8
r-> t- ,52 ri. 6 / 3,+r',+*;h"n / ----"----.i: \ \ \ \ ' k',n"li- <'4 8*Ji.["^"^n ; Jb,^,< - lsl"-e''^a wi (-/.** x, at 7a,"A',..tat- t). kP= :!:k - 2_ Wtss_^ k^, -E;A(try (.1." ^-tt t +t p^^t;.J*,j- tl:'"'-'-:tf. P, o D - o l,n lu.-v -"1 ,t) I I - I o \ ''r -' Pr= Po C(*rx*6,t) ; n r,. r: rt+ rz = t'oy.n (k,c1' *^* krfu:- o-cs>( +E) P=2P"6,f (r,* r) * * (a, + u,') e'/ x. -2'l .| ' r l, . I clD / (Kt -kLJ X tc,t) + t-(t,*-^"r)f /* ( ^.-8\ 7'-B'l,r;l; --L - N41 : IAI -wz 2

Lec15 Sept7 Beats GHroupVelocity

Embed Size (px)

DESCRIPTION

k

Citation preview

Page 1: Lec15 Sept7 Beats GHroupVelocity

r-> t-,52 ri. 6

/3,+r',+*;h"n /----"----.i:

\\\

\

' k',n"li-<'48*Ji.["^"^n ; Jb,^,< - lsl"-e''^a wi(-/.** x, at 7a,"A',..tat- t).

kP=

: ! :k -2_

Wtss_^ k^, -E;A(try(.1." ̂ -tt t +t p^^t;.J*,j-

tl:'"'-'-:tf.

P,

o

D - o l ,n lu . -v - "1 , t )I I - I o \ ' ' r - '

Pr= Po C(*rx*6,t)

; n r,.r : r t+ rz = t 'oy.n (k ,c1 '

*^* krfu:- o-cs>( +E)

P=2P"6,f (r,* r) * * (a, + u,') e'/ x.-2 ' l.|

' r l , . Ic lD / (K t - kLJ X

tc,t) + t-(t,*-^"r)f

/* ( ^.-8\

7'-B' l,r;l;

--L -

N 4 1 : IA I -wz

2

Page 2: Lec15 Sept7 Beats GHroupVelocity

P=2Foa.(urx- 3t) &-(xrx- +b

L t-.2-.1 .

P- p/t o

Vka ; fL^

(^(Lrx - upt) Po/ = 2Po c" (\a- wr)

(t+y 1."7"..*fl.) "-,.A ft- 4'-.,-Fhl'"-)o , .,U*^fr^ / ^ /-t 'r- / , , I

A-a P> = 2 / /6 l \D I kqV - Qst )

Tl x-.--,-t=--+Pv- d'--c'l- + l.^tn L^i'""a- tu-:.'-^-/+ -

* ( kp xo - ccrt). L- ( kS a- - KSt)

'L-

-T-^* + 4 s lrt'4 t-,;lt' t-7'r-1 /rp.

.1YaD vaj, bn lr

rL /-2.*^Z '+ "^--A^J^J-',5

nn"J^7*bez.j-

* w- t \'l1 cL

= 2l ' lq =-P t lA,-t,o')\- L-J

-- hl-N.

Page 3: Lec15 Sept7 Beats GHroupVelocity

A,(h qot- 4 C',.-+ V"L-;4

Fh^2:.-V"Jp-lt + n- /"-'''Jla'-l- l'"*'

ca^' 6<'

e6.L c"-t-L;d ,lr't-,- t'.^ vADc;5 + rE^ t- a'n t',t-'o''ti'<-

k>c,.teo. tt;-t- t'-'.hh.E lT^ of^^! s+ tL Pl"^-"'e

vetE<:lJ + tf-- h at, r,,.o-;- n*L *,u -

s* t-t'o-

It^ /'rr,r-)+"- l- ou ""t h oo tL- 3 o^ e v'-1"' c;5

C->-r--t: vJ'a ;(t t" fl'^ v"t'^;Q d- \d; J TL pu'; ho-'|-----.....----

S on.,,*i',-,-.,... G-"'l'''--h"<' i^I;'l''-^tz P"'ff; *

f||^ e.,-,r a-|,.F '|''r-1^''\rel ' 6 ",*^"-tt1,i,,xr-^nl dtff<'."jt1

CD AX e* '+ ^f- (c* LP

5c7.- f ,rk"^ + ha'- ''' 'n*i''

