theory of tuning, wave lengths and harmonics - electrical experimenter may 1918

8/9/2019 Theory of Tuning, Wave Lengths and Harmonics - Electrical Experimenter May 1918

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32

ELECTRICAL EXPERIMENTER

May , 9

18

Theory

of Tuning,

Wave

Lengths

and

Harmonics

*

By

Prof. F. E. AUSTIN

In

s t-ru

to

r of Ele

tr i

ca l En g

in

ee r

in g

, Thaye r Schoo l

of

C i

vil En g

inee r

in g

, Da r

tm o

u th Coll ege

S

O-

CALLED r so um .-c is

o f

ve

ry

great

imp

o

rt<t

n

cc

iu

the ope

r

at

io n

of

wire

l

ess

a p p a every

op

era

t

or

sh

ould

h

ave

a

good

working

kn

owle

d

ge of th

e

theo

ry

of reso

nance and

of

its pr a

ctical

applica

tion.

Even

t he

experim

e

nter

w ill

work

to

mu ch

g

reater

D

I

E

employed

itt the g iven

equat

io n

it may

be

not

ed ft

r

t tha

t the

llltt11

CratoJ· E den

ot e

s

1he

app

lied a lt

ernating-pressu

r e, ha vi

ng

a

f r

eq

uen

cy

den

oted

hy f

f mean

s the

num

be r

of comp

l

ete

cyc

l

e, per secoml). R de

notes th

e resis

tan

ce

of

the

co

il.

exprest

in

oh ms . C t

he capacity

of the co nd ense r in

INDUCTIVE

R SISl A : >ICE

- v ~

~ · ~ N - 1 - - - - - - - - - - - - -

K

CO

N OF

NSER

Fi

g. 1.-The Fundamen

tal

Th

eory of Wire less May be

Better

Understood by

Stu

dy

ing

Th

is

Elementar

y

Alternating

Current Cir

c

uit,

Comprising

an

I

nduct

ive Re

sista

nce

and

Capa city Con nected in Series.

advan

t

a c.

wi th a

kn

ow ledg-e o f t

he

f

unda

me

nta l l

aw

a

nd

i

ts ca

r

eful

app

lication, in

ma

ki

ng

and

ope

rati

ng-

luning- coil< :

md

sim

il

ar dc\'iccs.

When

a ·coi l.

cons

ist ing o r a

number

of

turns of insul

ated

wire is co

nnec

ted in

se

ri e

s with a

condense

r,

and an

a lt

ernating

press ur e

app

lied to the

terminal

s of the

a rran

geme

nt.

as

ind

icated diagra

ma ti

ca

lly

in figure l . the a lte

rnati

ng c

urr

e

nt

in

th

e

ar ran

geme

nt

indicated by

an ammeter

con

mTte

d

as

sho

wn

m

ay h<· cx prc, hy ·

E

1 -

f arads, while

L

denotes

the o

-call

ed co

efficiem

or

ind uc

tance

oi

the

coil, c:

xp

r

est

in ' '

'

')

s

L

depend, upon the

s

quar

e o£

the

number

•Jf t

urn,

o f w

ir

e of

wh

ich

th

e

I

I

I

D

am ount of energy. The

symbo

l 1r denotes

the val

ue

of 3. 141

6.

I t is instru

ctive

to

note

tha t if

the con

denser be remove

d fr om

the circuit

and a

direct-pressure be applied

to th

e term

inals

of th

e

co

il,

th

e

di

r

ect

c

ur r

e

nt may

be

ex

-

E

prest

by

l = :

hat is, acco

rding

to

Ohm 's

R

law

.

:Now.

h ~ ·

l

ookin

g a t t

he

fi rst

equat

i

on

it

is evide

ut th

at t

he

la

st eq

uation may

be

ob tained fr

om

th

e fir st w

he

n

the numerical

val ue o f 2'iif L is made

equa

l to - - - .

271 / C

Wll

en

such nnmeri

c

al

re l

at ionship dbta

ins

in

any

ca e, t

he

n rPsoumtce is said to exist.

T he va lue

of 7i

is, o(

course,

a

constan

t

a t

all t

ime

s a

nd

the value o f f is definitely

fixt for

any

gi vcn circuit.

t

is, therefore,

appa r

ent

th

at

with a

given

ftxt value fo r

. 1

27r j

L,

a s imilar nume

ri

cal value

for

27TfC

m

ay

be

found

by

varying

the va l

ue

o f

C.

T he

value

o£ C for any co

ndenser depends

upon the number

of sheet s

o f

di

electr i

c

u

sed in making the condenser. u

pon

the

lli1rd

o

materia./ the diel

ectric co

nsists of,

up

on th

e

si=c of th

e diel

ec

tr ic sheets,

and

upo n a

numerical ons

lw

whi

ch

is

depend

e

nt

upon

the kind

of

un

its employed in ex

pressing

size or

area,

attd t

hickness

.

