Background
A wave is a disturbance that carries energy, a disturbance that transports energy
from one place to another without the transfer of matter. After a wave passes
through a medium, there are no residual effects; the medium remains unchanged.
For example, if you throw a stone in a pond, a circular wave will spread out from
the point of impact. If the wave encounters an object floating in the water, the
object will briefly bob up and down. However, once the wave has passed, the
object, and the water that buoys it up, will be left undisturbed.
We encounter waves everyday. Some are apparent; others go unnoticed. The room
in which you are sitting is being criss-crossed by all sorts of waves. These include
light waves, radio waves, and sound waves. While we have receptors for
light and sound, our bodies are not capable of sensing radio waves directly.
What travels in all waves? Energy! Energy is the quantity that travels in a wave. A
wave is a disturbance that transfers energy, frequently repeating in a regular
pattern.
The Anatomy of a Wave—Key Components
In the above diagram the straight line represents the position of the medium when
no wave is present. This medium could be imagined as a rope fixed at one end a
few feet above the ground and held by you at the other end.
The curved line represents the position of the medium as a wave travels through it.
We simply say that the curved line is the wave. Often, when several waves are
traveling along a medium as shown above, the continuous group of waves is called
a wave train.
Crest and Trough
The section of the wave that rises above the undisturbed position is called the
crest. That section which lies below the undisturbed position is called the trough.
These sections are labeled in the following diagram:
draw
Amplitude
The term amplitude can have slightly different meanings depending upon the
context of the situation.
Its most general definition is that the amplitude is the maximum positive
displacement from the undisturbed position of the medium to the top of a crest.
This is shown in the following diagram:
draw
In some discussions, it is important to distinguish between positive and negative
amplitudes. These displacements are shown in the following diagram:
Sometimes it is necessary to discuss amplitude at a certain point along the wave.
Several of these amplitudes are shown in the following diagram:
draw
Notice in the above diagram that three of the amplitudes are positive and two are
negative.
Here are some other labeled examples of positive and negative amplitudes:
draw
In general, if the question simply is 'What is the amplitude of the wave?', the answer
follows the description of amplitude shown in the first of the above four amplitude
diagrams. It is the maximum positive displacement of the medium from its
undisturbed position to the top of a crest.
In many discussions, though, the term amplitude takes on a slightly more complicated
meaning. For example, in a discussion about wave interference the later descriptions
of positive and negative amplitudes at certain points would surface. In such contexts,
amplitude means the displacement of the medium from its undisturbed position to its
disturbed position at a certain point along the wave.
All of this becomes clear as you study waves further and understand the context of
your situation.
To sum up amplitude, we would say:
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It is the displacement of the medium from its normal position.
Usually this simply means the maximum positive displacement.
Often, especially in discussions about interference, amplitude means the
displacement of the medium from its normal position at certain points, and this
displacement can be positive or negative.
Wavelength
The wavelength of a wave is the
distance between any two adjacent
corresponding locations on the
wave train. This distance is usually
measured in one of three ways:
crest to next crest, trough to next
trough, or from the start of a wave cycle to the next starting point. This is shown in the
following diagram:
Actually, the a wavelength exists between any point on a wave and the
corresponding point on the next wave in the wave train. A few of such distances are
shown below:
Frequency is often not termed as a part of a wave, but it makes sense to introduce
its meaning in this section.
Frequency refers to how many waves are made per time interval. This is usually
described as how many waves are made per second, or as cycles per second.
The following interactive diagram lets you adjust the frequency of the wave train.
(The animation may jitter a tiny bit the moment that you change frequency. This
means nothing.)
Some waves, such as sound and water waves, require a material medium. On the
other hand, light and other forms of electromagnetic radiation can travel through
the vacuum of space.
Double Waves
A fascinating feature of waves is that two of them, traveling in opposite directions,
can pass right through each other and emerge with their original identities.
However, while the pulses overlap, the height at any point is simply the sum of the
displacements due to each pulse itself. If the pulses are on the same side of the
medium they add; if they are on opposite sides, they subtract. This is called
interference.
The importance of wave phenomena in everyday life cannot be overstated. It is
estimated that human beings receive over 90% of their information from light and
sound. The experiments that follow will allow you to gain first hand experience with
the properties of waves in general and sound in particular.
Sound is caused by small areas of high and low pressure progragating outward from the
source.
One convenient way to diagram a sound wave is to graph the pressure at each point in time, the
way it might be picked up by a microphone for example:
This simplest kind of pressure wave is called a sine wave. Interesting things to measure for a
sine wave:
1. amplitude (or loudness, size of pressure differences)
usually measured in decibels (dB)
2. wavelength
3. frequency (or pitch)
usually measured in cycles per second, or Hertz (Hz)
Frequency and amplitude are independent of each other. Two sine waves may have the same
frequency and different amplitudes, and vice versa.
What is Sound?
Sound is a type of energy made by vibrations. When any object vibrates, it causes movement in
the air particles. These particles bump into the particles close to them, which makes them vibrate
too causing them to bump into more air particles. This movement, called sound waves, keeps
going until they run out of energy. If your ear is within range of the vibrations, you hear the
sound.
Picture a stone thrown into a still body of water. The rings of waves expand indefinitely. The
same is true with sound. Irregular repeating sound waves create noise, while regular repeating
waves produce musical notes.
When the vibrations are fast, you hear a high note. When the vibrations are slow, it creates a low
note. The sound waves in the diagram show the different frequencies for high and low notes.
Low frequency notes
High frequency notes
1. Can sound travel under the water?
Yes sound can travel under the water. It moves four times faster through
water than through the air. It can travel such long distances that whales can
hear each other when they are nearly a hundred miles apart.
2. Is there sound on the moon?
No, there is no sound in space. Sound needs something to travel through like
air or water.
3. What is the speed of Sound?
Sound travels through air at 1,120 feet (340 meters) per second.
Waves of light
Demonstration #1
Waves in Motion (requires two persons)
Materials: Phone cord or slinky
Key Concept: A wave is a disturbance that travels
through a medium. Waves are characterized by
wavelength, frequency, and amplitude. Waves reflect
when they encounter a barrier or different medium.
A rope or a long spring may be used to demonstrate
many properties of waves. Hold one end of the
stretched medium in your hand while your partner holds
Figure 1 Helical Spring "Snky"
the other end. Now move one end up and down at
different rates (frequencies). What happens to the
wavelength as you increase the frequency? Decrease the frequency?
Does the tension in the medium have any observable effect on the speed of a wave? To find
out, send a sharp pulse down the medium when the medium is under various degrees of
tension. What do you observe?
Send another sharp pulse down the medium. This time watch carefully as the pulse reaches
the fixed end. Does the pulse reflect? If so, is the reflected pulse the same as the incident
pulse or is it upside down? Do the incident and reflected
pulses travel at the same speed?
Stretch out the phone card across an area. Have one student
come up and hold one end of the cord. Have the student hold the
cord still and move your end up and down to create a standing
wave. A standing wave is where one or more parts of the card do
not move. You will need to find the right frequency to create a
standing wave. It is fairly easy with a little practice.
The Unusual Way of Waves
Key Concept: The overlapping, or superposition, of two waves produces reinforcement in
some instances and cancellation in others.
You can witness wave interference on a phone cord, rope, or Slinky. After producing one
pulse on the medium, generate a second shortly thereafter. Watch carefully as the two
pulses meet and pass through one another. How would you describe the medium when the
two pulses overlapped? Did the pulses produce a larger or smaller resultant pulse? What
procedure must you follow to produce constructive interference (a larger net pulse)?
Destructive interference (a smaller net pulse)?
Nice Nodes
Key Concept: Standing waves are formed when two sets of identical
waves pass through a medium in opposite directions.
Move the end of the medium of choice (rope, phone cord, Slinky) up
and down at the right frequency to create a full wave. When this has
been accomplished you will notice that the center of the medium
appears to stand still. This stationary point is called a node. At a
node, the destructive
interference of the
incident and reflected
waves is total. On either
side of the node are
regions of maximum
displacement called
antinodes. Have someone gently pinch the node
with their fingers. What happens?
Increase the frequency of the up and down
motion of your hand until two nodes appear on
the medium. How many antinodes are there
now? How many wavelengths do you observe?
What happens when you continue to increase the
frequency of the waves? Can you obtain three
nodes, four nodes, etc.? Describe what happens
to the wavelength as the frequency is increased.
Are You Chicken?
Key Concept: A surface set in motion by a vibrating string amplifies sound.
Using a toothpick, puncture a small hole in the center of the base of a paper or plastic cup.
Pull a ½ meter, or so, length of string through the hole. With the cup turned upside down, tie
the string around the toothpick (see figure).
Rub a little rosin on your thumb and index finger. Using a jerking motion, pull down on the
string while gently pinching it between the thumb and index finger. Describe what you hear
as the string moves between the fingers.
What is the source of the sound you hear? Why is the sound so loud? To answer this
question, it may be helpful to pull on the string when it is not connected to the cup.
What's it sound like?
Directions
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Line up eight glasses of
about the same size and
shape.
Fill the first glass about
1/8th full of water for the
high note, the second glass
should be 1/4 full, the third
glass should be 3/8ths full
for the next note, and so
on.
Each glass should sound
like a note on the music
scale (do, re, mi, fa, sol, la,
ti, do). You may need to
tune your music scale (add
or remove water with
teaspoon) until each note
rings true.
Have the children use a metal teaspoon to gently tap out the scale and any
other melodies they know (Mary had a Little lamb, Twinkle Twinkle).
Hints for Water Chimes
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Don't use expensive crystal glasses to make water chimes.
Add a bit a food coloring to help children identify which glass is which sound.
Changing the amount of water will change the musical note. The amount of
water in the glass changes the pitch of the sound wave.
DO NOT TAP BOTTLES
Use alcohol wipes between visitors
Can you use the notes to play a simple tune?