&t'^'z

** r*GE 6\;u Ll- -1"..-t2-t-. e.a ,,,b*q +tr- c'-,,;et'

gec* lT- P "-"-)<^ % ff- L<n;n'- f..**--l + ",- t; h"^^

dn- 1-V-. p d-a- o'- a tT.-,J a-PP"-.^ 4- u*li

il- 4.L- Ih.- b*+. ^.-f ll'-''a'ql, ',! c-^'l V6';s,t^ rfL

G-[_ tt \-rt+

wie,.az/ 'a.4

4

l"fz"r44 cI a4^ fF r^4Lt r

Page 4: Lec15 Sept7 Beats GHroupVelocity

( a l' 1 J- 11- 1z,.u:sh-

e'*f?;'"^i*l'

. L L . II h- trr^s

a\^ t"t"", ,,--,o^ """J

e, <--r"---<1z4lt" 3 F"-4OlLan a,-4 l-,,-w- ^

J- a*--^+-^,Yrea*!;e Eho d" ct*.a'f: azd

c.\n'fl a areH fl,.^ 2I-+,'s"-T

I^y-t h^r u

V^,y"-,"tv lk"*?t*

+t^Jc,r-2,.,,-<'lp--a k' tr VL^ t'--'z

J*7" *n s1 fia

6 4-\,o tr P+* t.crnc cf'-"rr'-'. .-6'c Pr.ar L lf ho'-

"{;4 S L^+.-1, t-'?-t-p v* QatA

! l

lt't -.k*-:,. . fr.^ alj-.h'+^ *t"4 "!'

^ k c-^,!; J.d L-t^-,-z p aok4' '1'^--l- ("'

/^.1D 4t- ,vlu*L tL1 ,rf h aa t*oz-;c t'r<"v:

7L! -,-z^A','^.'1 Vik-15

R1 7r; k|LN€Pc'.'lL '- T l

t t* t*-hl-L* N^^A

nY

7*""Y

e)

lF^ vJn;fi

v"L;q 6+

H o* f+.^nb w-1 e-,u/:,^-u\L *,

Ytr^,"'*a,.LL

'I; f''.,-''"-t ,-*/t z"''L oFn \ tlF;U^6 a

tLJ-; U 1','"'"t

l,.D 17 4 L.st e,*-'li P"U'

lf^ t. --+ .r,^f" .- JL.^ fl'."1

"f x-.*1"-5n. '

a-217;.1- fL +.-'^,"-;.s,' 4'c lE'..-t' [r^ Lz* d^a^ppeo"'

d.u * FL'4'."D1"'',,".\s \- '.z"-( 1"7-n-"-k c- P^^r;J-h

,ot^,'-Jl;r,- a",-'l 'z'Lt>'71.- ''''o'^''"' tf a-E'4-7 or^*a

l*f*-"t a; {fe^'^ct<'

@.4 k^

Page 5: Lec15 Sept7 Beats GHroupVelocity

V: ? . , ) :

Vp = Ph ^"-z

vq . C n.*u

ca lr.VaLo iLL -

.J-

UJa;14 :

CJ r t Hz

kt + kz

dt 'N '

k j - k t

( * * ,o ' )n^Ko

6Jg

kg( t dn

L1

R,

R, -t^L; Lnf ,oon^ u.t"-=a:)(t

d (t<vo1 = vs+ R(!k\dk ' 'dk, /

Va= d6 -J , ,

-

* a,,K

N"dr,.)- dvo ^ J l . \ -' - I - J -

d,k " tK \ ' t " /*. / anl

* \ VrJ

Vp- R g_,....= ( dnta^\n" v9z \ , /

,P

( t t rJ__ vP il r_ _l! t7!\l' L Y1 \a l l< / l

v1 .vp-

- "P-

kc

t' - "P_;

/ dn\l - t ?x d+< "/

I dn\\ {xl

I

zfrxn

"7t

,9* +--,."- + nY : aFf,t a"-d ak=-("n/,s')dl

dnT;.6

,c

/azu\\ "in/,r+ ) ( d,+)l

Y\ \ ot '1 ')v3 = vPttfl

Page 6: Lec15 Sept7 Beats GHroupVelocity

Pt:ft!-t^tf- *+ ',. tI- .+vr

t"^ +h'b,7

YI^J- 6".t ox a--*7le +

9-- op [;.. :.-t-

€r)))

ois p tn"-+E-. to t"

W:"+:tY:e:;

Prz-r.Szr

e+:a:: /s lE' fh"non^.'1aa ta ^4rA

( p^* v"u;Q * f,f v"t';fr) "b"-'4(* l-"2.*^V ) ' lt'/'a;o l" ̂ 'n:'5

\ - { l J

v (A) 6"* t^"11 )'t = {(r)l * n (A)

fel>'<..1-'u'<- T-4o""'

a "IL. l.,,qr*Lj \c'w iv^

C--.+-.-v fu".-.O "-@

lh^ VeLa.i'

.<'. TL^

1t 'd- +

€ \ t/ , {11 At

^ I "U'^-* f"F u94il tI

' Ttf < lzva it'= w-tli a'n^^^ l"s ir.rLJ I l}€Y- tr;'l"^'r'u' s-^'- I Wlt *ru

-5. =TT - r) ,A vc-,- - ) ,-- | r*ttt-"'Ivgr

' tm^"+ - v

- ^ * -. I r : !-^- 7

j"ir}"{-,-"-- -- }--** a T*, L^..^,-)A,-qlr_

. . . \7t, : ] ts..)

