19.84 m. very good night station. Switzerland on about 9.53 mcs. 31.46 m. is a nice signal in afternoons; no English heard. HCJB 25 and 31 m. very good; 19 not so loud. The Panama station, XO YA, is not as good as the 19 m. HCJB alongside it. Maroc 9.08 mcs. 33.03 m. at 7.30 a.m., quite good signals; no English heard from this one. XEW W the best Mexican as usual; XEQQ reasonably good. Radio Sofia 9.35 mcs. 32.09 m. is better than Belgrade on 6.15 mcs. which is usually good enough, as are many 48/49 m. in a.m. FZI, Brazzaville, 31 and 30 m. in а.m., 25 m. in afternoon, and 19 m. at night, are all good signals. All the ’Frisco Yanks are good at any time and of the W ’s old WGEO, 9.53 mcs., 31.48 m. at breakfast time takes some beating. Rex Gillett of Adelaide, says Radio Club of Mozambique is now' back on their old frequency of б.135 mcs., 48.90 m. They have an English session at 5.55 a.m. and close at 6.30. CR7AA is in relay with CR7BJ on 9.65 m.c. 31.09 m. Referring to Belgian Congo he says although Radio Nationale Belge is interfered with by PCJ and Radio Paris they can be followed at 11 p.m. on 17.77 mcs., 16.88 m. Another station that is spoilt by someone on the same frequency, believed to be Russia, is Berlin on 6.07 me., 49.42 m. This occurs at 6.30 a.m., but at 7 o’clock Berlin is identified by piano notes. (According to my records, Berlin is' on 6.072 mcs., whilst a Russian, Kamchatka Petropavlovsk is on 6.07 mcs., as also GRR— L.J.K .) Mr. Gillett as usual catches the unusual and reports DTCY, the American shortwave station in Munich as testing on Mondays, Wednesdays and Fridays at 1—I.30 a.m. on 5.302.5 mcs., 56.58 m. Should you desire to report same send to The Military Government Station, DTCY, APO, 170. Ern. Suffolk, of Lobethal, advises XORA, Shanghai is easily heard from opening at 6.30 p.m. on II.7 0 mcs., 25.64 m. (For the benefit of those who may be calibrating their dials, this Chinese is generally on a measured frequency of 11.705 mcs., but is liable to fluctuate.— L. J.K .) XG O Y, Chungking, is now on 6.14 mcs., 48.86 m. from 12.30 a.m. This is a special broadcast in English to the U.S.A. Signal is better than when on 41 m. OLR2A, Prague, 6.01 mcs., 49.92 m. can be heard at 6.30 a.m. Several clarion notes serve as an identification signal. ❖ ❖ ❖ Desmond A. Hickey, writing from Petone, N.Z., admits that in the Shaky Isles they seem to hear the Latin Americans better than us, and to substantiate this claim forwards some fine information regarding his loggings. "I get excellent reception from South America during the winter, and this winter from June 1 to the end of September I logged fourty new Latin stations. So far eleven verifications have arrived. Here, now, is some information on these and other verifications that I have recently received from Latin America. HC4EB, Manta, Ecuador, "Radio Manta.” This station operates on 6.87 mcs. and their schedule is 11 а.m. to 2 p.m. Power is 375 watts. Address, Apartado 69, (verified by air mail Spanish from the Director, Emilio Bowen.) CXA3, Montevideo, "Radio Ariel.” This station operates on б.075 mcs. relays CXIO. Power is 1,000 watts. Address, Avenida 18 De Julio 1275. Heard here opening at 8p.m. (Verified by air mail, Spanish letter from R. M. Borde, Tech. Division.) H i2A, Santiago De Los Caballeros, Dominican Republic. "La Voz De La Reeleccion.” This station operates on 6.52 mcs. Schedule is 2—5 and 8— 11 a.m. Power 250 watts. Address, El Cafe Del Yaque. (Verified by card). H 12T, Monsenor Nouel, Dominican Republic. "La Voz Del Yuna”. This station operates on 6.485 mcs. 8 a.m. to 3 p.m. Power 250 watts. (Verified by card.) HCIAC, Quito, Ecuador. "La Voz De La Democracia.” This station operates on 6.21 mcs., relaying medium-wave station on 1280 kcs. Schedule 9 a.m. to 2 p.m. Power is 200 watts. Address: Apartado 288. (Verified by card with picture of transmitters.) OAX4M, Lima, Peru. "Radio Miraflores La Voz De La Democracia”. This station operates on 6.22 mcs. 9 a.m. to 3 p.m. relays OAX4L. Address: Jesus Nazareno 113. (Verified by picture postcard.) OAX4H, Lima, Peru, "Radio Mundial.” This station operates on 6.368 mcs. Power is 1,000 watts. Address: Apartado 1098. Relays OAX4F, 1080 kcs. This station is off the air at present. (Verified by letter from chief engineer, Amador Salazar.) Y V IR X, Maracaibo, Venezuela. "Ondas Del Lago.” This station operates on 4.80 mcs. Power is 1,500 watts, will increase to 10,- 000 watts soon. Relays YV IRF, 1120 kcs. Address: Apartoda Postal 261. (Verified by letter from Francisco Artinano, chief engineer.) CE960, Santiago, Chile. "Radio La Americana.'’ This station operates on 9.59 mcs. moved from 9.60 mcs. Power is 1,000 watts, relays CB130. Schedule 10 a.m. to 3 p.m. Address: Casilla 13155, Correo 15. HJDE, Medellin, Colombia, "L* Voz De Antioquia.” This station operates on 6.145 mcs., relaying