(

2rrfL - -

1

)

E

INDUCT

IY

E R SISTA\ CE

.7</C

N

K

•

CONDE

N

SER

J a

di r

ect

c

ur

rent pressure

,

hav

ing

the

<amc

numerical \'alue

a- the al

ternating

press

ure he applied to the same arran

gc

mcttt , the amme te r will sho\\' no indicatio n

at

a ll :

th

e

co nd

ens

er,

h

aving

a

ve

ry high

r

esistanc

e.

re all

y

prevents

any d

irec

t

cu r

rent

fr om pass

ing.

Of

course,

a di

r

ect

current does exist while the

condenser

is

being ch

arged, but thi

s is

so

s

mall

the o r

d

inan

·

ammeter

w ill se ldom

ind

i

ca

te thi s

minnie

mo

men

tary curr

ent.

vVith an ap

pli

ed al t

em

ating pressur

e. h

O\I

C\ Cr,

the

resu

lt is

ver y different : ittcc the con

de

n

se

r is ve

ry rapid

ly c

harge

d

and

d is

charged. th

e

am

met

er indicates

the

pr

es

en

ce

of

the

CLtrrent

continuo

us

ly.

Fig. 2

This

Alternating

Current

Ci

rcuit

Shou td Be Carefully Studied by All Radio

Students.

as

It

Contains

Similar

Eleme

nts to

Rad io Circuits, I. e., a Variable I

n

duc t ive Resistance and a

Capacity or

Condenser.

Considering

now

the d ifferent sy mbo

ls

• This

r

iC le rspeciall y prepared f or 1he uElcc·

: ~ l Expl rimf nt i l'.

coil is

compose

d ;

that

i

s, of

uwo

co

ils o f

th

e arne

ge

nera l sha

pe

.

the

o

ne

tw ice

as

many

turns as the other

wtll

have fo ur time

s

the inducta

n

ce.

A l

so

a

co

il h

aving

an iron co

r e \\'ill

have ve

ry

much

g r

ea

ter in

ductanc

e th

an

th

e same o r a

simi la r coil with

o

ut th

e core.

When ,

as

in

wire

l

ess

wo

r

k, it

is

desi

r

ed

to

e

mploy

v

e r y high

fr e

quencies, co

i I s,

ha

v

in

g

no ir

on

co

res

are

used.

s ince

they may

be

ma

g

netized

and

demagne t

i

zed

very

qu

ick ly and

D

iagram

Representing

th

e

Gener

a tion of

the Sine Curve -the Form withou

t absorb-

of the Average Alternating Current Wave. i

ng

an excessive

T he

capac

it

y

of ordinar

y

co

ndenser

s

made

up

of

sh

eets of di

el

ectr i

c a

nd me

ta l pl

ates,

m

ay

be

ex pr

est by:

An

c = 000,000,000.224 k

f a ~ · a d

ln

th

e

equa

tion A

d

eno

t

es

t

he area

o f

eac

h

diel

e

ctric

sh

eet

in

square

inc

he

s, n t

he

number of

sh

eets

u

sed.

k

the so

-ca.Jied

s

pecific inductive ca

p

ac

ity of t

he

dielectric

,

and

t

the t

hi

ckness of each dielectric sheet

in

thousandth

s o f an inch ; that

is

,

in

mils.

T he

coe

fficient of

inductance of

a coil

having an ir

on c

or

e

may be

approximately

ex pres t by:

471

n A

L

= -

b

X DO'



May, 19 18

in

w

hi

ch 7i h

as its

us

ua

l

va

lu

e,

11 de

no t

es

the

num

ber

of I II YIIS

of w ire wou

nd

on

the

coil,

1

de note s the area o f

the

ho

lt

thru

the center

of

th

e coil, exprest

in

sqmzre

reHiimetrrs,

a

nd b de

no tes

the length of

the coil

(n o

t o f t

he

wi

re), cx p

rc t

in centi

me

ters.

Re

wrning

to th

e

con>idcration

o f

the

initial equat

io

n . a

nd

the co

ndition

1

for re

so

nance as when 27i/ L = - - - it i'

].7if c

evident that

the t'IJ

ila t ion m

ay

ch a

11gcd to:

I

2:r.fC

= - - .

27i/L

T he reason fo r t lte la

tter

a

rr

an gement

of

th

e

C£tuati

on is

beca

u

se

it is

mu

c h ea s i

er

to

co

nstr uct

o co

il to produ

ce a ' '" riab

lc

inductance than it is to cons I ruct a con-

dense

r to g i

ve

a

variab

le

capacity.

Co

nsidering the las t eq uation, it is ev i

dent that i [

271 [

C has a ny g iven nu me rical

va lu

e,

with a definite va

lu

e o i fr equency

( value o f

f

t

hen some va

lue m

ay he

given

L, so th

at

the nume

ri

cal va lue oi

I

- ·ha ll

be equal

to

the num

e

rica

l

va

lu

e

2r.f

L

o f

2 ffj

C.

1 / I J ~

'

ndf/t we res

lndf/cl vo res

~

~ m f er/ a

Di

agra

ms

Showing Effect

of

Resonance

on

E.

