1. ______________________occurs when ____________ waves
(or pulses) are in the same ____________ at the same
______________.
 Interference is a property of______________.
The waves can be:
_________________
________________
________________________________________
Interference
2 or more
medium
time
waves
sound
light
water
electrons or other particles
Principle of ______________________:
The results of interference are found by
adding the ________________________ of all the waves at ____________________ in the medium.
Superposition
displacements
every point

3. Ex 1: The results of superposition can be found by
adding the _________________ of each part of the pulse
displacements +1 -2
Shown here at the
moment that they
______________ . +1
overlap -2
The ____________________ of these two pulses can be
found be ________________ their two _______________ :
superposition
adding
displacements
resultant
superpostion -1

4. Show below as
separate pulses:
Shown here
separately as
they overlap:
The resultant
superposition
will look like:
Ex 2:
Ex 3:
Ex 4:

5. Ex. 1: 2 sine waves, same f, _______________, unequal A’s
in phase
wave 1: A1
wave 2: A2
The superposition:
Movies:
The Core
and The
Perfect
Storm
A = A1+ A2
Constructive
______________ interference – the resultant _______________
have a ____________ magnitude because both waves move
the medium in the __________ direction everywhere.
displacements
larger
same

6. In the oceans, extreme __________________ interference
can result in very rare _____________ waves.
constructive
rogue
damage inflicted by
a rogue wave.

7. 21 July 2004 This rare photo of a rogue wave was taken by first mate Philippe Lijour aboard the supertanker Esso Languedoc, during a storm off Durban in South Africa in The mast seen starboard in the photo stands 25 metres above mean sea level. The wave approached the ship from behind before breaking over the deck, but in this case caused only minor damage. The mean wave height at the time was between 5-10 metres.

8. The Draupner wave is the name of the first rogue wave to be detected by a measuring instrument, occurring at the Draupner oil platform in the North Sea off the coast of Norway on January 1, Prior to this measurement, such freak waves were known to exist only through anecdotal evidence provided by those who had encountered them at sea.
Minor damage was inflicted on the platform during this event, confirming the validity of the reading made by a downwards-pointing laser sensor. In an area with significant wave height of approximately 12m, a freak wave with a peak elevation of 18.5m (maximum wave height 30m) occurred. Engineer Paul Taylor estimated the Draupner wave was a one in 200,000 wave.

9. Ex. 2: Same f, 1800 ______________________, unequal A’s
out of phase
l/2
wave 1: A1
wave 2: A2
shifted ___
or _______
l/2
1800
The superposition:
A = A1- A2
Destructive
______________ interference – the resultant _______________
have a ____________ magnitude because both waves move
the medium in the __________ direction everywhere.
displacements
smaller
opposite

10. Ex. 3: 2 waves, same f, 1800 out of phase, ___________A’s
equal
wave 1: A1 A2
wave 2:
The superposition:
A = 0
_________________interference is _______________________
 the resultant A ________________ everywhere
The destructive
complete or total
is zero

11. C D C D slightly different
Ex 4: Same A, but at __________________________ f’s
constr.
total
destr.
constr.
total
destr. C D C D

12. _____________are a variation in _______________ caused by
the _____________________ of 2 waves whose frequencies
____ and _____ are ________, but ________________ :
Beats
amplitude
interference f1
close f2
not equal
envelope
The amplitude of the envelope varies at the beat frequency:
beat frequency =
|f1 – f2|

13. Ex. A 440-Hz tuning fork is struck while a string
vibrates at 443 Hz. What will be the beat f?
beat frequency =
|440 Hz – 443 Hz|
|f1 – f2| =
= |-3Hz| = 3Hz
Ex. A 256-Hz tuning fork is struck while a string
vibrates. If beats occur at 2 Hz, what is the frequency
of the string?
beat frequency = |f1 – f2|
2 Hz =|256 Hz – x Hz|
x = 254 Hz OR Hz

14. Ex 5: Waves X and Y exist in the same medium at the same time.B C D E F G H I J K +4
wave X -4 +4
wave Y -4
Draw the interference of X and Y at points A-H: +8 +4 C C D D C -4 -8
Label each of the above points as constructive (C) or destructive (D)

15. Ex. 6: _____________________ occur as a result of the
___________________________ of ___________ waves that
have ___________________ frequency and _________________
amplitude & are traveling in __________________ directions
in ___________________ medium.
Standing waves
interference
two
the same
the same
opposite
the same
Ex: Typical patterns:
Although it appears to be _______________that
is _____________________ , it is actually made up of
_____________ that are interfering _____________________
and _____________________ at different points.
one wave
standing still
constructively
two waves
destructively

16. Each of these different patterns of possible standing
waves is called a ___________ :
mode
mode 1: 2
___ nodes
___ antinodes 1
wavelength
mode 2:
___ nodes
___ antinodes 3 2
increasing__________
increasing__________
mode 3: 4
___ nodes
___ antinodes
frequency 3
________________ - no displacement of medium;
caused by ______________________ interference
__________________ - maximum displacement of medium;
= node
destructive
= antinode
constructive

17. Solve the 2 examples below for standing waves.
Ex: If L = 4.0 m, how long is the wavelength? L
L = l/2
4.0 m = l/2
8.0 m = l
Ex: If L = 5.0 m, how long is the wavelength?
L = 1.5l
5.0 m = 1.5l
3.3 m = l L

18. discrete
Standing waves only occur at certain ___________
(special) ___________________ . These are determined by
the ______________________ properties of the system,
such as _______________, __________ , __________,
and the conditions at the ____________________ , also
known as the _________________ conditions.
frequencies
physical
material
size
shape
ends or edges
boundary
During ___________________, an object is undergoing
standing waves that have a large ___________________
The special frequency at which this occurs is called
the _________________frequency of the object.
resonance
amplitude
natural

19. Ex: On air tube open_____________________, or a string
tied down ________________:
at both ends
at both ends
mode 1: ________________
fundamental
mode 2:
mode 3:
Ex: An air tube closed __________________or a string tied
___________________ :
at one end
at one end only
fundamental
mode 1: ________________
mode 2:
mode 3:
In both examples above, the frequencies of all modes are
_________________________ of the ________________ mode.
fundamental
integer multiples

20. Ex. Drum vibrations:
In this case, the frequencies of all modes are NOT
_________________________ of the ________________ mode.
integer multiples
fundamental

21. Ex: The electron in an atom acts like a wave!
The electron is wrapped around
a nucleus.
The electron must interfere with
itself constructively
This is only possible with an integer number of electron wavelengths in an orbit.
DeBroglie
nucleus
electron

22. This explains why electrons are only allowed to “orbit” at certain discrete distances from the nucleus.

23. As a result, the electrons in an atom can only have certain discrete energies.

24. And that is why spectra have discrete colors: