Wave Phenomena
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2.
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Wave Fronts
The Doppler Effect
Interference of Waves
Standing Waves
Resonance
Diffraction
Light Polarization
Wave Fronts
A wave front is the curve
of all adjacent points on a
wave that are in phase.
Doppler Effect
Lower frequency,
longer λ
Higher frequency, short λ
Moving source
The Doppler effect can be described as the effect produced by a
moving source of waves, the observer, or both –
an apparent upward shift in frequency if the observers and the
source is approaching each other
an apparent downward shift in frequency if the observers and
the source is moving away from each other.
Relative motion creates an apparent change in frequency.
Explaining the Doppler Effect
• The Doppler effect is observed because the distance between the
source of sound and the observer is changing.
• If the source and the observer are approaching each other, then
the distance is decreasing and the waves is compressed into the
smaller distance. The observer perceives sound waves reaching
him or her at a more frequent rate (_______
pitch).
high
• If the source and the observer are moving apart, then the distance
is increasing. the waves can be spread apart; the observer
perceives sound waves reaching him or her at a less frequent rate
low
(____pitch).
• It is important to note that both the speed and the
frequency of the source does not change.
• The Doppler effect can be observed for any type of wave
- water wave, sound wave, light wave, etc.
• car horn - coming and going
• As the car approached with its siren blasting, the pitch of
the siren sound (a measure of the siren's frequency) was
high; and then suddenly after the car passed by, the pitch
of the siren sound was low. That was the Doppler effect an apparent shift in frequency for a sound wave produced
by a moving source.
Shock Waves and Sonic Booms
• If a moving source of sound moves at the same speed as
sound or faster than sound, then shock waves will be
created and sonic boom is heard.
• http://edweb.sdsu.edu/doppler/elab/elab1.htm
..\..\RealPlayer Downloads\Plane break sound barrier - sonic boom.flv
Blue shift and red shift
The human eye perceives light waves of different frequencies as
differences in color. The lowest frequency we can see is red and the
highest frequency we can see is blue-violet.
Due to Doppler effect, the apparent color of an approaching light
source is shifted toward the blue end of the spectrum, while that of
a receding source is shifted toward the red end.
Applications of the Doppler Effect
• Police work – the speed of a car is determined by a radar system.
– when a car is at rest, the sent out frequency is the same as
received frequency.
– If the car is moving toward the source of radar, the reflected
waves have higher frequency, the greater the car’s speed, the
greater the Doppler shift in frequency.
– If the car is moving away from the source of radar, the reflected
waves have lower frequency.
• Weather stations – Doppler radars are used to determine the
location and intensity of precipitation as well as directions and speed
of the winds blowing around rain drops.
Example
1. A police officer's stationary radar device
indicates that the frequency of the radar
wave reflected from an automobile is less
than the frequency emitted by the radar
device. This indicates that the automobile is
a. moving toward the police officer
b. moving away from the police officer
c. not moving
example
2. The diagram shows radar waves being emitted from a
stationary police car and reflected by a moving car back to
the police car. The difference in apparent frequency
between the incident and reflected rays is an example of
a. constructive interference
b. refraction
c. the Doppler effect
d. total internal reflection
3.
As observed from the Earth, the light from a star is shifted
toward lower frequencies. This is an indication that the
distance between the Earth and the star is
a. decreasing
b. increasing
c. Constant
4. Suppose you are standing on the passenger-loading platform
of the commuter railway line. As the commuter train
approaches the station, what pitch or changes in pitch will
you perceive as the train approaches you on the loading
platform?
Wave Interference
• A phenomenon which occurs when two WAVES MEET while
traveling along the same medium.
• The interference of waves causes the medium to take on a
shape which results from the SUPERPOSITION of the two
individual waves.
The two waves meet,
produce a net resulting
shape of the medium,
and then CONTINUE on
doing what they were
doing before the
interference.
Constructive interference
• Occurs where the two interfering waves have a displacement in
the same direction. The result is a LARGER AMPLITUDE.
MAXIMUM constructive
interference occurs when the
waves are in PHASE (phase
difference is 0o or 360o) and
crest superposes on crest or
trough on trough.
1 unit
2 units
The point of maximum displacement
of a medium when two waves are
interacting is called an ANTI-NODE.
-1 unit
-2 units
Destructive interference
• Occurs where the two interfering waves have a displacement in
the opposite direction. Destructive interferences result a
SMALLER amplitude.
• Maximum destructive interference occurs when two waves of
equal frequency and amplitude whose phase difference is 180o
or ½ λ meet at a point. Maximum destructive interference
results in the formation of NODES. Which are regions of ZERO
displacement of the medium
Constructive
Destructive
principle of superposition
• When two waves interfere, the resulting displacement
of the medium at any location is the ALGEBRAIC SUM of
the displacements of the individual waves at that same
location.