M. F

. 's

in Different Parts

of A.

C. C i r-

c

u it

;

Also Simple

R

adio

Circui ts

Used for

Comparat ive

Study.

I f a

conde

nser hav

in

g a

deli

n

ite

fixt

v:tlt'' o f

capaci

ty

C

be

connected, as

shown

in

ligure 2.

in

se

ries with

a coi l

so

ar

ran

ge

d

as to

allow

a di ffere n t

num

ber of turns o f

w

indin

g to

be introdu ce

d into th e ci

rcuit

as d

es ired,

the n

th

e

ph

ysica

l

appa

r

at

us wilt

fu

lfill all

of

t

he vari a

ble

cond

it ions

poss

ible.

w

it

h a

fox

t frequen

cy f.

Lo ok

in

g

at

the proposi

ti

on fro m a sl igh t

ly

different

s tandpoin t. s\oppose the con

de

n

se

r in fig

ur

e 2.

ha

s

an

u

nchangeab

le

,·a lue

o[

capa city and suppose th e co nt act

point P is

so

a

r r

;m

gc

d as to inc

lude

in

the

circui

t more a

nd

mo re

turn

s of the coil

as the

contac

t

move

s

toward the right.

With any defoni te va lue

of the

fr equency

of

the

applied

po

ess ur

e,

some

p

os

ition o f

the cont a

ct P will be found such that

the

ind ica

ti

on

o[

the ammet

er

will be a

IIW.ri-

mtwt.

I f the

contac

t be m

oved

tow a

rd

the

left from the position g iv

in

g a max im um ,


the ammete

r

ind ication decreases,

and

if

the

(On tact

be

m

ove

d lo

wanl

the right

from po ,itio n,

the

amm etc •· ind i

ca

t ion

f

II

1\

I

1

I

'

I

\

I

i,

/

......

1

...-

.. .

·

..

,,

\\

:

·-

·..f.

II

,\

j

II

'•

' •

.

\

/

..

'

,

· . . : ~

·.

,

'

/

.,

1/

'

..

I

,,

\

.Y

\l

I

\

.

'

J

1\

/

I

33

d

cp,·

n

d , upo

n

th

e

nu m

e ri

ca

l

value

in \ Olt '

of lhe

applied

pr

ess

ur

e,

;111d up

on the

n ·-

sista

ncc in CJ

iom

s o f the

co

il o r pa rt

of

llt l

/

.......

v

\

I

I\

/

•J.

\' '

'

.

'

/ \

·

' /I

•

.

i/

;1

\

~ : ~ .

/

.

•.

.-;---

.

· .

-.

II/

\ '

/

L

.

\\

..

..

.

\

.,-

I

.....

/

...........

/

..

.

...

\.

\ I

I r\ I

7

\

\

J

v

q

69

8

.,

Every

True A l terna t i

ng

Current,

of

An

y Sh

ape

Wh

a

te ver,

I s M

ade

Up

of

a C e

rt

ain N u

mber

of

Simple Sine

Curves

Added Together.

Th

e He avy Line Represents the

Result

a

nt

W ave

F o

rm,

P ro duc ed by

the

Addit i

on of

th e

Th

ree

Sine

W aves In

dicated

i1

L igh t

L ines.

Th

ese

Componen t Curves are Called the Harmonics .

a l

so dracuses.

Tu make th

e

matter

clearer

and

more

co

n

cr e

t

e,

it will

be we

ll

to

a

ss ign de

fi

ni t

e

a nd p

racti

cal

numer

ica l values

to

the

\ 'ar

ious

sy

mbols

in

th e l

ast eq

uation . L

et

u

s

uppo

se the

frequency

f of

the

a

ppli

ed a l

te rnat ing pr essure io; 60

cycles

per sec ond ;

t

he

u

2r. j

is

equa

l to

ve

ry

ne

a

rl

y

3i7

.

S

up

p

ose

f ttrth

er

t

hat th

e

capac

ity C

of th

e

I

lixt

co

ndcm

er

is 10 microiarads or - - -

1

00

,

00

0

( .(J()(J()I fu rctd ). On e

mi

ll i

on m

ic r

o fa

ra d

s

arc equ:al to one fa rad. According to th is

a

ss umption l,r.f C hcco

m

cs

e

<]

u

rt

l to

377 X

1 I

- - -

.

:\ext

;,

upp

o r

th a

t

- - -

=

.

0037

7.

100.000 .'Hf

c

T h

en,

s

in

ce

2r.1

= 377.

L -

377 X .00377

= 0.703 ltcttr\ .

If, ther efo re, a

condc

t

';cr

lta ,·

in

g a capac-

l

it\'

of - - -

far:od i>

conncc

t

cd in

' e

ri c

>

. 1

00,000

\\ith

a

coi

l

ha

v

in

g

an indu

c

tanc

e oi 0.703

hen ry, then

reso

nance

obtains

in

the

c

ir

cuit for a frequency o f

60 cycles,

and

th

e

current in the

ci

rcuit is a m ax ·imum. The

nu m

er

ica l va

lu

e

of

the maxim

um

current

1 1

· ~ ; ; ,,

o

rmo 1c

' )

;;

/

..