H JD K, 1250 kcs. Power is 5,000 watts. Schedule 6 a.m. to 2 p.m. Here now are some of my recent loggings: 6.145 mcs., LRR, Rosario, Radio Ovidio Lagos, heard Sundays to 3 p.m. 6.025 mcs., HCITR, Ibarra, "Radio Equinoccial.’’ Sundays to 5 p.m. 4.960 mcs. HC5HC, Riobamba, "Ondas Del Chimborazo.” Now, noon— 2 p.m. 7.876 mcs. HCICG, Quito, "Radio Ecuador Amazonico.” Opens 9.30 p.m. 7.660 mcs. YN DG, Leon, "Estacion Gilfillan.” Sundays to 4 p.m. and later. 9.925 mcs., X D Y, Mexico City. Sometimes heard to 4 p.m. and later relaying XEDP, political speeches, etc., very irregular. Usual sign off is 1.15 p.m. 8.700 mcs., COCO, Havana, "Radio America,” heard daily till 3.50 p.m. 6.117 mcs., HUG, Ciudad Trujillo, "Radio La Opinion." Sundays till 4 p.m. with H 12G on 9.21 mcs. 6.275 mcs. YSR, San Salvador daily sign off is 3 p.m. "La Vox Del Salvador.” 6.010 mcs. XEO I, Mexico City, "Radio M il” heard till 4 p.m. Well, that’s a fine list and should be of great help to our readers.— L.J.K. LATEST SCHEDULES FROM CROSLEY CORPORATION, CINCINNATI W LW K— 6.08 mcs. 49.34 m: 8.30 — a.m.— 4.00 p.m. To Latin America. W LW O — 11.79 mcs., 25.45 m.: 9.00 a.m.— 1.00 p.m. To Latin America. W LW S— 15.20 mcs., 19.73 m: 7.45 a.m.— 4.00 p.m. To Latin America. W LW S— 11.71 mcs., 25.62 m.: 7.45 a.m.— 4.00 p.m. To Latin America. 'W LW K— 17.80 mcs., 16.85 m .: 9.45 p.m.— 7.30 a.m. To Europe. W LW K — 9.59 mcs., 31.30 m.: 8.00 a.m.— 9.15 a.m. To Europe. W LW O — 11.71 mcs., 25.52 m.: 9.45 p.m.— 1.30 a.m. T. Europe. W LW O, 15.35 mcs., 19.54 m.: 2.00 a.m.— 7.30 a.m. To Europe. W LW R— 15.25 mcs., 19.67 m.: 9.45 p.m.— 7.30 a.m. To Europe. W LW S— 21.65 mcs. .13.85 m.: 9.45 p.m.— 5.00 a.m. to North Africa. W LW S— 11.71 mcs., 25.62 m.: 5.15 a.m.— 7.30 a.m. To Europe. W LW S— 21.65 mcs. 13.85 m.: 9.45 p.m.— 5.00 a.m. To Europe. W LW S— 11.71 mcs., 25.62 m.: 5.15 a.m.— 7.30 a.m.— To North Africa. W LW L— 17.955 mcs., 16.70 m.: 9.45 p.m.— 4.30 a.m. To Europe. W LW L— 17.955 mcs, 16.70 m.: 9.45 p.m.— 4.30 a.m. To North Africa. W LW L— 9.70 mcs, 30.93 m.: 5.00 a.m.— 7.45 a.m. To Europe. W LW L — 9.70 mcs, 30.93 m.: 5.00 a.m.— 7.45 a.m. To North Africa.

