Review for Waves: Properties and Applications
TEKS: P7 A-F
1. Examine and describe oscillatory motion and wave propagation in different types of media
2. Investigate and analyze characteristics of waves, including velocity, frequency, amplitude, and wavelength, and calculate
using the relationship between wave speed, frequency, and wavelength.
3. Investigate behaviors of waves, including reflection, refraction, diffraction, interference, resonance, and the Doppler effect.
4. Describe and predict image formation as a consequence of reflection for a plane mirror ad refraction through a thin convex
lens.
5. Describe the role of wave characteristics and behaviors in medical and industrial applications.
Overview:
This lesson examines classical wave properties, including how they are created (vibrating objects), how they are characterized
(wavelength, frequency, amplitude, etc.), how they propagate and interact with different media (speed, reflection,
refraction...), and also how waves behave (diffraction, interference). This lesson illustrates the “wave properties” common to
all waves and uses sound and light as primary examples. The lesson begins by reviewing terminology and linking them to the
wave properties through demonstrations and simulations. The creation of standing waves is also examined for different waves
(rope, sound, transverse) and linked to the properties of wavelength, frequency, and speed. Students gain experience with the
equation f λ = v, which relates these variables in an equation.
Key Understandings:
All waves have properties in common, such as wavelength, frequency, and energy transmission.
Waves travel at different speeds in different media and undergo reflection and refraction (bending) at boundaries.
Waves also bend around edges (diffraction) producing additional wave fronts which can interfere, producing new wave
patterns.
Waves are produced by oscillating objects.
Modern devices use the properties of waves for medical, industrial, scientific, or social purposes.
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Wave – a disturbance or variation which travels through a medium
Transverse wave – oscillations (vibrations of the wave) are perpendicular to direction of the waves (string, water)
Longitudinal wave – oscillations are in the same direction as the wave (slinky, sound waves)
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Review for Waves: Properties and Applications
Specificity:
Demonstrate
THE USE OF COURSE APPARATUS, EQUIPMENT, TECHNIQUES, AND PROCEDURES
Including, but not limited to:
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Plane mirrors
Convex lenses
Pendulum support
Polarized film
Prisms
Slinky springs
Wave motion ropes
Laser pointers
Examine, Describe
OSCILLATORY MOTION IN VARIOUS TYPES OF MEDIA
Including, but not limited to:
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Oscillatory motion
o Spring
o Pendulum
o Tuning fork
Examine, Describe
WAVE PROPAGATION IN VARIOUS TYPES OF MEDIA
Including, but not limited to:
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Waves terms
o Transverse
o Longitudinal
o Surface
o Seismic
o Pulses
o Periodic
Investigate, Analyze
CHARACTERISTICS OF WAVES
Including, but not limited to:
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Frequency (f)
Wavelength (‫)ג‬
Velocity = (frequency)(wavelength)
Amplitude
Crest
Trough
Period
Phase
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Review for Waves: Properties and Applications
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Energy
o
E = mc2
Calculate
USING THE RELATIONSHIP BETWEEN
Including, but not limited to:
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Wave speed
Frequency
Wavelength
Investigate
BEHAVIORS OF WAVES
Including, but not limited to:
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Reflection
Refraction
Diffraction
o Grating
o Diffraction pattern
Interference
o Constructive
o Destructive
o Nodes
o Antinodes
Resonance
Doppler effect
Describe
ROLE OF WAVE CHARACTERISTICS AND BEHAVIORS IN MEDICAL AND INDUSTRIAL APPLICATIONS
Including, but not limited to:
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Ultrasound (sonograms)
Doppler weather and police radar
Echolocation
Seismic waves
Electronic communications
Vocabulary of Instruction
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amplitude
crest
phase
polarization
diffraction
standing wave
periodic
Doppler
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frequency
trough
transverse
reflection
interference
traveling wave
node
pitch
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period
longitudinal
refraction
media
Fourier Analysis
anti-node
resonance
focus
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Review for Waves: Properties and Applications
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oscillate
dispersion
overtone
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ray
grating
wave
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spectrum
harmonic
wave velocity
Miscellaneous Additional Information as a pre-Spring Break present from Yoder!!!!!
Polarization via Physics Classroom
Polarization of light by use of a Polaroid filter is often demonstrated in a Physics class through a variety of demonstrations.