\

..

.

~ · ,

.

.....

v

..

\

-

• nl

It").,

II/ ..

.

.........

v '

'

·.,

tw ·· '

\.

'

· - ~ ~ : . :

rt ·

/

B I

'

\

,

'

.,

q

\

.X.

¥,-

'

;:..

'

·.

;

-

'

/ I

--

coi l that is conn ected in the ci

rc u

it.

S

uppose

t

he

pr

essu

o

e

is 110

volts

ami

the

oh m ic r

es

ista

nc

e o f

th

e w

ir

e on

the co

il

is

]0

o

hm

s,

then

un de r the

condit

ions

of

resonance me

nt ioned,

the cu rrent " ill be

L

O

...;-

10 =

I I a

mp

e re

s.

A ve

ry s t

rik

ing and

impo

rtan t ph

enome

no

n

IJe

no

ted at th

is

poi

m, n

am e

ly.

the

n

um

e r i

ca

l va l

nc of the dr

op

in

pres-

s

ure between

t he te

rmin

als o f th e

co

il and

a lso

between

the ter m

in

a ls

of th

e

co

n

d·en

se

r . The d rop

in pres ur

e

between the

te rm inal s

of

a

when

rc>onancc

obtai

n,

in a c

ircuit

is exprcst bv I ( -

1

- - )

. 2r.f c

w

hi

c h in

the case

under d i<cu>sion

i

e

qual

I

t

o: 11 X -

=

?.91.'> vo lt

s

(a

pp ro

xo

-

.

00377

m

ately).

T he pre

ss

u re drop

be

twe

en

the

terminals

of

th e coi l may be stated by ;

I \ 1

'

+

(

l. ffj L)

0

which

is

numer

ic

al l

y

equa

l to 11

\.J

1

0' +

(377)' = 2915

vo

lts;

ve rv nearly. T his co

ndi

tion

of affa

irs

SCCnll

S a

bit'

Ull\:31ln)'.

1t does

not Jook ex -

ac tl

y log

ical

that the pre ssure between

the

(Co t illlll d

0

pagl 59)

I

/

/

·,

/

,

.

X:

/\

'

\

h

t;.

'

I

\

• l

',

'

\

" : ~ ..

'

'

.

/ f

rr

...

7'

...

\

'}

/

~

'·

lr /

.·

\

)

·· .•.

_ .

~

\

.

v

\

1

L

l ig.7

Graphic

l l lustrat

lo ,

of

Res u ltan t A. C. Curve

Made

U p

of

Th

ree So

mpte

Sine Curves, o r th e

1st

3rd,

and

5t

h • H

armonics.



M

ay

, 19 18

o

rd

er to ope:rate the val

ve

efficiently

the

filament must burn br ight ly and should be

fed a t abo

ut

20% above t

he sp

ecified volt

age, t he ex

ac

t

amou

nt varying with chang

ing conditions. An accur

ate

low voltage

rheostat is essent ial for the pr oper ha ndling

o f any hot fi lament

rec

tifier,

and

espe·

cially so in the case of o

ur

instrument.

T

he

r

egu

l

ation

of

the hig

h

vo

l

tage bat

tery, however , presents the g reatest varia

tion

fr o

m common practise, an d

there

f

ore

affo

rd

s

mu

ch op

po

rt

un

ity f

or

research

work.

A

'phone circuit batte

ry

of

ab o

ut 60

volts

is generally consider ed quite sufficient for

the majo

rity

o f present-day va lve de tec

tors, but in t he case of t he bulbs un?er

c

on

sideration

it is

best

to comma

nd a

h1

gh

potential of up to 70 volts, altho

very goo

d

resu

l

ts

can

be obtained with as

little as

SO volts.

The

c

ur r

ent fr

om the

cells which

fo rm this

battery

must be con trolled by a

p

otent

i

ometer of

very

hi

gh res

is

tan

ce or,

b

et t

er st ill, several

pa

irs of high r

es

istance

'phones

ca

n be substituted

the

refor..

Th

e

author has

found du r

ing his tests

th a

t a

potent ial of

abo

ut 75 volts, subjected to

the

reta rding effect encountered by using the

s

kin

of

the

ha nd or fingers as a rheostat,

gave unusua

ll

y good results.

T he idea of using part of one's body as a

current regula t or is, of cou rse, impractica l,

but

th

e r es

ul t

a

nt

effect is

so

st

r

iking

t

hat

it leads the au thor to believe t h

at

a new

i

nstr

u

me

nt . m

ay be

developed to take th e

place of t he pr

esent po

ten ti

omete

r , which

is

known to be

a very wasteful instrument.