Displacement of Pulse
1
Displacement of Pulse
2
=
Resulting
Displacement
+1
+1
=
+2
-1
-1
=
-2
+1
-1
=
0
+1
-2
=
-1
Two sources in phase in the same medium
• ..\..\RealPlayer Downloads\Wave Motion Interference YouTube.flv
Constructive interference: Point A, B are anti-nodes
Destructive interference: Point C, D, E, F are nodes
crests
troughs
Nodal lines
• Although both sources are repeatedly producing waves which
move across the medium, a stable pattern is set up. The
regions of constructive interference do not move, nor do the
regions of destructive interference.
• These motionless regions have a pattern which can be
measured. These measurements can be used to calculate the
wavelength of the waves which are producing the pattern. In
this way one can find the wavelength of a moving wave.
Example #1
Determine type of interference of each section as constructive or destructive.
III
I
II
Example #2
Apply superposition principle to determine result of interference by sketch the
resultant wave.
Example
1.
a.
b.
2.
Two waves having the same amplitude and the same
frequency pass simultaneously through a uniform
medium. Maximum destructive interference occurs when
the phase difference between the two waves is
0°
c. 90°
180°
d. 360°
The diagram shows two pulses, each of length, traveling toward each other at
equal speed in a rope. Which diagram below best represents the shape of the
rope when both pulses are in region AB?
a.
b.
c.
d.
3.
Maximum constructive interference between two waves of
the same frequency could occur when their phase difference
is
a. 1λ
b. ¼ λ
c. ½ λ
d. 1 ½ λ
4.
The diagram below represents shallow water waves of wavelength λ passing through
two small openings, A and B, in a barrier. How much longer is the length of path AP
than the length of path BP?
a. 1λ b. 2λ
c. 3λ
d. 4λ
8. Determine the interference pattern
Sound Interference and Beats
• When sound waves meet, interference occurs. The interference
causes the medium to take on a shape which results from the net
effect of the two individual waves upon the particles of the
medium.
• Constructive interference occurs if compression meets up with
compression and rarefaction meets up with rarefaction (in phase).
Constructive interferences produce a anti-node, results a louder
sound.
• Destructive interference occurs if compression of one wave meets
the rarefaction of another wave (out of phase). Destructive
interference produce a node, results no sound at all. It is used in
noise reduction systems.
• ..\..\sound_en.jar
Musical Beats
• When sound waves with slightly different frequencies traveling in
the same direction, the effect of interference is perceived as a
variation in loudness, called beats.
• Note: the diagrams represents a sound wave by a sine wave.
Because the variations in pressure with time take on the
pattern of a sine wave. Sound is not a transverse wave,
sound is a longitudinal wave.
Beat frequency
• The beat frequency refers to the number of beats per second.
For example, if two complete cycles of high and low volumes
are heard every second, the beat frequency is 2 Hz. The beat
frequency equals to the difference in frequencies of the two
interfering notes.
• For example, if two sound waves with frequencies of 256 Hz
and 254 Hz are played simultaneously, a beat frequency of 2
Hz will be detected.
• http://www.phys.unsw.edu.au/jw/beats.html#sounds
• http://www.acoustics.salford.ac.uk/feschools/waves/super3.ht
m#beats
Interference of monochromatic light waves
• When two same color light sources meet while traveling along the
same medium, Bright and dark bands appear on the screen as a
result of interference.
• Constructive interference results in bright band, produced by two
interfering waves have a displacement in the same direction.
• Destructive interference results in dark band, produced by two
interfering waves have a displacement in the opposite direction.
Thin Film Interference
• Another example of light interference is colorful soap bubbles
or streaks of color in a thin film of oil resting on a driveway.
Standing Waves
• Standing wave is A WAVE PATTERN that results when two waves of
the SAME frequency, wavelength, and amplitude travel in
OPPOSITE DIRECTIONS and interfere.
• A standing wave pattern is formed as the result of the perfectly
timed interference of two waves passing through the same medium.
A standing wave is NOT actually A WAVE; rather it is the
PATTERN.
Nodes and anti-nodes in a standing wave
Nodes: the points of ZERO displacement of the resultant wave
Antinotes: the points of MAXIMUM displacement of a medium
The distance between two successive nodes is ½ λ
standingWaveDiagrams1/StandingWaveDiagrams1.html
1st harmonic
• Standing wave patterns are only
created within the medium at
SPECIFIC FREQUENCIES OF
VIBRATION. These frequencies
are known as HARMONICS.
• ..\..\RealPlayer
Downloads\Standing Wave on a
String.flv
• Standing waves can be created for
both transverse and longitudinal
waves.
• pipe-waves.html
2nd harmonic
3rd harmonic
Harmonic
# of
Nodes
# of Antinodes
1st
2
1
Pattern
λ
2L
2nd
L
3rd
2/3 L
4th
½L
5th
2/5 L
6th
1/3 L
nth
n+1
n
--
Standing waves in water
• Standing waves in water are produced most
often by periodic water waves REFLECTING
FROM A BARRIER.
Example #1
•
What is the number of nodes and antinodes
in the standing wave shown in the
diagram?
8 nodes
7 antinodes
Example #2
The diagram represents a wave moving toward the
right.
Which wave shown below could produce a standing
wave with the original wave?
1
2
3
4
Example #3
•
1.
2.
3.
4.