Filters are used to look through and view objects. The filter does not distort the shape or dimensions of the object; it merely
serves to produce a dimmer image of the object since one-half of the light is blocked as it passed through the filter. A pair of
filters is often placed back to back in order to view objects looking through two filters. By slowly rotating the second filter,
an orientation can be found in which all the light from an object is blocked and the object can no longer be seen when
viewed through two filters. What happened? In this demonstration, the light was polarized upon passage through the first
filter; perhaps only vertical vibrations were able to pass through. These vertical vibrations were then blocked by the second
filter since its polarization filter is aligned in a horizontal direction. While you are unable to see the axes on the filter, you will
know when the axes are aligned perpendicular to each other because with this orientation, all light is blocked. So by use of
two filters, one can completely block all of the light that is incident upon the set; this will only occur if the polarization axes
are rotated such that they are perpendicular to each other.
A picket-fence analogy is often used to explain how this dual-filter demonstration works. A picket fence can act as a
polarizer by transforming an unpolarized wave in a rope into a wave that vibrates in a single plane. The spaces between the
pickets of the fence will allow vibrations that are parallel to the spacings to pass through while blocking any vibrations that
are perpendicular to the spacings. Obviously, a vertical vibration would not have the room to make it through a horizontal
spacing. If two picket fences are oriented such that the pickets are both aligned vertically, then vertical vibrations will pass
through both fences. On the other hand, if the pickets of the second fence are aligned horizontally, then the vertical
vibrations that pass through the first fence will be blocked by the second fence. This is depicted in the diagram below.
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Review for Waves: Properties and Applications
In the same manner, two Polaroid filters oriented with their polarization axes perpendicular to each other will block all the
light. Now that's a pretty cool observation that could never be explained by a particle view of light.
Via physics Classroom
The Doppler Effect
Suppose that there is a happy bug in the center of a circular water puddle. The bug is periodically
shaking its legs in order to produce disturbances that travel through the water. If these
disturbances originate at a point, then they would travel outward from that point in all directions.
Since each disturbance is traveling in the same medium, they would all travel in every direction at
the same speed. The pattern produced by the bug's shaking would be a series of concentric circles
as shown in the diagram at the right. These circles would reach the edges of the water puddle at
the same frequency. An observer at point A (the left edge of the puddle) would observe the
disturbances to strike the puddle's edge at the same frequency that would be observed by an
observer at point B (at the right edge of the puddle). In fact, the frequency at which disturbances
reach the edge of the puddle would be the same as the frequency at which the bug produces the
disturbances. If the bug produces disturbances at a frequency of 2 per second, then each observer
would observe them approaching at a frequency of 2 per second.
Now suppose that our bug is moving to the right across the puddle of water and producing
disturbances at the same frequency of 2 disturbances per second. Since the bug is moving
towards the right, each consecutive disturbance originates from a position that is closer to
observer B and farther from observer A. Subsequently, each consecutive disturbance has a shorter
distance to travel before reaching observer B and thus takes less time to reach observer B. Thus,
observer B observes that the frequency of arrival of the disturbances is higher than the frequency
at which disturbances are produced. On the other hand, each consecutive disturbance has a
further distance to travel before reaching observer A. For this reason, observer A observes a
frequency of arrival that is less than the frequency at which the disturbances are produced. The
net effect of the motion of the bug (the source of waves) is that the observer towards whom the
bug is moving observes a frequency that is higher than 2 disturbances/second; and the observer
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Review for Waves: Properties and Applications
away from whom the bug is moving observes a frequency that is less than 2 disturbances/second. This effect is known as
the Doppler effect.
The Doppler effect is observed whenever the source of waves is moving with respect to an observer. The Doppler
effect can be described as the effect produced by a moving source of waves in which there is an apparent upward shift in
frequency for observers towards whom the source is approaching and an apparent downward shift in frequency for
observers from whom the source is receding. It is important to note that the effect does not result because of
an actual change in the frequency of the source. Using the example above, the bug is still producing disturbances at a rate
of 2 disturbances per second; it just appears to the observer whom the bug is approaching that the disturbances are being
produced at a frequency greater than 2 disturbances/second. The effect is only observed because the distance between
observer B and the bug is decreasing and the distance between observer A and the bug is increasing.
The Doppler effect can be observed for any type of wave - water wave, sound wave, light wave, etc. We are most familiar
with the Doppler effect because of our experiences with sound waves. Perhaps you recall an instance in which a police car or
emergency vehicle was traveling towards you on the highway. 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.
The Doppler effect is of intense interest to astronomers who use the information about the shift in frequency of
electromagnetic waves produced by moving stars in our galaxy and beyond in order to derive information about those stars
and galaxies. The belief that the universe is expanding is based in part upon observations of electromagnetic waves emitted
by stars in distant galaxies. Furthermore, specific information about stars within galaxies can be determined by application
of the Doppler effect. Galaxies are clusters of stars that typically rotate about some center of mass point. Electromagnetic
radiation emitted by such stars in a distant galaxy would appear to be shifted downward in frequency (a red shift) if the star
is rotating in its cluster in a direction that is away from the Earth. On the other hand, there is an upward shift in frequency
(a blue shift) of such observed radiation if the star is rotating in a direction that is towards the Earth.
Via Physics Classroom #3 – Lenses and ray Diagrams
Converging Lenses - Ray Diagrams
One theme of the Reflection and Refraction units of The Physics Classroom Tutorial has been that we see an object because
light from the object travels to our eyes as we sight along a line at the object. Similarly, we see an image of an object
because light from the object reflects off a mirror or refracts through a transparent material and travel to our eyes as we
sight at the image location of the object. From these two basic premises, we have defined the image location as the location
in space where light appears to diverge from. Because light emanating from the object converges or appears to diverge from
this location, a replica or likeness of the object is created at this location. For both reflection and refraction scenarios, ray
diagrams have been a valuable tool for determining the path of light from the object to our eyes.
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Review for Waves: Properties and Applications
In this section of Lesson 5, we will investigate the method for drawing ray diagrams for objects placed at various locations in
front of a double convex lens. To draw these ray diagrams, we will have to recall the three rules of refraction for a double
convex lens:
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Any incident ray traveling parallel to the principal axis of a converging lens will refract through the lens
and travel through the focal point on the opposite side of the lens.
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Any incident ray traveling through the focal point on the way to the lens will refract through the lens and
travel parallel to the principal axis.
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An incident ray that passes through the center of the lens will in effect continue in the same direction
that it had when it entered the lens.
Earlier in this lesson, the following diagram illustrating the path of light from an object through a lens to an eye placed at
various locations was shown.
In this diagram, five incident rays are drawn along with their corresponding refracted rays. Each ray intersects at the image
location and then travels to the eye of an observer. Every observer would observe the same image location and every light
ray would follow the Snell's Law of refraction. Yet only two of these rays would be needed to determine the image location
since it only requires two rays to find the intersection point. Of the five incident rays drawn, three of them correspond to the
incident rays described by our three rules of refraction for converging lenses. We will use these three rays through the
remainder of this lesson, merely because they are the easiest rays to draw. Certainly two rays would be all that is
necessary; yet the third ray will provide a check of the accuracy of our process.
Step-by-Step Method for Drawing Ray Diagrams
The method of drawing ray diagrams for double convex lens is described below. The description is applied to the task of
drawing a ray diagram for an object located beyond the 2F point of a double convex
lens.
1. Pick a point on the top of the object and draw three incident rays traveling towards
the lens.
Using a straight edge, accurately draw one ray so that it passes exactly through the
focal point on the way to the lens. Draw the second ray such that it travels exactly
parallel to the principal axis. Draw the third incident ray such that it travels directly to
the exact center of the lens. Place arrowheads upon the rays to indicate their direction
of travel.
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Review for Waves: Properties and Applications
2. Once these incident rays strike the lens, refract them according to the threerules of
refraction for converging lenses.
The ray that passes through the focal point on the way to the lens will refract and
travel parallel to the principal axis. Use a straight edge to accurately draw its path.
The ray that traveled parallel to the principal axis on the way to the lens will refract
and travel through the focal point. And the ray that traveled to the exact center of the
lens will continue in the same direction. Place arrowheads upon the rays to indicate
their direction of travel. Extend the rays past their point of intersection.
3. Mark the image of the top of the object.
The image point of the top of the object is the point where the three refracted rays
intersect. All three rays should intersect at exactly the same point. This point is
merely the point where all light from the top of the object would intersect upon
refracting through the lens. Of course, the rest of the object has an image as well and
it can be found by applying the same three steps to another chosen point. (See
note below.)
4. Repeat the process for the bottom of the object.
One goal of a ray diagram is to determine the location, size, orientation, and type of
image that is formed by the double convex lens. Typically, this requires determining
where the image of the upper and lower extreme of the object is located and then
tracing the entire image. After completing the first three steps, only the image
location of the top extreme of the object has been found. Thus, the process must be
repeated for the point on the bottom of the object. If the bottom of the object lies
upon the principal axis (as it does in this example), then the image of this point will
also lie upon the principal axis and be the same distance from the mirror as the image
of the top of the object. At this point the entire image can be filled in.
