I D sinusoidal wavess
Io : total phase , pri .
dic
by π
Wavwe Cquahion ~
Mekinn GSILATES, krpuonagome Cousr y- y
.= A :
I
팬
A %]
2
펜± 만
=
2
[
: ]
sin [
ycuit 조여는
+
)
Y
Wa물는 PRDPAGATZoN oL nekirm -
=
uylly y
'
irlalemm yoyof-
yolis . -
- A
1: 따
, .
y : Io = π
ourput
.
ㅡ
Yc(t ). Posinbn . f medinmparticle at blmet &
Posibon scon medium- [ mJ
도시
Eiplalemwdivecion is :
i : y
cquilibrium
.
posiron
f mediun
Parniles Cm3 0
( ± mabtrs )
fomequ ilibrium
papandicoln
yco ) Y Displacemer modiuwParn ile
☆
Tronnese
tpopagatin ㅡ
돈paradldl (6
-
:
Ln)
K -
r
☆prapayabdn ㅡ Longivnbinul , .
아 ' at ( 1, )away 네
t ,
,
Input
ㅡ
tepudw A :
s o
siEe 아
-
fun
w l. 호 .c
e mat [ (l/ ) - ] Amplitude ,
matiml displacemet eqnl . n
/
.
yl t
y
. l
[ m3
variable t : time . f obzevvalion CSJ
sonrue
tpenkur T :
*
dPe
vi the Gime
reqnind for amplele e Y(1 ,rtT = yl, t2 y Es 7
cyle )
.
-
-
-
. a
1
/ : y .
, .
vaniable x :
positiononmediunf obsvvabon [ mJ
Soume & mediuml
denendew X: Wavelenguh ,
the
lengah fov n
complele
yale ,
:e -
ycpltx
.
(
t)
y
-
.
=
ycx 6) y ,
-
.
cm3
dpendur % phaseconslant
s o ( NoTtvlkal
deheminedconslauv offse ' ntopl
phase Io)w
Roe a Io radians phase
- -
. ]
: 와 E
,
sonce -
depadule f :
Frequency f 는 =
ES -
7 = cHz]
/
t: wave 1s
moving rte
t. LEFTF
*
excopbon fr thps fa
: waves teRIGHT The 또an
maviny
-
t . - →
SiANDNG wAves ONL.
…
propagmin Speed V
fMedian
λ
depadan
V = -
= > λ=
f
뉴지 와 =
vinfleuidby
changes L
midiun Welalel waM > -.massdasiy/ tesionfboce,
propagamronCe
vempooouveldashcivy
IM
pope6r@ ) m S
~
~
그 ea ) .
lsing Graphs of
.
ID wavess
zcD
y
yEousltmv CousoavvK
"
constavt
)
yi a
N N
constam t .m다 . V zlo
p~ N&
y '
가
,
급 ~~
많
v
i i.
넥
. "
o
. vi .. . fr . -
라 g, ~
- .
vepo
~
so ) ~
chouse sc
Poin , comparc ycasky
라 Chouse t
Choose Le Cr. )) poinv componc yl l 3
, y
poin
>
g
.
t.
for . each & for each L & xy
afdererin
1
.
, .
daterminedimechiong
compeve to bind direnion , dnmchvnkend
아 λ find F&T . hoan f 용 = Rend fL ,deramme
.
f 수&= * =
ff λ homsc-
T
read
.
Tfum
1
.
,
graph tgoaph ) ' Same ) wae
.
,Eame a yhex as i
A froameither
.
'
com
puhe D by plugging .
the foand valvess
vfoand
y
u=
xf
, 일 212 & 3 D waves
Dimensionalioyo waves
아
waves ID if propaganon di "echin rpresenved by uroW D
E
an : I1 5r
2
relal-ek
if Propagunion
Noo to
dechdn nmlsible
medinmns
space
E
nquig orosbhum in sancplance -
3 D if divedron
nequing mmlhiple arons all아 3 D' pace
propagalion M
Wavefuws &
Rays
Wavefronvs
Rays :
:
Linesfndicahhg
Lhe
)crests
( -
-
=A )ㅇ
6
y
propagavion
y
.
~ trong &Ly-
n
y
. =
-A
EvI
여피 여레설
0
-
l, ↓ S,
→
d
U
Wavefronrz d bs
Raysly fcuis3 am example . =→
oI
-
0 그따
중 오 Dwave :
]
mulrple rays allin
Iulensity
ca
2D
plauee
I α A2 ⇒ A 2 도
Fov a 3D amalogme )
imagive woauefronvs
2D cinaulearwavy α 차 distancefom as
spherical shells
:
I r s
souwce
inslecd .
.
,
3D
sphoicalmares: I α 금초
. Doppler effhewr
% f
]
obsenel N , source
g
F
②
Hearer .- - -
" @
문강 K
v IV는 +
강 . - → Vs
fr
~
Qw .licamnely
ohsevv to 2 t
ttIL
hvadiEavnyfhasomce
)
th버
울 f cf
if novuing /
: B .
GR . .
if
movingiwatawayhun
B
영
1 약,ok ha f 7t
온F
c
sovce . ,
'
(+)
.