Two waves traveling in the same medium and
having the same wavelength (λ) interfere to create
a standing wave. What is the distance between two
consecutive nodes on this standing wave?
λ
½λ
¼λ
¾λ
Forced vibration and resonance
Natural Frequency
• Nearly all objects, when hit or struck or plucked or strummed
or somehow disturbed, will vibrate. The frequency or
frequencies at which an object tends to vibrate with when
disturbed is known as the natural frequency of the object.
..\..\RealPlayer Downloads\Natural Frequency.flv
Forced vibration
• If you were to take a guitar string and pluck it, you would hear
a small sound; On the other hand, if the string is attached to
the sound box of the guitar and you pluck it, the sound
produced would be much louder.
• This is because the vibrating string force the bridge of the
guitar to vibrate, and the bridge force the sound box to vibrate
and the sound box forces air particles inside the box to vibrate.
This forced vibrations are called sympathetic vibrations.
• The tendency of one object to force another adjoining or
interconnected object into vibratio is referred to as a forced
vibration. The forced vibration causes an increase in the
amplitude and thus loudness of the sound.
Vibration at natural frequency
produces resonance
• Resonance - when one object vibrating at the
same natural frequency of a second object
forces that second object into vibration.
Condition for resonance:
1. when the frequency of the periodic force
equals to the natural frequency of the object
it applied to.
2. The amplitude of the original wave is big
enough.
Examples of resonance
• A non vibrating tuning fork, having a natural
frequency of 256 Hz, will resonate when a vibrating
tuning fork with a natural frequency of 256 Hz is
brought near it.
• It is possible for an opera singer to Shattering a glass
by maintaining a note with a frequency equal to the
natural frequency of the glass.
• Collapse of the Tacoma Narrows Bridge due to high
wind induced resonance.
• Pushing a child on the swing with the same rhythm as
the swing will make the swing go higher.
Blue Skies
• The two most common types of matter present in the
atmosphere are gaseous nitrogen and oxygen. These particles
are most effective in _____________________________
portions of the visible light spectrum such as blue and violet
light. This scattering process involves the absorption of a light
wave by an atom followed by reemission of a light wave in a
variety of directions.
• All high frequency light are scattered. However, our eyes are
more sensitive to light with blue frequencies. Thus, we view
the skies as being blue in color.
What Makes a Red Sunset?
•
1.
There are two reasons:
As the Sun gets lower in the sky, its light is passing through
more of the atmosphere to reach you. Even
________________________________, allowing the reds
and yellows to pass straight through to your eyes.
2. The sky appears red because ________
______________________, pollution, and water
vapor in the atmosphere reflect and scatter more
of the reds and yellows.
In conclusion
• In conclusion, resonance occurs when two
interconnected objects share the same vibrational
frequency. When one of the objects is vibrating, it
forces the second object into vibrational motion. The
result is a large vibration. And if a sound wave within
the audible range of human hearing is produced, a
loud sound is heard.
Diffraction
• Diffraction involves a change in direction of
waves as they pass through an opening or around
a barrier in their path.
How much diffraction?
• The amount of diffraction
is determined by the how
the wavelength and the
size of opening of the
barrier compare.
• When the opening is
comparable to the
wavelength, most
diffraction occurs
• When the opening is
much larger than the
wavelength, diffraction is
less.
example
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2.
3.
4.
The diagram shows straight wave fronts
passing through an opening in a barrier. This
wave phenomenon is called
reflection
refraction
polarization
diffraction
example
•
1.
2.
3.
4.
The diagram shows a wave phenomenon. The
pattern of waves shown behind the barrier is the
result of
reflection
refraction
diffraction
interference
example
•
1.
2.
3.
4.
A wave is diffracted as it passes through an opening
in a barrier. The amount of diffraction that the wave
undergoes depends on both the
amplitude and frequency of the incident wave
wavelength and speed of the incident wave
wavelength of the incident wave and the size of the
opening
amplitude of the incident wave and the size of the
opening
Polarization of light waves
• Light is a transverse wave that vibrate in different planes. A
light wave which is vibrating in more than one plane is
referred to as un-polarized light.
Light can be polarized
• Polarized light waves are light waves in which the vibrations
occur in the same plane.
• The most common method of polarization involves the use of a
Polaroid filter. Polaroid filters are made of a special material
which is capable of blocking one of the two planes of vibration
of an electromagnetic wave. When un-polarized light is
transmitted through a polaroid filter, it emerges with one-half
the intensity and with vibrations in a single plane; it emerges as
polarized light.
Note: a longitudinal wave can not be polarized.
Sound wave is a longitudinal wave, sound wave
can not be polarized. Only transverse wave can
be polarized.
Applications of Polarization
Used in sun glasses.
• Light reflected from surfaces such as a flat road or
smooth water is generally horizontally polarized. This
creates an annoying and sometimes dangerous
intensity of light that we experience as glare.
• Polarized lenses contain a special filter that blocks
this type of intense reflected light, reducing glare.
Polarization and 3D films
• Three-dimensional movies are actually two movies being
shown at the same time through two projectors.
http://www.physics.org/article-questions.asp?id=56