WAVES - ANATOMY #5

 transverse wave is a wave in which the particles of the medium are displaced in a direction perpendicular to the direction of energy transport. 

• A transverse wave can be created in a rope if the rope is stretched out horizontally and the end is vibrated back-and-forth in a vertical direction. If a snapshot of such a transverse wave could be taken so as to freeze the shape of the rope in time, then it would look like the following diagram.

The dashed line drawn through the center of the diagram represents the equilibrium or rest position of the string. This is the position that the string would assume if there were no disturbance moving through it. Once a disturbance is introduced into the string, the particles of the string begin to vibrate upwards and downwards. At any given moment in time, a particle on the medium could be above or below the rest position. Points A, E and H on the diagram represent the crests of this wave. 

The crest of a wave is the point on the medium that exhibits the maximum amount of positive or upward displacement from the rest position. Points C and J on the diagram represent the troughs of this wave. 

The trough of a wave is the point on the medium that exhibits the maximum amount of negative or downward displacement from the rest position.

The wave shown above can be described by a variety of properties. One such property is amplitude. The amplitude of a wave refers to the maximum amount of displacement of a particle on the medium from its rest position. In a sense, the amplitude is the distance from rest to crest. Similarly, the amplitude can be measured from the rest position to the trough position. In the diagram above, the amplitude could be measured as the distance of a line segment that is perpendicular to the rest position and extends vertically upward from the rest position to point A.

The wavelength is another property of a wave that is portrayed in the diagram above. The wavelength of a wave is simply the length of one complete wave cycle. If you were to trace your finger across the wave in the diagram above, you would notice that your finger repeats its path. A wave is a repeating pattern. It repeats itself in a periodic and regular fashion over both time and space. And the length of one such spatial repetition (known as a wave cycle) is the wavelength. The wavelength can be measured as the distance from crest to crest or from trough to trough. In fact, the wavelength of a wave can be measured as the distance from a point on a wave to the corresponding point on the next cycle of the wave. In the diagram above, the wavelength is the horizontal distance from A to E, or the horizontal distance from B to F, or the horizontal distance from D to G, or the horizontal distance from E to H. Any one of these distance measurements would suffice in determining the wavelength of this wave.

A longitudinal wave is a wave in which the particles of the medium are displaced in a direction parallel to the direction of energy transport. A longitudinal wave can be created in a slinky if the slinky is stretched out horizontally and the end coil is vibrated back-and-forth in a horizontal direction. If a snapshot of such a longitudinal wave could be taken so as to freeze the shape of the slinky in time, then it would look like the following diagram.

Because the coils of the slinky are vibrating longitudinally, there are regions where they become pressed together and other regions where they are spread apart. A region where the coils are pressed together in a small amount of space is known as a compression. A compression is a point on a medium through which a longitudinal wave is traveling that has the maximum density. A region where the coils are spread apart, thus maximizing the distance between coils, is known as a rarefaction. A rarefaction is a point on a medium through which a longitudinal wave is traveling that has the minimum density. Points A, C and E on the diagram above represent compressions and points B, D, and F represent rarefactions. While a transverse wave has an alternating pattern of crests and troughs, a longitudinal wave has an alternating pattern of compressions and rarefactions.

As discussed above, the wavelength of a wave is the length of one complete cycle of a wave. For a transverse wave, the wavelength is determined by measuring from crest to crest. A longitudinal wave does not have crest; so how can its wavelength be determined? The wavelength can always be determined by measuring the distance between any two corresponding points on adjacent waves. In the case of a longitudinal wave, a wavelength measurement is made by measuring the distance from a compression to the next compression or from a rarefaction to the next rarefaction. On the diagram above, the distance from point A to point C or from point B to point D would be representative of the wavelength.

 

Check Your Understanding

Consider the diagram below in order to answer questions #1-2.

1. The wavelength of the wave in the diagram above is given by letter ______.

2. The amplitude of the wave in the diagram above is given by letter _____.

3. Indicate the interval that represents one full wavelength.

a. A to C

b. B to D

c. A to G

d. C to G

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1)   Answer: A
The wavelength is the distance from crest to crest (or from trough to trough) (or between any two corresponding points on adjacent waves).

 2)   Answer: D
The amplitude is the distance from rest to crest or from rest to trough.

3)Answer: D
The wavelength is the distance from crest to crest, trough to trough, or from a point on one wave cycle to the corresponding point on the next adjacent wave cycle.

