C-hC:;l P I-u-z. 3 3 ( CnvJ f d. . )
~!:i9fV"'S P>-""'.,'ple ,
HiAlJ9cliI 5'5 princA fie iIJ a geomemCA,{ "Yhodd. /Ji~{r- atto{;r)S UA
h, dejo-u'h/ne ts: fxJs/ha-n of a UJC?vefYcn,f- ~ lli:e i<Yl0wleolge dfti\S
a 11 ecth-Ue.n.. wave ~. It 1/ ~/'hf-s dY) ct toa r« jYtJnl- bei-'?lV€" ~ouya_~
~ SphlhA'cev{ $~UJ)1~~ CVQlleS) ~ ttJQve!e!-s1 r~Cv{- pro/:;>Qga/e..-6 Uf-VXif1.d sur! fh ~t 5~Qo( OJ- ~9 h I- [n !TCe med t' uvn .
A ;B
AT . ;f3
(
4:s tt: -hjUY€. 9hOWS) a.fk.;'t-- h'me tIN P (0 he CUOIve ~i- onoies /-0 ~ Y1e LU
.{ec.a..!-;dn 9hrrWn cv.> B; (3 : 'The 'Ylew tvave~1-
, I b IJ rr , -en ve..troe 0f trLt too vd eb 0-1-VJ rWCh v IjIU.. I
hYne t-.
Irne fav ct 5phV>1'~ wave f;tiN, Each
porn+- behClU€~ as' q 5>'b'tNlO< 6)-=:': .ik ia~ 10 Iw. toaie Id-s c4-- hrr.e f-91\\Ie~ W toaie frv7--.1- 0.--1- h'rne f.
US I~ IN 1+(A:J9~5 () V/'n (Alple one ca.a
o{~r' lie rtk Lawt; eft 'refU t-h'Cfh ~ 'Ye-fyaej-/OM)'.
Ct-«..c{ ceco: ~p iulY'! beVlcLfh8 "f ~y/ttf ~d c;.e;rhVZ5
(~~. fjr-ach'on) 0/} w.w L0 I'm~~~ce,
IT II I tee. "res,u-AJs o b I~(\~-ec{ ~ ltCA.!j9LVt5 is p n'n t--/f l-e
~,o../56 he. ab/-c~./Vled. fwm I1ClA ~1Ie..tl J5 ~LLd-({IC17,§. II,{AS
~ VI 1'l0 ~ (A11 /'v,dep-ewdlAAf p n'h (.;/pfe.) htvf- UJ71 f/el1{'u1--!-
. Pv ca[Ut-(A-h'm 5 tu)'fh itlQve thel10mehrJrl.
CJ1QpkrL SY
I 'Y"o(h ..~ VJ ca
The p""D~enhes of ~flhf- fT-£lf we have dt'sc,l.A.ssed. <;0 feV}.. [ctapfoz 33)
CVl..(. ta5eo{ CD" the .fCH..-f. we CD h 'Ye/:>d""eSe.ht £t'g hf- CV::I 'YClYS t.•.) t; t'Ch ?JJOve
;'Y\ SIYaiqhl- UY}~S thwi- ~ beVlI- O\..~ I11-t reffel.-h'~ ov- -ref yo Lfln,9 5uvfrta.
t)~t- /lttw Cth.JI. 0n th· pYO~V2-h'es of ,t.-Igh I- tv'" I'd. CCI.-u be ob<_pf.£t/n eel
lJ"hl~ oYv 11U.. /oasi's of tooce 01al-uyf of ~3hf. rV)krtfUUJ~'c.t ccccd
d; ffrCLc,hCrn tv)L lw7> S"U-h pYbfUz.h'es to l-Jc]; LN'-€ tv/II c//swsl> wszo .\ At'9h ~ (vtrn-l
I'ht~~VJ(Jl V'? C\.. phe.h(rmeVlOY) w/-"/ch OCUtYS e»heJ-'1A. fe;rzJ
Co~~n~ SoL~ytes ~bi'YJe. Wheh wCtv~s aVId ~DUYC<S have ~
CcJ-nsktn f /? A tt/.J.t rre.-[aA-/(f)'1 s h/p ,i/cfe CovU. (i;?V/- toa oe uf\o.urc vi ?
A lo,S-e,,~ -G/fjAf- ca« b.2 ~i-'lf aud ?'Y1OYJDvhyt),Ynechc I Pcr/ytf.
)OCO'LeS on..- Cl ~Jh~ hiLI b f-/(C-tWJtVi+ osulla-h'ng "'row;Mm/y ~
CL<.{ e.'itlYhple of CtM j'Y)C~he.-yeVJ~ 5Dl-tYG? 0 (~/(JYS SeeM /'" oH f/(m5
Cthd 5(')Ct.() h"tbloie s CtJZ.X- a. yesw 0 F "h~reno01U be--huee--n ~'gt, I-
Yef1~C+-...e{ fYrnn- ttu ~ Ctl-1d bca---k ~ur~uS 6}- Ct.. /1i/h ~'(W\
OY ~'O0- (::> S6 Lcd.,'c'h .
IhMfVuhc.€ o·F -hAro wave 5 C,c; bctsed on tt: f:!Y1'ne-lple cf)-
~Uz.-(?(')s;/)dY\ - When hvo OY 'h1oYe. WCtl/es Ol/en.lap Ii«- ryt'.suLfctn~
01 (SP rl< UYl1tVl + c.-/-- a h'j f:xnnf- h fo-wnd. bfj adtLih~ n: c! ISfr Will flAbD} flu Ihot /1/ i vl kCL{ toa ~/e5 cJ- thctf- ih5!al-'\? .
Can> ~ c,h'l-,e t''h f..o1--/-ot£VJLe (~s Pledo£. toheu: fvvv tdCll/e S
CUV1'-/V~a)- ~ 1)01')1 f- ~ /rv (r;) has«, Desh-uch've ,'vi kA-ft;uncc
bt~s pIaL{ loAth ftu. twv Wlll/e8 ~lvl\h3 c4- lru po1V1r ~01v1- 0f Phcvu. I ,'. e, C-l eve. ,I- ()f (JYUL cca. t-e: ~'v€/.J Cv{- 1M
)Cll11e hme lA-Q CL fvoUJh of {(c tJltu/L wave.
5,. -ry~? It C£th be che.vkec£ 'c..-f YcY. ::: "')yJ/\ (m:::o; I) 2· - )-~ s-«:~ Coy}5tntc17've /vd-vtfvun c.R5~· 'Y?-1..
3I-f 1"l.-Y, -- t111+-\. ) A (VVl::' 0, 1}2 - .. ) dV)(YULh"ve jVtt~v/Li.
[SGE FU;l>I2.E Of\!LA5r PAt;~J
(D~mcrn"3;.iYah'crY\ w/f'h IvaUSPCVVl--r1L,i~s ~d Of/OLt1eP4. I:JYa)~c.k;y)
A c)t1.551C ~ d~trn5(ya.h'oYl of (Vt~rl1a effeG/-s ~ ihe
50 eot-A,,(e,o{ YOUVl9'S do~dole 5u'{- -{J<.Perzihlet1" /)e.nfrrymecf ,y, 1&'06 bLj
EYlJUsh 5r.)eM.h·)~ Thu""'mC0 YOC,{h9'r- -...
'iou. \19' S Dot,dole 5&1'1- fi<p-eJ'l..-i Yh~1--!