A.B.C. NATIONAL SHORTWAVE STATIONS. VLR, Melbourne, 2 Kilowatts; VLH , Lyndhurst, 10 kilowatts; VLG, Melbourne, 10 Kilowatts; VLQ, Brisbane; VLW , Perth SUNDAYS VLR C A L L SIGNS: VLR 2 ............... 6.45am — 9.00 am VLR ................ 9.15am — 6.15 pm VLR2 .............. 6.28pm — M / N W EEKDAYS Mondays to Saturdays VLR2 ............... 6.00am — 9.00 am VLR ................ 9.15am — 6.15 pm VLR2 .............. 6.28pm — M / N Fridays VLR2 VLR 6.00am — 8.55 am 9.1 5am — 6.1 5 pm VLH C A LL SIGNS— SUNDAYS VLH4 VLH5 VLH3 . 6.45am — 8.15 am . 8.30am — 6.30 pm 6.45pm — M / N Metres 48.78 31.45 48.78 48.78 31.45 48.78 25.25 19.69 31.32 Mcs. 6.15 9.54 6.15 6.15 9.54 6.15 11.88 15.24 9.58 W EEKDAYS Monday to Saturday VLH4 VLH5 VLH3 VLG C A LL SIGN VLG7 SUNDAYS VLQ C A LL SIGNS SUNDAYS 6.00am — 8.1 5 am 8.30am — 6.30 pm 6.45pm — M / N 6.00am— 8.00 am 6.45am — 8.15 VLQ VLQ3 VLQ2 W EEKDAYS VLQ VLQ3 VLQ2 6.45am — 10.30am 10.50am — 6.1 5 pm 6.28pm — M N .. 6.00am — 9.55 am 10.00am — 6.1 5 pm 5.20pm— 1 1.30 pm 6.28pm — M / N VLW C A LL SIGNS DA ILY VLW7 8.00aro— 1 1.45 am 8.30pm — 1.30 am .. 1.30pm— 8.15 pm 25.25 19.69 31.32 19.79 41.44 31.06 41.58 41.44 31.06 41.58 31.51 31.51 25.36 11.88 15.24 9.58 15.16 7.24 9.66 7.215 7.24 9.66 7.215 9.52 9.52 11.83


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A-level Mathematics/CIE/Pure Mathematics 2

 * /Algebra/
 * /Logarithmic and Exponential Functions/
 * /Trigonometry/
 * /Differentiation/
 * /Integration/
 * /Numerical Solution of Equations/


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A-level Mathematics/CIE/Pure Mathematics 2/Algebra

The Modulus Function
The modulus function $$|x|$$ returns the magnitude of $$x$$. For instance, $$|\!-\!3|$$ will return $$3$$, $$|5|$$ will return $$5$$.

The modulus function can be defined as $$|x| = \begin{cases}-x,& \text{if } x < 0 \\ x,& \text{if } x\geq 0 \end{cases}$$.