The nature of a wave was discussed in Lesson 1 of this unit. In that lesson, it was mentioned that a wave is created in a slinky by the periodic and repeating vibration of the first coil of the slinky. This vibration creates a disturbance that moves through the slinky and transports energy from the first coil to the last coil. A single back-and-forth vibration of the first coil of a slinky introduces a pulse into the slinky. But the act of continually vibrating the first coil with a back-and-forth motion in periodic fashion introduces a wave into the slinky.

Suppose that a hand holding the first coil of a slinky is moved back-and-forth two complete cycles in one second. The rate of the hand's motion would be 2 cycles/second. The first coil, being attached to the hand, in turn would vibrate at a rate of 2 cycles/second. The second coil, being attached to the first coil, would vibrate at a rate of 2 cycles/second. The third coil, being attached to the second coil, would vibrate at a rate of 2 cycles/second. In fact, every coil of the slinky would vibrate at this rate of 2 cycles/second. This rate of 2 cycles/second is referred to as the frequency of the wave. The frequency of a wave refers to how often the particles of the medium vibrate when a wave passes through the medium. Frequency is a part of our common, everyday language. For example, it is not uncommon to hear a question like "How frequently do you mow the lawn during the summer months?" Of course the question is an inquiry about how often the lawn is mowed and the answer is usually given in the form of "1 time per week." In mathematical terms, the frequency is the number of complete vibrational cycles of a medium per a given amount of time. Given this definition, it is reasonable that the quantity frequencywould have units of cycles/second, waves/second, vibrations/second, or something/second. Another unit for frequency is the Hertz (abbreviated Hz) where 1 Hz is equivalent to 1 cycle/second. If a coil of slinky makes 2 vibrational cycles in one second, then the frequency is 2 Hz. If a coil of slinky makes 3 vibrational cycles in one second, then the frequency is 3 Hz. And if a coil makes 8 vibrational cycles in 4 seconds, then the frequency is 2 Hz (8 cycles/4 s = 2 cycles/s).

The quantity frequency is often confused with the quantity period. Period refers to the time that it takes to do something. When an event occurs repeatedly, then we say that the event is periodic and refer to the time for the event to repeat itself as the period. The period of a wave is the time for a particle on a medium to make one complete vibrational cycle. Period, being a time, is measured in units of time such as seconds, hours, days or years. The period of orbit for the Earth around the Sun is approximately 365 days; it takes 365 days for the Earth to complete a cycle. The period of a typical class at a high school might be 55 minutes; every 55 minutes a class cycle begins (50 minutes for class and 5 minutes for passing time means that a class begins every 55 minutes). The period for the minute hand on a clock is 3600 seconds (60 minutes); it takes the minute hand 3600 seconds to complete one cycle around the clock.

Frequency and period are distinctly different, yet related, quantities. Frequency refers to how often something happens. Period refers to the time it takes something to happen. Frequency is a rate quantity. Period is a time quantity. Frequency is the cycles/second. Period is the seconds/cycle. As an example of the distinction and the relatedness of frequency and period, consider a woodpecker that drums upon a tree at a periodic rate. If the woodpecker drums upon a tree 2 times in one second, then the frequency is 2 Hz. Each drum must endure for one-half a second, so the period is 0.5 s. If the woodpecker drums upon a tree 4 times in one second, then the frequency is 4 Hz; each drum must endure for one-fourth a second, so the period is 0.25 s. If the woodpecker drums upon a tree 5 times in one second, then the frequency is 5 Hz; each drum must endure for one-fifth a second, so the period is 0.2 s. Do you observe the relationship? Mathematically, the period is the reciprocal of the frequency and vice versa. In equation form, this is expressed as follows.

Since the symbol f is used for frequency and the symbol T is used for period, these equations are also expressed as:

The quantity frequency is also confused with the quantity speed. The speed of an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. For a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given period of time. So while wave frequency refers to the number of cycles occurring per second, wave speed refers to the meters traveled per second. A wave can vibrate back and forth very frequently, yet have a small speed; and a wave can vibrate back and forth with a low frequency, yet have a high speed. Frequency and speed are distinctly different quantities. Wave speed will be discussed in more detail later in this lesson.

Investigate!

How do changes in the frequency of a wave affect the wavelength of a wave? Use the Wave plotter widget below to find out. Alter the frequency and observe how the pattern changes.

