PHYSICS 5B Lecture Notes - Lecture 18: Standing Wave
Interference of waves : the principle of superposition .
Considered two wave pulse
y,
=y,(xit )
yi Yzcxit )
A
A'into ~
t.it .
=
At=t .y=y ,
'Yz
÷
.
r
for two harmonic waves
withdifferehtyphases
Y,(x. t)=
,
=Y.
+Yz .
sin At
sin B=2sin (ICATBD cos (£(ATBD
Y(x,-4=2 Asin (I(2kx -2wt -0
,
-0.))cos I(02 .0,)
=2Asin (kx -wt -(0
,
+%))
cos
I(Ok .0,)
-
anew wave with same frequency but
with an amplitude
2A cos (I(02+0
.))
look at 2limits
when 02 =¢,
2A cos #(¢
,+02))=2A
or 0/0 =0< t¢.
=2T .nn=0,
I1
,
t2.
±3,...
2A cos (I(0
,
-Old -2A
⇒Constructive interference
in ahe
On the other hand
02 -0,
=180° (a)
2in cos CIC 02.0 ,))=0
or In general 00=2 #(n+I)n=o ,
±I,±2 . . ..
=>destructive interference
~µ
"'92
←
no wave
Document Summary
Interference of waves the principle of superposition . Considered two wave pulse y , y , ( xit ) yi. 2 sin ( icatbd cos ( ( atbd. 2 a sin ( kx a new wave wt ( 0 with same with. 0 cos frequency but an amplitude look at. 2a cos ( i ( 0 in a. 1 pull down s g cayseibmtion patterns due to the interference of two waves traveling in opposite direction. Let"s consider two harmonic waves (equal amplitude and frequency ) moving in opposite directions. Y , tyz the of ( kx yz = Y , ( wt ) equation ( kx ) ( os ( a ) The displacement ( kx ) ( us ( wt ) Standing traveling important ( kx ) = property anti nodes the nodes . there ate all the time not a. 2 he k= when you have an integer of half wavelength . it"s a node of nodes.