TW7J <:-0h eJlJLlit I- toa lie5 CffYY11 n [}
'(Yv-m 5'ul-5 SI 0.. n& S2 fYYJee_}- <:-4- I t:PO(~f- P on n; ~c Ye.fn {~{Ctuti. ar:a d l'sl-one£. r«. frr7m 1M /-va> 50(~yUs,
A-II (:xrjn I-s 011 /7;u S'cr ee n ors« YW ~
fA. YJiforrn1y /{kLm ;nCt(-u{, SOYne /){),'n/--s
htt lie 'l'Yl "-)C i1Tl (AfT] I'y\ la< 51'~ CUA-c\ SD>n e pn'n rs f,a lie ~ ('11 /-l.-vts" f-o .A-55("{vYJe ffievf- lti:i. h-v" [.Jo,{,le.5 t10ve 9·H11e ClYf1.pl//l1.C{-e C'a.<.c( SQ1'J-')e
Wet lie t eng tJ:. .ThY- path
P v.>
Jyf~ges (jy lV1I<IlfwY)Le {nhJ'ts pa./7-a11e1 /-lJ ti: sU'1-s ), aVId 52
l DeVYJOVJ5/~h(rn of c{lJu-lofe sL/{- o1.l'HyCiL!-r'on)
FClV smiLU I/odues cJf 'h1 C m ~ 16) J 111-e. CCJYY0/')(JYJeijngaas (e') en, aru. 5 rn a..U. -:::3)
5' I i., AI _ 7Yl /\In em ~ run v/n - "jjf
·------1
!Ir:£::: m: :::,)t ~m z:
5 trn t{o.1'z./,y ~+I = (1'11 +-I) A ~2.
43::: \}rn+1 - Ym = ()11 + I) A :. - '1rJ)\ :; .:
Exo.Wlpie LeJ d = 0 -03 rnrn
Se..UlY!& aydVl b'Y(9h I- (-n'Y7Je ?;;
~'YI~' WhClf-?? 1M Wave /ettJlT1/\ = 01.fdz. _ (3)( ID-s-hJ) (Lt·!:'X /6 -~ ) ..-7
\..: -- ~. G. X ID
R Yh L(- 2WJ) (2)
a.. rid 1<= {.2 m
I
l-r - { o-~-{'j eCh1'c f-ru d o.--f- Pvu.. aVYlI:> UIL-td e r
Ep -:: 2 E LOS ~
So flU. I'Y'Iku S (\~ O-JL IW. puiYl i: P kJ 2-
1::1. iEcE.r S c- p _ .-::::.-:;- 0 p)::. av:::: Z)AoC e...
'1'-..... " r: C .'- C6) 2..:E._ L C:;-O E 2.
c.::: .L.J ~f(~
'TVi€: 'h1CLximUW1 1''Y)f.ev\S'''~ .to OCOUy5 wh.eJ'Z.R. /he pt-,as'e d('~J1U?
h ?A J7Jl ( q, ~0 ) < Sot1~-- .•... 1.'10 z: 2 foC' £ l J11{-cu.S.(ftt Ct)- rru Cbl~ ml,K(}yJIAI1l)
Nok ihai- Thl's IhCL/drnum I'Vlf.euS;~ 0 4 HYnes (nof hv7'frL) Ct4
,f.A;~ ,M 1M iY\~7;ha .£ ~() C E '2, frvF1'7 e9-c.t, i'V1&lvt'd~ coaie-~uJ~JC fJ&h'd'rt \) ,t,.,'
:> or 10 in I~ -e"preSSfO'r1 JLlY :r- glve.5
II= 10 Cor/-fJ"TVI ('5 i"Y\ku s i~ d /5 fy,'blAHon Ixd/t.hV) Ca-a be I';) Lo!+e.d. Qs be.] rnJ
-4,---+~---+t---+'---+----~I---4r------~.....,tt -4H --2.0 d z.n 4-.,.. 6ft
~3) -L~ J,A-O
l hI's '}resu..U CQV! be ofol-o..ln~ b'tf dYG.wlng /JhCt5(JY cl/afJram
(}../)done (h ;J()'Ur fc.;e.1- .
{<EV(flAJ FOR MIDTERMI
This is possible because waves can be added and subtracted., -----------1
Ct ;;:;;;2~A----C----- ------- ~.4iI1:..1p
Source 1
Source 2 "
phase
~ f. = 2~"\ .1
$(Jurce 1
---Ir.>
/'-.>(2 - ~1 .----.--~-A--'" ..•.
./"- .•.•..--","""' »>/'r-/~
Out of phase
c.o nstruCliVGinterterence
s~~r0JV+
$OP'0,J'v...••
uesseucelveifllerierence
/./