Page 7: Lec15 Sept7 Beats GHroupVelocity

s^; Y

\rLll l"A^t h^L^k-Lr ̂ ^*1'-n lL

/.fc.lJ /r1 = 9;icY-*< l-e tl

t -I

/ r'A_D I tw1 | e-tr-.-.11 o'n /- a^ft",,-^t-

//.r"^L toI .7 e<:l-><tv-'

a^-t->{ A.;

44^

.- A+

&, B +. b- dzlLo,'4"dt _ .

2* Petu hr'*^a-t bi "a

f*x y-"4"-______1!

( h >Li- +m ., d,^ n b zFn Ln'r1

\ oor.r,--- (,,',- 7"---+y f tnn.l[al-' pszt-,- A*"4-

p t J=.!

+**tr tr^ Lt-^e.

!< .n()r-.) < /h('.ry"-rr-) ( n (AbL.-)Cr;Att*-+)

d.rLJ-l--za '*

u. ''v'wu:v r't'"-a-'! P "1-^"'r:- <o.

cl.,.1

2 aaD pA a,,t-L-1,La cl,i < peri"_ d- >o.1J

c 3e-*"-,1;.r,u ttt"p,"^--,-*" -t- L^-Il.-d'/>

".-,7t'^.,' Zr- '11-

ct a-.'+1,^-7 lr

^ Ulf 4"-,f 4,-----1," /.I

cIo c,-o a,.zz d) s p 2,,---"

; c- rfi Co-| Ft'L ptoI

r Et sp e^--ri- G-'- f,t{ ;

1*t vt-a; t 1

d-pp,'^ ; (en) + z,^-ya<.2;Vt /r^*ole J-f 9r,-^rf, v*t-;f

3"- ryh-.^A F-'L-lr.. /

llLk;4 otr cA>'v---,<,1.>7 D[s7,,-LS c'...' c=e dL Di s t" n''"a,.,r-" \ ,n , -' =ffi+;:Z:_

Jrf e^44- .'.n',Lutro *

S"^a n; n^4t<f*."- C-YA a

. L

o.I ̂ 4!11 L-ft,"\<qlt

^,1-s o , n^7 t-^ /o-.a

Page 8: Lec15 Sept7 Beats GHroupVelocity

(i) \/g

(i) vu

li ii) vs

Vk"-p- ^1 A-{ 3 ta-aa .

r

r

r

.''-Lnnnot

4T >"da )

^l o da'sl€,v-.-.ri^ * =

" a.o Jn Va. cu qm ,

N c- z^"..{. a-i r>p<t.-;,o-n dn < O .alA

a, n e vv,*L6-,,<a & n-h.r^,-n 4n ,,_' n'"Otn t^a i

dn <o cvd^

tA" 7- t\^ CqAz (n) L{L^L

F -l-a-ci;v<, t'^^an t

, hc,\-L.^/21- e7r,\ a-4 a- -l=",^ "l'^r- "l ,{-q^.'."^2.

'f;"',--1.-.f d-'r*",^l (tt^-) a,*p".-*IL ,A-J

^G.;liE.^

a. \ p<^-

V-l"o;Q

L b'e-

J- t.,..."_ o .f"-+ 5 L'y^'t-

( ,:!:t_ !:ty::::) lL^^ E-

61 f,e-c^ ,n ( ^ d 6+.1-

aa- A"'\L"LL/

/&o l,--f**Z G-a) a-1.".,"'-t

o d* pr,^'s,n .

t^ [tri"] T ruatia.

?ha'.'- V"fn cr€

Cc",, lL^ phaar- Vclo "Jb

(r^ lL ffi V-tsc;q-

5,10^h.,.;O v'la;Q I

k&A- o,\r- oUS 7""v+; r'-<-

ets c"4 n^ .>7*a

an co.n-A "t* ,.f 4.d"/ "Sr+?

+ brr'?

2, *^la d) s P <,.,-,.-i v-t rr\aj)' 4 ,1I L

rIT:

/A7ELf(

4'

01.

n.