	Wave Plotter
	Enter a value for amplitude and select a frequency. Then click the Plot the Wave button to view the result. Amplitude (m): Frequency (Hz): mediumlowvery lowhighvery high NOTE: The on-screen height of the wave is the same each time; yet the vertical axis is scaled differently. Plot the Wave

 

Check Your Understanding

Throughout this unit, internalize the meaning of terms such as period, frequency, and wavelength. Utilize the meaning of these terms to answer conceptual questions; avoid a formula fixation.

1. A wave is introduced into a thin wire held tight at each end. It has an amplitude of 3.8 cm, a frequency of 51.2 Hz and a distance from a crest to the neighboring trough of 12.8 cm. Determine the period of such a wave.

WAVES - REVIEW

Light travels as waves. Waves can be described by theiramplitude, wavelength and frequency. The speed of a wave can be calculated from its frequency and wavelength.

What are waves?

Waves are vibrations that transfer energy from place to place without matter (solid, liquid or gas) being transferred. Think of a Mexican wave in a football crowd. The wave moves around the stadium, while each spectator stays in their seat only moving up then down when it's their turn.

Some waves must travel through a substance. The substance is known as the medium, and it can be solid, liquid or gas. Sound waves and seismic waves are like this. They must travel through a medium. It is the medium that vibrates as the waves travel through.

Other waves do not need to travel through a substance. They may be able to travel through a medium, but they do not have to. Visible light, infrared rays, microwaves and other types ofelectromagnetic radiation are like this. They can travel through empty space. Electrical and magnetic fields vibrate as the waves travel.

http://www.acs.psu.edu/drussell/demos/waves/wavemotion.html

Amplitude, wavelength and frequency

You should understand what is meant by the amplitude, wavelength and frequency of a wave.

Amplitude

As waves travel, they set up patterns of disturbance. The amplitude of a wave is its maximum disturbance from its undisturbed position. Take care, the amplitude is not the distance between the top and bottom of a wave.

Amplitude and wavelength

Wavelength

The wavelength of a wave is the distance between a point on one wave and the same point on the next wave. It is often easiest to measure this from the crest of one wave to the crest of the next wave, but it doesn't matter where as long as it is the same point in each wave.

Frequency

The frequency of a wave is the number of waves produced by a source each second. It is also the number of waves that pass a certain point each second. The unit of frequency is the hertz (Hz). It is common for kilohertz (kHz), megahertz (MHz) and gigahertz (GHz) to be used when waves have very high frequencies. For example, most people cannot hear a high-pitched sound above 20kHz, radio stations broadcast radio waves with frequencies of about 100MHz, while most wireless computer networks operate at 2.4GHz.

Check your understanding of this section by having a go at this activity.

Wave speed

You should know and be able to use the relationship between wave speed, frequency and wavelength.

How fast do waves travel?

The speed of a wave - its wave speed - is related to its frequency and wavelength, according to this equation:

wave speed (metre per second) = frequency (hertz) × wavelength (metre)

For example, a wave with a frequency of 100Hz and a wavelength of 2m travels at 100 × 2 = 200m/s.

Now try a Test Bite

An introduction to waves - Test

1.

The distance from the crest of one wave to the crest of the next wave is called:

The amplitude

The wavelength

The frequency

2.

What are the units of frequency?

m/s

s

Hz

3.

Which is a correct equation?

wave speed = frequency × wavelength

wave speed = frequency + wavelength

wave speed = frequency ÷ wavelength

WAVES #4

Waves come in many shapes and forms. While all waves share some basic characteristic properties and behaviors, some waves can be distinguished from others based on some observable (and some non-observable) characteristics. It is common to categorize waves based on these distinguishing characteristics.

 Longitudinal vs. Transverse Waves vs. Surface Waves

One way to categorize waves is on the basis of:

the direction of movement of the individual particles of the medium relative to the direction that the waves travel. 

Categorizing waves on this basis leads to three notable categories: transverse waves, longitudinal waves, and surface waves.

A transverse wave is a wave in which particles of the medium move in a direction perpendicular to the direction that the wave moves. Suppose that a slinky is stretched out in a horizontal direction across the classroom and that a pulse is introduced into the slinky on the left end by vibrating the first coil up and down. Energy will begin to be transported through the slinky from left to right. As the energy is transported from left to right, the individual coils of the medium will be displaced upwards and downwards. In this case, the particles of the medium move perpendicular to the direction that the pulse moves. This type of wave is a transverse wave. Transverse waves are always characterized by particle motion being perpendicular to wave motion.

