Lesson 3 on Superposition

1. Lesson #3Lesson #3
Waves at a Boundary
Wave Superposition
Nelson Reference Pages:Nelson Reference Pages:
420 - 422, 414, 416 - 418420 - 422, 414, 416 - 418

2. Waves at a Boundary
 A boundary is createdA boundary is created
when there is a changewhen there is a change
in medium.in medium.
 At a boundary, the waveAt a boundary, the wave
will be partiallywill be partially
transmitted and partiallytransmitted and partially
reflected. We will look atreflected. We will look at
two cases:two cases:
1.1. A wave moving from aA wave moving from a
slow medium to a fastslow medium to a fast
medium.medium.
2.2. A wave moving from aA wave moving from a
fast medium to a slowfast medium to a slow
medium.medium. T r a n s m i t t e d W a v e
B o u n d a r y
D O M
D O M
R e f l e c t e d W a v e
B
F a s t M e d i u m S l o w M e d i u m
B o u n d a r y
D O M
A
T r a n s m it t e d W a v e
B o u n d a r y D O M
D O M
R e f l e c t e d W a v e
B
F a s t M e d iu mS l o w M e d iu m
B o u n d a r y
D O M
A

3. Special Cases
F r e e
E n d
D O M
A
W h a t h a p p e n s t o t h e
r e f l e c t e d w a v e ?
F r e e
E n d
B
T h e W a v e d o e s n o t in v e r t. W e
tr e a t th e fr e e e n d a s a fa s t
m e d iu m .
D O M
E n d A t t a c h e d
t o w a l lD O M
A
W h a t h a p p e n s t o t h e
r e f l e c t e d w a v e ?
Wall
B
T h e w a v e in v e r t s . W e t r e a t
t h e w a ll a s a s lo w m e d iu m .
Wall
D O M

4. Superposition of Waves
{Interference of Waves}
 What happens when
happens when two
waves of equal λ and
equal amplitude, but
opposite phase, meet
and completely overlap
each other?
 We see that the twoWe see that the two
waves cancel each otherwaves cancel each other
out. We call thisout. We call this
______________________
interference.interference.
D O M
D O M
D O MD O M
A s h o r t t im e la t e r t h e t w o
w a v e s h a v e p a s s e d t h r o u g h
e a c h o t h e r
D O M
F u lly o v e r la p p e d b o t h
t h e w a v e s c a n e l o u t .

5.  What happens if two
identical waves traveling in
opposite directions meet
and completely overlap?
 TheThe λλ does not change butdoes not change but
the amplitude of thethe amplitude of the
resulting wave is doubleresulting wave is double
that of the initial waves.that of the initial waves.
We call this __________We call this __________
interference.interference. And a short
time later both waves will
have again passed through
each other.
D O M D O M
D O M

6.  Superposition ofSuperposition of
waves oftenwaves often
involves ainvolves a
combination ofcombination of
destructive anddestructive and
constructiveconstructive
interference. Theinterference. The
top graph showstop graph shows
two waves oftwo waves of
equalequal λλ but verybut very
different shapes.different shapes.
 Draw the
resulting wave
form once the two
waves are fully
overlapped.
D O MU p
E q u il ib r iu m P o s it io n
D O M
U p
E q u il ib r iu m P o s it io n
D O M

7. Practice Questions
Nelson TB:Nelson TB:
 Page 419 #1 (top)Page 419 #1 (top)
 Page 419 (bottom) #1, 2a, bPage 419 (bottom) #1, 2a, b
 Page 442 #1, 37, 47Page 442 #1, 37, 47
 Workbook Pg 74, draw only the fully overlapped wave form.Workbook Pg 74, draw only the fully overlapped wave form.
Questions from the McGraw-Hill TB:
A transverse wave pulse is traveling down a spring with aA transverse wave pulse is traveling down a spring with a
speed of 2 m/s toward a second spring attached to itsspeed of 2 m/s toward a second spring attached to its
opposite end. Sketch what the springs would look like afteropposite end. Sketch what the springs would look like after
the pulse has passed into the second spring if the speed inthe pulse has passed into the second spring if the speed in
the second spring is:the second spring is:
a.a. 1 m/s.1 m/s.
b.b. 4/ms4/ms
c.c. 2/ms2/ms

8. Practice Questions - Continued
An upright wave pulse travels from a spring where itsAn upright wave pulse travels from a spring where its
speed isspeed is 20 cm/s into a second spring where itsinto a second spring where its
speed isspeed is 10 cm/s..
a.a. What happens to the frequency and wavelengthWhat happens to the frequency and wavelength
in the second spring?in the second spring?
b.b. Draw what the waves will look like 2 s after theDraw what the waves will look like 2 s after the
initial pulse reaches the boundary.initial pulse reaches the boundary.
c.c. Redo parts “a” and “b” if the wave pulse hadRedo parts “a” and “b” if the wave pulse had
started in thestarted in the 10 cm/s medium and moved intomedium and moved into
thethe 20 cm/s medium.medium.
Note: Assume a transverse wave form for all parts.