An

a

dj

ustable

bank

of receivers of

di

ffe

r

ent

re

sis tance but s imilar p

it c

h , connected

with a comm

on

sound

chamber

or h

orn,

should entir ely eliminate t

he need

of a

po

ten

t iomete

r. Th

ere is also a chance of

employing a va riable condenser in this

co

nn

ec

tion to a

pp r

ox imate the capacity ef

fect obt ained in us ing

th

e body as a re

sistance.

During the

wa

r it will

na t

u

rally

be

im

possible to

test ou

t any fo rm of wireless

instruments, except in the laborat ory, where

so

me ty

pe of non-radiat i

ng

ci rcuits

must

be ut ilized, and even

the

re a buzzer p

rac

tise set would constitute the limit of send

ing p

owe

r

availab

le n

ow

.

No

aeria

l

or

ground connections are permitted under the

recent

Rad

io

Act.

For the real electrical experi

menter and

research worker there sti ll remains a wide

field

in

which to work with

any

type of

valve-amplifier

tha

t is

not too

highly valued

to

expe

rimen

t with. T

wo

of

the many

possible uses

to

which elec tron

ic

relays can

be

put ou

tside the radio field are conside red

separately in the following paragraphs .

Hot filamem va lves

are

slowly coming

into use as r ectifiers of electric current in

commercial stations, but are still consid

ered in t

he

c

hrysa

lis, or unfin ished state.

The great draw -back in using bulbs for this

p

ur

pose

lies in

the excessi

ve waste

of fila

ment which takes place, ma king the rectifie r

very

sho

rt lived. I t

wo u

ld be folly

to

use

an expe

nsi

ve

in

strument

fo r

experiment

s

al

ong

this line,

but one

of our lamps,

whi

ch

cost

on

ly

ab o

ut 60c to replace, may be

used wi thou t one's being considered ex trav

agant.

By

us ing the filaments interchange

ably at intervals of a few hours each it

may be possible, under the r ight conditions,

to greatly increase the active

life of

these

bu

lbs wh

en

used

as model

rec t ifiers.

T he

most

won d

erfu

l prope

rt

y of t

he

vacuum valve,

and

the one which holds

the most in store for the inventor, is

doubt

less

its

ability to

act as

a n amplifier.

For increasing, ind irectly, electrica l ene rgy

and mechani

ca

l

mo t

i

on the

electronic va lve

presents a

ve

ry

desirab

le

medium. Many

sy

stems o f automatic sound

contro

l

are

being de\·eloped

wi t

h the

aid

of the amp li-


bilities of experimentation in

this

di r ection.

Loud-speakng megaphones, phonographs,

te

lephones, horns,

ad

infinitum,

all

await

dev

el

opment. Submarine destroying de·

vices, aerial torpedoes, loc

at ing apparatus

of all kinds,

ca

n

be

invented which will

prove to be

the undoing

of

things

out of

sight.

but not

out of

the hea

r ing of

the

delicate ear of

the

microphone, augmented

and

sensitized

by

t

he

addition of

an amp

li

fier 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

th e

co

ngesti

on

existi ng at the

pre:sent time in

aJI ra i

l

ro a

d

mo v

eme

nts,

aJso on account of the fact that many tr ain

clerka ha ve

go n

e t o wa r, the:re is a con .

gestion

of mails all over th e U n

it e

d

State

s.

It may happen th at yo

ur

ma ga zine wi ll be

sl

ow

in reaching you,

an

d th is delay may

be from a few days up to s

evera

l weeks.

Kindly bear th is in mind before sending

in a complaint, as the ma gaz i

ne

will aurely

reach

yo

u in

du

e

tim

e. On ly

after

not

having received a cer tain copy for a

pe

riod of three weeks should

a comp

l

aint

be

sent

in .

Yo

u

will

co

n

fer

a

favor

lish

ers

not to

writ

e

until

elap sed, t h

ereby

sav

ing

am o

unt of cl

erical

l

abo

r.

upon

th

e p

ub

this time ha s

them a vast

T H

EO

RY OF

TU N

I

NG

,

WAVE

LENGT

HS AND HARMONICS.

(

Contin1ted fr

om

page

3

3)

terminals o f the parts of a circuit can be

more

than that which

is

applied to the

who le circuit.

The

r

ela

t

ion

of t

he different pressures

may perhaps

best

be

represe

nt

ed 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

vo

lts.

The two large pressures are very greatly

out of phase

wi

th each

othe

r,

so th a

t their

geometric res ulta nt on

this

composite

mu t ual effect is reall y

only

l l

O

volts.

T he

next step in

t

he

development of our

discussion

shou

ld be to consi

de

r

wh a

t will

happen in the circuit,

and

the numerical

effect on the equations given,

if

the fre-

queucy

of the

app

lied pressure is

doub

led;

tha

t is, f is to become 120 cycles. I n t

his

case 2 Trf

=

754

,

very

nearly

. Supposing

the

condenser is the same as used when the

frequency

was

60 cycles ; tlhe value of

I

2 TrFC =

754

X - - =

.00754 and

L =

100

,000

1

- --- - = .17 henry.

.00754 X

754

I t

is thus evident

that

with a given con

denser having an unchanging capacity, if

the

frequency is doubled,

the

value of the

i

nd u

ctance

mu

st be

decreased fou

r

times

in

or

de

r to

produce

a

condition

of

comp

lete

reso

nance in t

he se

ries circuit.

T he cu rre

nt in the

ci

rcuit under the new

con

dition

of doubled frequency will

be the

same as

with

the

original frequency of 60

cy

cl

es, provi

de

d

the ohmic

resistance

has

not been changed,

and

likewise

the

pres

su

res between

the

te rminals of

the

con

denser and

of

the coil will be 2,915 volts

as before.

In

order to decrease the

in

du

c

tance four time

s,

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. I f

the number of

turn

s were decre ased th ree

fold the inductance would be reduced nine

fold.

:59

. urlington

Tho

great Bo

rlinJrton

Wa t

eh sent

on

ei.n.tple r

eq

uest.

P:1y at

rato

of S2.50

a momth. Y

ou .ret

tho watch

at

t h , . ~ c pd c:c even

Lhe

w h o l

3 . l e )e welcr mu

at

p

ay.

Write Tod

ay

for Fr

ee

W

atc

b Book

Soo

hnnd3

omc

il

hUt4ltiona of

a ll

tbo

oewe8t

de

siJrns Jn

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Ji

OU

have to

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from.

Your »"me and addrds on a poatu.rd Jl enoug:b.

Get

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~ ~

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H

ERE'S ju

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formulas and other Eleclr ica

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Mech

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T HIS M

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INTERNATIONAL CORREP DENCE SCHOOLS

Box

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SC

R

ANTON.

PA.

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H

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Civ i l l l ( ' ( : r \Y i ndow Tr imuu.•r ' ,

Co

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nruiNo

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State-

fier valve. There is no limit

to

the possi- (Coutimted

011

page 62)

~

~ ~ ~ ~ ~ ~ ~ ~

~ ~ -

You

bene fit

by

mentioning lite uEicctrical Experimenter" 1ulum writing to adverti

strt.



May, 19 18


ampere-tun zs.

Wh

en

arranged

as

in

figure curve may be called t

he

first harmol ic.

An

-

5,

the

receiver

wo

uld

natura

lly h

ave

a much other component sine c

ur

ve h

as th r

ee

ti

m

es

gr

ea

ter r

es

istance than when

arran

g

ed as

in the frequency, hence one-t hird the wave

fi

gu

re

4,

si

nce wh

en

connected

acro

ss the length

of the

resulta

nt

cur ve.

This

sine

co

nd

enser they are subj

ec

ted to

very

h

ig

h c

urv

e is

ca

ll

ed

t

he third The

pressures

. T h c gr

ea

ter r

es

istance

does not ot

her component sine curve has five times

imply, however . that they

sho

uld be

wo

und the

fr

e

qu

ency and one- fi

fth

t

he

w a

ve

leng

th

with

wir

e having a high r

es

istance. In f

ac t

, o f

th

e r

es

ultant c

ur

ve. The result

an

t curve

such sh

ou

ld no t be the case,

sin

ce a la r

ge

is co nst

ru c

t

ed

by a

ddin

g t

oge

t

he

r

al

gcb

rai

val

ue

of ampere-t

urns

is d

es

i

ra

ble.

I f

cop-

ca l/y

the ve

rt

ical heig

ht

s o f a ll three of

per w

ir

e is

used

in

wi

nding

th

e electro- the com

po

nent sine cu rves a t each point

magn

ets of th e 'phones, a gi

ve

n

re

sis

ta

nce ch

osen

. The small circl

es

on

th

e r

esultant

wi

ll of cour se

mean

many

more

turns and cur ve ind ica

te

the

poin t

s

that

were chosen

the

ref

ore

more

amp

ere-

tu

rn

s,

th a

n

if

wire in

or

der to cons

tr

uc

t the pa

rt

icul

ar

curve.

hav ing a high

er

specific

re

sis

tan

ce is em- By alge

br a

ical addition is mean t that at

ployed. any gi

ve

n point on the h

or

izon

tal

all

ve

rti-

Coils wound with insu lated w ire so ar -

ca

l d istances of the compone

nt

sine curves

ranged with

a

var

i

ai.J

ie

con

t

act

d cvicc

as

to

ex

tending

be

low the

hori z

on

tal mu

st

be

sub

have their ind uctan

ce

var ied at will t

hru

-

tr a

cted from the vert ical or the sum of the

o

ut

a considerable r

an

ge, arc ca lled

hmiug

verticals

ex

tending abo ve the

ho

rizontal at

coils

when

used

in conn

ec

tion with

wire

less the same point.