A longitudinal wave is a wave in which particles of the medium move in a direction parallel to the direction that the wave moves. 

• Suppose that a slinky is stretched out in a horizontal direction across the classroom and that a pulse is introduced into the slinky on the left end by vibrating the first coil left and right. Energy will begin to be transported through the slinky from left to right. As the energy is transported from left to right, the individual coils of the medium will be displaced leftwards and rightwards. In this case, the particles of the medium move parallel to the direction that the pulse moves. This type of wave is a longitudinal wave. 
• Longitudinal waves are always characterized by particle motion being parallel to wave motion.

• A sound wave traveling through air is a classic example of a longitudinal wave. As a sound wave moves from the lips of a speaker to the ear of a listener, particles of air vibrate back and forth in the same direction and the opposite direction of energy transport. Each individual particle pushes on its neighboring particle so as to push it forward. The collision of particle #1 with its neighbor serves to restore particle #1 to its original position and displace particle #2 in a forward direction. This back and forth motion of particles in the direction of energy transport creates regions within the medium where the particles are pressed together and other regions where the particles are spread apart. 

• Longitudinal waves can always be quickly identified by the presence of such regions. This process continues along the chain of particles until the sound wave reaches the ear of the listener. 

• Waves traveling through a solid medium can be either transverse waves or longitudinal waves. 

• Yet waves traveling through the bulk of a fluid (such as a liquid or a gas) are always longitudinal waves. 
• Transverse waves require a relatively rigid medium in order to transmit their energy. As one particle begins to move it must be able to exert a pull on its nearest neighbor. If the medium is not rigid as is the case with fluids, the particles will slide past each other. This sliding action that is characteristic of liquids and gases prevents one particle from displacing its neighbor in a direction perpendicular to the energy transport. It is for this reason that only longitudinal waves are observed moving through the bulk of liquids such as our oceans. Earthquakes are capable of producing both transverse and longitudinal waves that travel through the solid structures of the Earth. When seismologists began to study earthquake waves they noticed that only longitudinal waves were capable of traveling through the core of the Earth. For this reason, geologists believe that the Earth's core consists of a liquid - most likely molten iron.

While waves that travel within the depths of the ocean are longitudinal waves, the waves that travel along the surface of the oceans are referred to as surface waves. A surface wave is a wave in which particles of the medium undergo a circular motion. Surface waves are neither longitudinal nor transverse. 

• In longitudinal and transverse waves, all the particles in the entire bulk of the medium move in a parallel and a perpendicular direction (respectively) relative to the direction of energy transport. In a surface wave, it is only the particles at the surface of the medium that undergo the circular motion. The motion of particles tends to decrease as one proceeds further from the surface.

Any wave moving through a medium has a source. Somewhere along the medium, there was an initial displacement of one of the particles. For a slinky wave, it is usually the first coil that becomes displaced by the hand of a person. For a sound wave, it is usually the vibration of the vocal chords or a guitar string that sets the first particle of air in vibrational motion. At the location where the wave is introduced into the medium, the particles that are displaced from their equilibrium position always moves in the same direction as the source of the vibration. So if you wish to create a transverse wave in a slinky, then the first coil of the slinky must be displaced in a direction perpendicular to the entire slinky. Similarly, if you wish to create a longitudinal wave in a slinky, then the first coil of the slinky must be displaced in a direction parallel to the entire slinky.

POWERPOINT SLIDES - these slides are a good review 

on the types of waves

TYPES OF WAVES - EXAMPLES

Electromagnetic versus Mechanical Waves

Another way to categorize waves is on the basis of their ability or inability to transmit energy through a vacuum (i.e., empty space). Categorizing waves on this basis leads to two notable categories: electromagnetic waves and mechanical waves.

An electromagnetic wave is a wave that is capable of transmitting its energy through a vacuum (i.e., empty space). Electromagnetic waves are produced by the vibration of charged particles. Electromagnetic waves that are produced on the sun subsequently travel to Earth through the vacuum of outer space. Were it not for the ability of electromagnetic waves to travel to through a vacuum, there would undoubtedly be no life on Earth. All light waves are examples of electromagnetic waves.  

A mechanical wave is a wave that is not capable of transmitting its energy through a vacuum. Mechanical waves require a medium in order to transport their energy from one location to another. A sound wave is an example of a mechanical wave. Sound waves are incapable of traveling through a vacuum. Slinky waves, water waves, stadium waves, and jump rope waves are other examples of mechanical waves; each requires some medium in order to exist. A slinky wave requires the coils of the slinky; a water wave requires water; a stadium wave requires fans in a stadium; and a jump rope wave requires a jump rope.