Graphing the modulus function
Graphs of the modulus function are just a straight-line graph that has been reflected for negative output values. The graph of $$y = |ax+b|$$ is like the graph of $$y = ax + b$$ except that every point below the x-axis folds upwards to produce a V-shaped graph.

Here is an interactive graph which shows the relationship between the graph of a line and the graph of the modulus of that line.

Solving Equations & Inequalities
To solve equations and inequalities involving the modulus function, we can square both sides.

e.g. Solve $$|4x+2| > |2x-3|$$

$$\begin{align} (4x+2)^2 &> (2x-3)^2 \\ 16x^2 + 16x + 4 &> 4x^2 - 12x + 9 \\ 12x^2 + 28x - 5 &> 0 \\ x^2 + \frac{7}{3}x &> \frac{5}{12} \\ (x + \frac{7}{6})^2 &> \frac{15}{36} + \frac{49}{36} \\ x + \frac{7}{6} > \sqrt{\frac{64}{36}} &\text{ or } x + \frac{7}{6} < -\sqrt{\frac{64}{36}} \\ x + \frac{7}{6} > \frac{8}{6} &\text{ or } x + \frac{7}{6} < -\frac{8}{6} \\ x > \frac{1}{6} &\text{ or } x < -\frac{15}{6} \\ \text{In interval notation, } x &\in \left(-\infty,-\tfrac{5}{2}\right) \cup \left(\tfrac{1}{6},\infty\right) \end{align}$$
 * 4x+2| &> |2x-3| \\

An alternative method is to look at the places where the functions inside the modulus change sign, i.e. where $$f(x) = 0$$.

$$4x+2$$ changes sign at $$x=-\frac{1}{2}$$

$$2x-3$$ changes sign at $$x=\frac{3}{2}$$

$$\begin{array}{ccc} \text{Where } x < -\frac{1}{2} & \text{Where }-\!\frac{1}{2} \leq x < \frac{3}{2} & \text{Where }\frac{3}{2} \leq x \\ -(4x+2) > -(2x-3) & 4x+2 > -(2x-3) & 4x+2 > 2x-3 \\ 4x+2 < 2x-3 & 4x+2 > -2x+3 & 4x+2 > 2x - 3 \\ 2x < -5 & 6x > 1 & 2x > -5 \\ x < -\frac{5}{2} & x > \frac{1}{6} & x > -\frac{5}{2} \\ & & \text{Out of range} \\ \end{array}$$

$$\text{In interval notation, } x \in \left(-\infty,-\tfrac{5}{2}\right) \cup \left(\tfrac{1}{6},\infty\right) $$

Dividing Polynomials
Dividing polynomials uses the same method as dividing numbers with long division.

Dividing Numbers
Suppose we need to find $$22253 \div 17$$. We can use the method of long division:

______ 17|22253

__1___ 17|22253 17 goes into 22 once with 5 left over -17↓       52    Next we bring down the 2 __13__ 17|22253   -17↓↓    52↓   17 goes into 52 thrice with 1 left over -51↓    15   Next we bring down the 5 __1309 17|22253   -17↓↓↓  17 doesn't go into 15, so we bring down the 3 52↓↓  -51↓↓     153  17 goes into 153 nine times with nothing left over -153      0

Thus, $$22253 \div 17 = 1309$$

Dividing Polynomials
We can use the same method to divide polynomials.

e.g. $$(x^3 + 2x^2 + 2x + 1) \div (x + 1)$$

____________________ x + 1 |x^3 + 2x^2 + 2x + 1

________x^2_________ x + 1 |x^3 + 2x^2 + 2x + 1   (x + 1) goes into (x^3 + 2x^2) x^2 times with x^2 left over -(x^3 + x^2)   ↓ x^2 + 2x        Bring down the 2x

________x^2_+__x____ x + 1 |x^3 + 2x^2 + 2x + 1   (x + 1) goes into (x^2 + 2x) x times with x left over -(x^3 + x^2)   ↓   ↓ x^2 + 2x  ↓     Bring down the 1 -(x^2 + x)  ↓ x + 1