Some students have difficulty understanding how the entire image of an object can be deduced once a single point on the
image has been determined. If the object is merely a vertical object (such as the arrow object used in the example below),
then the process is easy. The image is merely a vertical line. In theory, it would be necessary to pick each point on the
object and draw a separate ray diagram to determine the location of the image of that point. That would require a lot of ray
diagrams as illustrated in the diagram below.
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Review for Waves: Properties and Applications
Fortunately, a shortcut exists. If the object is a vertical line, then the image is also a vertical line. For our purposes, we will
only deal with the simpler situations in which the object is a vertical line that has its bottom located upon the principal axis.
For such simplified situations, the image is a vertical line with the lower extremity located upon the principal axis.
The ray diagram above illustrates that when the object is located at a position beyond the 2F point, the image will be located
at a position between the 2F point and the focal point on the opposite side of the lens. Furthermore, the image will be
inverted, reduced in size (smaller than the object), and real. This is the type of information that we wish to obtain from a
ray diagram. These characteristics of the image will be discussed in more detail in the next section of Lesson 5.
Once the method of drawing ray diagrams is practiced a couple of times, it becomes as natural as breathing. Each diagram
yields specific information about the image. The two diagrams below show how to determine image location, size,
orientation and type for situations in which the object is located at the 2F point and when the object is located between the
2F point and the focal point.
It should be noted that the process of constructing a ray diagram is the same regardless of where the object is located.
While the result of the ray diagram (image location, size, orientation, and type) is different, the same three rays
are always drawn. The three rules of refraction are applied in order to determine the location where all refracted rays appear
to diverge from (which for real images, is also the location where the refracted rays intersect).
Ray Diagram for Object Located in Front of the Focal Point
In the three cases described above - the case of the object being located beyond 2F, the case of the object being located at
2F, and the case of the object being located between 2F and F - light rays are converging to a point after refracting through
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Review for Waves: Properties and Applications
the lens. In such cases, a real image is formed. As discussed previously, a real image is formed whenever refracted light
passes through the image location. While diverging lenses always produce virtual images, converging lenses are capable of
producing both real and virtual images. As shown above, real images are produced when the object is located a distance
greater than one focal length from the lens. A virtual image is formed if the object is located less than one focal length
from the converging lens. To see why this is so, a ray diagram can be used.
A ray diagram for the case in which the object is located in front of the focal point is
shown in the diagram at the right. Observe that in this case the light rays diverge
after refracting through the lens. When refracted rays diverge, a virtual image is
formed. The image location can be found by tracing all light rays backwards until
they intersect. For every observer, the refracted rays would seem to be diverging
from this point; thus, the point of intersection of the extended refracted rays is the
image point. Since light does not actually pass through this point, the image is
referred to as a virtual image. Observe that when the object in located in front of the
focal point of the converging lens, its image is an upright and enlarged image that is
located on the object's side of the lens. In fact, one generalization that can be made
about all virtual images produced by lenses (both converging and diverging) is that
they are always upright and always located on the object's side of the lens.
Ray Diagram for Object Located at the Focal Point
Thus far we have seen via ray diagrams that a real image is produced when an object is located more than one focal length
from a converging lens; and a virtual image is formed when an object is located less than one focal length from a
converging lens (i.e., in front of F). But what happens when the object is located at F? That is, what type of image is formed
when the object is located exactly one focal length from a converging lens? Of course a ray diagram is always one tool to
help find the answer to such a question. However, when a ray diagram is used for this case, an immediate difficulty is
encountered. The diagram below shows two incident rays and their corresponding refracted rays.
For the case of the object located at the focal point (F), the light rays neither converge nor diverge after refracting through
the lens. As shown in the diagram above, the refracted rays are traveling parallel to each other. Subsequently, the light rays
will not converge to form a real image; nor can they be extended backwards on the opposite side of the lens to intersect to
form a virtual image. So how should the results of the ray diagram be interpreted? The answer: there is no image!!
Surprisingly, when the object is located at the focal point, there is no location in space at which an observer can sight from
which all the refracted rays appear to be coming. An image cannot be found when the object is located at the focal point of a
converging lens.
Next Section: Converging Lenses - Object-Image Relations
Jump To Lesson 6: The Eye
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Review for Waves: Properties and Applications
NOW will you believe me when II tell you to go to Physics
Classroom!!!!!...especially when you miss class due to sports . fair,
whatever…aaauuuggghhhhhhhhhh!
Y’all better make good grades on this test or Yoder WILL NOT be
pleased!!!!!...
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