At

poi

nt

s where all t

he

receiving appa

ratu

s, and it

is in t

er

es

ting

to compone

nt

cu

rv

es

pa

ss

thru the h

or

izontal

note th

at

as

th e contact

P

sh

own in fi

g

ur

e

2 da

t

um

l

in

e, there

of

co

ur

se the

res

u/

ta1Jt

is

moved

so

as to redu

ce

the m unb er of nrrve al

so pa

sses

thru the

ho

rizo

ntal.

turns,

th a

t is to decrease the imluctance, a t I t is

evid

ent t

ha

t a gr

ea

t va

ri

ety of r

c

the

sa

me time the

re

si

stauce

of t

he ci

rcuit s

ultant

c

ur

v

es could be co

ns

tr u

cted from

has also .been dec r

ease

d. That is, the d

e-

three simple sine curves by simply varying

cr

ea

se in inductance

and

o f resis tan

ce

must the he ights or amplitudes of th ese cu rves:

occur si

multaneously in such a d evice.

Re-

o r o f o

nl

y

on

e

of

them. E very alte

rnat

ing

clue

ing the

nu m

ber

of

tu

rns red

uces the

wave of

pressu

re if

applied to a

ny

c

ir

c

uit

act

ua

l length o f w

ire

in

ci r

cuit. will

pr

o

du c

e in the c

ir

cuit an

alterna

ting

cur

ve

of c

ur r

ent

th a

t is

also

ma

de up

o f

The

tuning

m ight

be

e

ff

ected by dr

awing comp o

nent sine c

urves

. It m

ay

, f

or ex am·

an

iron core in a

nd

out o f a co il,

wh

ich pte, be supposed t

ha

t fi

gu

re 7 denot

es

an

w

ould

give a

ve

ry wide variation, but which alternat ing

pr

essure E

impre

st

on

a circuit

would be

slug g

ish in

ac t

ion, a

nd

of

co

ur

se as show

n in figure 5.

By properly ad ju

st

wo uld not va ry the olzmic resi

stance

con- ing th e movable co

ntact

P, resonance may

nected

in

ci

rcui

t . Ano

th

er met h

od of

v

ary-

be

pr o

duced in the c

ir

cui t w

it

h

referen

ce

in

g

the

in

ductan

ce might be effected by to

the

third

hannollic

c o m p

~ > t of

t he

copst

ruct

ing th e coil of two po

rt i

ons, ar- applied pressure,

cau

sing a maxi

mu

m cu r

ranged to move with refere

nce to

each rent in the receiving

ci

r

cuit

h

aving

a

fre

o

th

er . I n

such

a case t

he va

r ia

ti

on is said quen cy just

th r

ee

tim es

that

o

the

fwzda

to

be

e

ff

ected by m tual

iu

ductio11, a

nd the

mental o r

re

sulta

nt pr

e

ssure

and cu

rr

en

t.

ohmic r isistance o f s

uc

h

ap

para tus

is con

- T

he pr

edominating

tone in

the receiver h

as

stant.

a

pi

tc

h o r

fr

equen

cy

three

times th

at of t

he

Harm

o11ics. A very inter

es

ti ng and in- f undamental or r

es

ult

ant

cur ve. By still

s

tr u

cti

ve

u

se of

the tuning

coil

is

in

tuning f

ur t

h er

adjust

ment

of

the

var

iable

indu

e

the r

ec

eivi

ng

circ

uit to

respond loudly to

tanc

e,

th

e

fifth ha rm

onic

may be made pre

the

va

r ious

h

ar

m

on

ics

of a

ny single

fund a-

do

minan t. I f

an

im

pres

t pre

ssur

e

is

m

ade

mental wave t

ha

t is being

se

nt out

fro

m a up

of,

say, fifteen h

armonic

s

and the

tun ing

s

end

ing

station

. This m

ay

per

haps

be best coil h

as

sufficient r

ange

in adjus

tment

, t

he

e

xplain

ed by

co

nsi

de

ring t

he shape

a

nd Fift

eenth

ha

rmo

nic

might be m

ade

the

pr

e

composition

of

a lte

rnatin

g-c

ur r

ent

waves or

domina

nt one. As the

fre

quen

cy

g

oes

up

a

nd it

is

ad

visable to

define just

t

he wave

length inverse

ly

becomes lower.

wha

t is

meant

by an "alte

rn

at ing-c

ur rent Thus the th

ird harmonic

ha

s a

fr

e

qu

ency

c

urve

or wav

e.

A t

rue

al

ternating pres-

t

hr

ee

times

the f

un

damental,

and

a

cor

sure, c

ur r

ent,

or

magnetic

fie

ld is o

ne

which r

espo

n

ding wave

len

gt

h of o

ne-th

i

rd

that

has exactly th e s

am

e

wa

ve sh

ape durin

g of th e f

undam

en

ta

l,

et

c.

ea

ch

successive second, a

nd

o

ne

t hat

is pr

o- An o

the

r i

nt

eresting h ct in co

nn

e

ct

ion

d

uced

in acco

rd

ance w

ith

a definite l

aw:

with the

matt

er of

''

tunin

g

may

be alluded

63

255 OURAY BLD

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to anyone It your

ben prott:ction. \

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•mprovt:r

nenu

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their

n ~ h u : rende

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by

our

Scr

\l

lcc Gua ran tee Con tr:lc t . Refe ren ces.:

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i.