The above categories represent just a few of the ways in which physicists categorize waves in order to compare and contrast their behaviors and characteristic properties. This listing of categories is not exhaustive; there are other categories as well.  

Check Your Understanding

1. A transverse wave is transporting energy from east to west. The particles of the medium will move_____.

a. east to west only

b. both eastward and westward

c. north to south only

d. both northward and southward

 2.A wave is transporting energy from left to right. The particles of the medium are moving back and forth in a leftward and rightward direction. This type of wave is known as a ____.

a. mechanical		b. electromagnetic
c. transverse		d. longitudinal

3. Describe how the fans in a stadium must move in order to produce a longitudinal stadium wave.

4. A sound wave is a mechanical wave, not an electromagnetic wave. This means that

a. particles of the medium move perpendicular to the direction of energy transport.

b. a sound wave transports its energy through a vacuum.

c. particles of the medium regularly and repeatedly oscillate about their rest position.

d. a medium is required in order for sound waves to transport energy.

 5. A science fiction film depicts inhabitants of one spaceship (in outer space) hearing the sound of a nearby spaceship as it zooms past at high speeds. Critique the physics of this film.

6. If you strike a horizontal rod vertically from above, what can be said about the waves created in the rod?

a. The particles vibrate horizontally along the direction of the rod.

b. The particles vibrate vertically, perpendicular to the direction of the rod.

c. The particles vibrate in circles, perpendicular to the direction of the rod.

d. The particles travel along the rod from the point of impact to its end.

7. Which of the following is not a characteristic of mechanical waves?

a. They consist of disturbances or oscillations of a medium.

b. They transport energy.

c. They travel in a direction that is at right angles to the direction of the particles of the medium.

d. They are created by a vibrating source.

 8. The sonar device on a fishing boat uses underwater sound to locate fish. Would you expect sonar to be a longitudinal or a transverse wave?

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1.   Answer: D

The particles would be moving back and forth in a direction perpendicular to energy transport. The waves are moving westward, so the particles move northward and southward.

2.   Answer: D

The particles are moving parallel to the direction that the wave is moving. This must be a longitudinal wave.

3.   Answer:

The fans will need to sway side to side. Thus, as the wave travels around the stadium they would be moving parallel to its direction of motion. If they rise up and sit down, then they would be creating a transverse wave.

4.  Answer: D

Mechanical waves require a medium in order to transport energy. Sound, like any mechanical wave, cannot travel through a vacuum.

5.   Answer:

This is an example of faulty physics in film. Sound is a mechanical wave and could never be transmitted through the vacuum of outer space.

6.   Answer: B

The particles vibrate in the direction of the source which creates the initial disturbance. Since the hammer was moving vertically, the particles will also vibrate vertically.

7.   Answer: C

The characteristic described in statement c is a property of all transverse waves, but not necessarily of all mechanical waves. A mechanical wave can also be longitudinal.

8.   Answer: Longitudinal

Only longitudinal waves are capable of traveling through fluids such as water. When a transverse wave tries to propagate through water, the particles of the medium slip past each other and so prevent the movement of the wave.

WAVES #3

Waves are everywhere. Whether we recognize it or not, we encounter waves on a daily basis. Sound 

• Sound waves, visible light waves, radio waves, microwaves, water waves, sine waves, cosine waves, stadium waves, earthquake waves, waves on a string, and slinky waves and are just a few of the examples of our daily encounters with waves. 
• In addition to waves, there are a variety of phenomena in our physical world that resemble waves so closely that we can describe such phenomenon as being wavelike. 
• The motion of a pendulum, the motion of a mass suspended by a spring, the motion of a child on a swing, and the "Hello, Good Morning!" wave of the hand can be thought of as wavelike phenomena. Waves (and wavelike phenomena) are everywhere!

We study the physics of waves because it provides a rich glimpse into the physical world that we seek to understand and describe as students of physics. Before beginning a formal discussion of the nature of waves, it is often useful to ponder the 

• various encounters and exposures that we have of waves. 
• Where do we see waves or examples of wavelike motion? 
• What experiences do we already have that will help us in understanding the physics of waves?

For many people, the first thought concerning waves conjures up a picture of a wave moving across the surface of an ocean, lake, pond or other body of water. The waves are created by some form of a disturbance, such as a rock thrown into the water, a duck shaking its tail in the water or a boat moving through the water. The water wave has  a crest and a trough and travels from one location to another. 