________x^2_+__x___1 x + 1 |x^3 + 2x^2 + 2x + 1   (x + 1) goes into (x + 1) once with nothing left over -(x^3 + x^2)   ↓   ↓ x^2 + 2x  ↓ -(x^2 + x)  ↓ x + 1 -(x + 1) 0

Thus, $$(x^3 + 2x^2 + 2x + 1) \div (x + 1) = x^2 + x + 1$$

The Remainder Theorem
A remainder occurs when the divisor does not fit into the dividend a whole number of times.

e.g. $$22256 \div 17 = \frac{22253}{17} + \frac{3}{17} = 1309 + \frac{3}{17}$$ has a remainder of $$3$$.

It can also occur in polynomials:

____________________ x + 2 |x^3 + 3x^2 + 3x + 3

________x^2_________ x + 2 |x^3 + 3x^2 + 3x + 3 -(x^3 + 2x^2)  ↓ x^2 + 3x ________x^2_+__x____ x + 2 |x^3 + 3x^2 + 3x + 3 -(x^3 + 2x^2)  ↓   ↓ x^2 + 3x  ↓ -(x^2 + 2x) ↓ x + 3

________x^2_+__x_+_1 x + 2 |x^3 + 3x^2 + 3x + 3 -(x^3 + 2x^2)  ↓   ↓ x^2 + 3x  ↓ -(x^2 + 2x) ↓ x + 3 -(x + 2) 1

Here, the remainder is $$1$$.

This can be expressed as $$x^3 + 3x^2 + 3x + 3 = (x^2 + x + 1)(x + 2) + 1$$

In general, a quotient and remainder can be expressed as $$Dividend = (Quotient)(Divisor) + Remainder$$

This expression leads to a useful theorem in mathematics: the remainder theorem.

If we divide a polynomial $$p(x)$$ by a given divisor $$(ax-b)$$, the expression can be written as $$p(x) = (Quotient)(ax-b) + Remainder$$.

If we substitute the value of $$b/a$$ into the polynomial, we get:

$$\begin{align} p(b/a) &= (Quotient)(a(b/a)-b) + Remainder \\ p(b/a) &= (Quotient)(b-b) + Remainder \\ p(b/a) &= (Quotient)(0) + Remainder \\ p(b/a) &= Remainder \\ \end{align}$$

Thus, the remainder theorem states that for a given polynomial $$p(x)$$, $$p(b/a)$$ gives the remainder obtained from $$\frac{p(x)}{ax-b}$$.

e.g. If $$p(x) = x^3 + 3x^2 + 3x + 3$$, $$p(-2)$$ will give the remainder obtained from $$(x^3 + 3x^2 + 3x + 3) \div (x + 2)$$:

$$\begin{align} p(-2) &= (-2)^3 + 3(-2)^2 + 3(-2) + 3 \\ &= -8 + 3(4) - 6 + 3 \\ &= -8 + 12 - 3 \\ &= 1 \end{align}$$

The Factor Theorem
The factor theorem is a special case of the remainder theorem for when the remainder is zero.

If the remainder is zero, that means that the divisor is a factor of the dividend.

Thus, if $$p(b/a) = 0$$, $$(ax-b)$$ is a factor of $$p(x)$$

e.g. $$p(x) = x^3 - 5x^2 + x + 10$$. Use the factor theorem to find a factor of $$p(x)$$.

$$\begin{align} p(1) &= 1^3 - 5(1^2) + 1 + 10 = 1 - 5 + 1 + 10 = 7 &\neq 0 \\ p(-1) &= (-1)^3 - 5(-1)^2 - 1 + 10 = -1 -5 -1 -10 = -17 &\neq 0 \\ p(2) &= 2^3 - 5(2^2) + 2 + 10 = 8 - 5(4) + 2 + 10 = 8 - 20 + 12 &= 0 \\ \therefore \ &(x-2)\text{ is a factor of } x^3 - 5x^2 + x + 10 \end{align}$$

 * Notes


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