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the

luventor

KEEPS

Wortb

more

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other pateat

books eombt

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FR

EE.

Write

LACEY

&

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BR6MNN MTORWORKS. 12

83

NAGARA ST•

BUf

fAlO. II. Y.

T he very simp lest alternating c

urve

is

the to

h ere, t hat has a very import

ant

relation

so

-called

sine curve,

shown

in fi

gure 6.

to mu

sic

and

m

us

ical in

stru

me

nts. Ne a

rly

Such a cu rve is constmcted by first d raw-

every

person can distinguish

the mu

si

ca

l

ing a

ci

rcle, as shown at

the

left,

and

l

ay

ing tones given out

by

a violin f r

om tho

se

o

ff on

a ho

riz

o

ntal st

r

aig

ht line, t

he

l

ength

given

out by

a

cornet

or a piano.

That

is,

of t

he

circu

mf e

rence of the

given

circle. a tone h

aving

a definite

pi t

ch

or

frequency

The

length

is

shown as 0 X in the figure. given out by a violin has a very different

Op is t

he

refo re one

-half

a circu

mf

erence, qu

a fi

ty

from

t

he same

tone or note

(same

Og

one-fou

rth o f a cir

cu

mfer

ence

. The

frequency

) gi

ve

n out

by

a piano or by a

sine

curv

e

may be co

n

st

ruct

ed by

first erect- cornet. When a ll th

es

e ins truments are

ing at po

int

g a vertical line e

qu

a l in le

ngth

tu

ne

d t

o,

say, midd le C, they e

ac

h

produce

to

the

r

ad

i

us

of the cir

cl

e, then

at

point n a note

having

the

same

f

requency

or

the

a

ver

t ical li

ne

equa l to th e line

A'

B, w

hi

ch s

am

e pitch, but

the shape

of

the so

und

0

is

. call

ed the

sine of the angle A ' 0 A. I n wa

ve

s sent

out

by

eac

h

in

s

trum

ent is

very

R

shor t, all the

vert

icals erected on the hori- diffe rent.

8

D

zontal base line rep resent

the sine

s of cor- T h is m

ay

be illustrated diagramatically A E

responding

angle

s about

the

cent er of th e b fi 7 d fi

8

given circle.

The

dot

t

ed hori

z

on

t

al

lines Y

gure

an gu

re

·

The

r

es ultant

curve R R

·

fi

6 ., · d in figure

8

is

ma d

e up of

the

sum

of th r

ee

C

m 1

gu

re wu l g1vc

an

i

ea

as to

the

con- sine wav

es

as indicated,

but

has a very • ....

s

truct

ion of t

he

sine

cur

ve. " ""

diffe rent shape f r

om th

e r esu lt

an

t c

urve

1

0

Now

every t rue alternating wave of

an

y in figure 7. t' w

shape whatever is ma

de

up

of

a certain T h e two res

11

ltant curv

es

might h

av

e THE MI DGET

SLID

E RULE

nu

mb

er of these simple sine cur ves

added exac

tly

the

s

am

e w

ave

length (

di

stance :J'J : ~ ~ \ ~ ; :

to

gethe

r. T he so-designated res

ul tant cu

rve f rom 0

to

X ) , that is t

he

s

ame freq

uency,

an d •m ••en <0013and powore.

A.I.M

in figure 7 is a true alter11ating curve, which yet" th

ey

will never

be

mist

ak

en for one ,_ : .'":"

is m

ade up of three

sim

pl

e sine curves all

anot

h

er. Two wir

eless wa ves having ex-

W •

JC1U

n

d Cotanaeot.. or

o.no.ng

he

.

sta

rt in

g at

the ze

ro

point

0 , a

nd

all in

creas

- actly

th

e same

fr

eq

uency ma

y readily be

1 Jr Iu oporo.Uon

. . •ery

olmple: aul

el<-

ing in t

he vert

i

ca

l or p

osit

i

ve

direction. I t

distingu

ish

ed by an

expe

rt

operator simply •· · l m ~ l l :

~ ~ ~ ~ ~

~

ed f or Aboo and. omce tue. Fi t

ma

y

be no

ted th

at one of

t

he

compon

ent because of

the c

haracteri

stic of

quality.

,

tho

PookoL 8%

ln

e

h ' dl a

motor.

si

ne

curves

has

t

he

same fre

qu

en

cy

or wave I t

may be

valuable to have devices that will - . . ·.

~ ~ , . m : . : ~ " : ' f r ' : . ~ ~ ~ ~ ~ ·

as

t

he

r

esu

lta

nt

c

ur

ve. This sine tune not only

for pitch

but

also

for

qual

it y

.

·

Cibon S6d; R,t, Co. Ni

les

,

~

~ ~

~ ~

Yo

1t

b

tn c

fit by

me

trti

o

ng

tlr t

Elec

tr ic

al

ExPcr

ime

Jtcr 1 vlten writiufJ to ad1:rrtirrr .

theory of tuning, wave lengths and harmonics - electrical experimenter may 1918

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