• The crest of a wave is the point on the medium that exhibits the maximum amount of positive or upward displacement from the rest position. 
• The trough of a wave is the point on the medium that exhibits the maximum amount of negative or downward displacement from the rest position.

One crest is often followed by a second crest that is often followed by a third crest. Every crest is separated by a trough to create an alternating pattern of crests and troughs. A duck or gull at rest on the surface of the water is observed to bob up-and-down at rather regular time intervals as the wave passes by. The waves may appear to be plane waves that travel together as a front in a straight-line direction, perhaps towards a sandy shore. Or the waves may be circular waves that originate from the point where the disturbances occur; such circular waves travel across the surface of the water in all directions.

The thought of waves often brings to mind a recent encounter at the baseball or football stadium when the crowd enthusiastically engaged in doing the wave. When performed with reasonably good timing, a noticeable ripple is produced that travels around the circular stadium or back and forth across a section of bleachers. The observable ripple results when a group of enthusiastic fans rise up from their seats, swing their arms up high, and then sit back down. Beginning in Section 1, the first row of fans abruptly rise up to begin the wave; as they sit back down, row 2 begins its motion; as row 2 sits back down, row 3 begins its motion. The process continues, as each consecutive row becomes involved by a momentary standing up and sitting back down. The wave is passed from row to row as each individual member of the row becomes temporarily displaced out of his or her seat, only to return to it as the wave passes by. This mental picture of a stadium wave will also provide a useful context for the discussion of the physics of wave motion.

Another picture of waves involves the movement of a slinky or similar set of coils. If a slinky is stretched out from end to end, a wave can be introduced into the slinky by either vibrating the first coil up and down vertically or back and forth horizontally. A wave will subsequently be seen traveling from one end of the slinky to the other. As the wave moves along the slinky, each individual coil is seen to move out of place and then return to its original position. The coils always move in the same direction that the first coil was vibrated. A continued vibration of the first coil results in a continued back and forth motion of the other coils. If looked at closely, one notices that the wave does not stop when it reaches the end of the slinky; rather it seems to bounce off the end and head back from where it started. A slinky wave provides an excellent mental picture of a wave and will be used in discussions and demonstrations throughout this unit.

We likely have memories from childhood of holding a long jump rope with a friend and vibrating an end up and down. The up and down vibration of the end of the rope created a disturbance of the rope that subsequently moved towards the other end. Upon reaching the opposite end, the disturbance often bounced back to return to the end we were holding. A single disturbance could be created by the single vibration of one end of the rope. On the other hand, a repeated disturbance would result in a repeated and regular vibration of the rope. The shape of the pattern formed in the rope was influenced by the frequency at which we vibrated it. If we vibrated the rope rapidly, then a short wave was created. And if we vibrated the rope less frequently (not as often), a long wave was created. While we were likely unaware of it as children, we were entering the world of the physics of waves as we contentedly played with the rope.

Then there is the "Hello, Good Morning!" wave. Whether encountered in the driveway as you begin your trip to school, on the street on the way to school, in the parking lot upon arrival to school, or in the hallway on the way to your first class, the "Hello, Good Morning!" wave provides a simple (yet excellent) example of physics in action. The simple back and forth motion of the hand is called a wave. When Mom commands us to "wave to Mr. Smith," she is telling us to raise our hand and to temporarily or even repeatedly vibrate it back and forth. The hand is raised, moved to the left, and then back to the far right and finally returns to its original position. Energy is put into the hand and the hand begins its back-and-forth vibrational motion. And we call the process of doing it "waving." Soon we will see how this simple act is representative of the nature of a physical wave.

Finally, we are familiar with microwaves and visible light waves. While we have never seen them, we believe that they exist because we have witnessed how they carry energy from one location to another. And similarly, we are familiar with radio waves and sound waves. Like microwaves, we have never seen them. Yet we believe they exist because we have witnessed the signals that they carry from one location to another and we have even learned how to tune into those signals through use of our ears or a tuner on a television or radio. Waves, as we will learn, carry energy from one location to another. And if the frequency of those waves can be changed, then we can also carry a complex signal that is capable of transmitting an idea or thought from one location to another. Perhaps this is one of the most important aspects of waves and will become a focus of our study in later units.

Waves are everywhere in nature. Our understanding of the physical world is not complete until we understand the nature, properties and behaviors of waves.