Sf ,
X
(
고 F 2미로 D wawes
draw urrnhSourcefobseva locubons,andtracur setup
as tlhesame ' ray counecting
single linve ay above along thar
ray
Io : total phase , pri .
dic
by π
Wavwe Cquahion ~
Mekinn GSILATES, krpuonagome Cousr y- y
.= A :
I
팬
A %]
2
펜± 만
=
2
[
: ]
sin [
ycuit 조여는
+
)
Y
Wa물는 PRDPAGATZoN oL nekirm -
=
uylly y
'
irlalemm yoyof-
yolis . -
- A
1: 따
, .
y : Io = π
ourput
.
ㅡ
Yc(t ). Posinbn . f medinmparticle at blmet &
Posibon scon medium- [ mJ
도시
Eiplalemwdivecion is :
i : y
cquilibrium
.
posiron
f mediun
Parniles Cm3 0
( ± mabtrs )
fomequ ilibrium
papandicoln
yco ) Y Displacemer modiuwParn ile
☆
Tronnese
tpopagatin ㅡ
돈paradldl (6
-
:
Ln)
K -
r
☆prapayabdn ㅡ Longivnbinul , .
아 ' at ( 1, )away 네
t ,
,
Input
ㅡ
tepudw A :
s o
siEe 아
-
fun
w l. 호 .c
e mat [ (l/ ) - ] Amplitude ,
matiml displacemet eqnl . n
/
.
yl t
y
. l
[ m3
variable t : time . f obzevvalion CSJ
sonrue
tpenkur T :
*
dPe
vi the Gime
reqnind for amplele e Y(1 ,rtT = yl, t2 y Es 7
cyle )
.
-
-
-
. a
1
/ : y .
, .
vaniable x :
positiononmediunf obsvvabon [ mJ
Soume & mediuml
denendew X: Wavelenguh ,
the
lengah fov n
complele
yale ,
:e -
ycpltx
.
(
t)
y
-
.
=
ycx 6) y ,
-
.
cm3
dpendur % phaseconslant
s o ( NoTtvlkal
deheminedconslauv offse ' ntopl
phase Io)w
Roe a Io radians phase
- -
. ]
: 와 E
,
sonce -
depadule f :
Frequency f 는 =
ES -
7 = cHz]
/
t: wave 1s
moving rte
t. LEFTF
*
excopbon fr thps fa
: waves teRIGHT The 또an
maviny
-
t . - →
SiANDNG wAves ONL.
…
propagmin Speed V
fMedian
λ
depadan
V = -
= > λ=
f
뉴지 와 =
vinfleuidby
changes L
midiun Welalel waM > -.massdasiy/ tesionfboce,
propagamronCe
vempooouveldashcivy
IM
pope6r@ ) m S
~
~
그 ea ) .
lsing Graphs of
.
ID wavess
zcD
y
yEousltmv CousoavvK
"
constavt
)
yi a
N N
constam t .m다 . V zlo
p~ N&
y '
가
,
급 ~~
많
v
i i.
넥
. "
o
. vi .. . fr . -
라 g, ~
- .
vepo
~
so ) ~
chouse sc
Poin , comparc ycasky
라 Chouse t
Choose Le Cr. )) poinv componc yl l 3
, y
poin
>
g
.
t.
for . each & for each L & xy
afdererin
1
.
, .
daterminedimechiong
compeve to bind direnion , dnmchvnkend
아 λ find F&T . hoan f 용 = Rend fL ,deramme
.
f 수&= * =
ff λ homsc-
T
read
.
Tfum
1
.
,
graph tgoaph ) ' Same ) wae
.
,Eame a yhex as i
A froameither
.
'
com
puhe D by plugging .
the foand valvess
vfoand
y
u=
xf
, 일 212 & 3 D waves
Dimensionalioyo waves
아
waves ID if propaganon di "echin rpresenved by uroW D
E
an : I1 5r
2
relal-ek
if Propagunion
Noo to
dechdn nmlsible
medinmns
space
E
nquig orosbhum in sancplance -
3 D if divedron
nequing mmlhiple arons all아 3 D' pace
propagalion M
Wavefuws &
Rays
Wavefronvs
Rays :
:
Linesfndicahhg
Lhe
)crests
( -
-
=A )ㅇ
6
y
propagavion
y
.
~ trong &Ly-
n
y
. =
-A
EvI
여피 여레설
0
-
l, ↓ S,
→
d
U
Wavefronrz d bs
Raysly fcuis3 am example . =→
oI
-
0 그따
중 오 Dwave :
]
mulrple rays allin
Iulensity
ca
2D
plauee
I α A2 ⇒ A 2 도
Fov a 3D amalogme )
imagive woauefronvs
2D cinaulearwavy α 차 distancefom as
spherical shells
:
I r s
souwce
inslecd .
.
,
3D
sphoicalmares: I α 금초
. Doppler effhewr
% f
]
obsenel N , source
g
F
②
Hearer .- - -
" @
문강 K
v IV는 +
강 . - → Vs
fr
~
Qw .licamnely
ohsevv to 2 t
ttIL
hvadiEavnyfhasomce
)
th버
울 f cf
if novuing /
: B .
GR . .
if
movingiwatawayhun
B
영
1 약,ok ha f 7t
온F
c
sovce . ,
'
(+)
.
Sf ,
X
(
고 F 2미로 D wawes
draw urrnhSourcefobseva locubons,andtracur setup
as tlhesame ' ray counecting
single linve ay above along thar
ray
