Topic #15



Topic #15(. Wave Phenomena and Energy

1. Energy Transport

2. Types of Waves

3. Wave Characteristics

4. Amplitude of a Wave

5. Wave speed in a Medium

6. Behavior of Waves at Boundaries

7. Transmitted Waves

8. Interference

9. Nodes, Antinodes, and Standing Waves

10. The Law of Reflection

11. Refraction of Waves

12. Diffraction and Interference of Waves

Notes should include:

Energy Transport: There are two methods for transporting energy. The first way is to transfer matter between two points. A hammer can transfer energy to a nail. Electrons moving through a circuit carry energy between two points. Where matter is concerned, a force acting over a distance results in an object moving. This means that work is done and work is equal to a change in energy. The second way is by means of waves. Waves are a means of transmitting energy between two points. Water, sound, and light waves are examples of waves which carry energy. Waves have some general characteristics such as reflection and refraction.

Types of Waves: Some types of waves require a medium (a material) to pass through. These types of waves are merely a disturbance passing along through the medium. Since the disturbance requires the movement of particles work is done and energy is transferred through the medium. Mechanical waves are the kind of waves that require a medium. A rope or a spring are examples of a medium where the energy is transferred from particle to particle. There is a second type of waves called electromagnetic waves. These types of waves require no medium to travel through. Visible light waves, microwaves, radio waves, and x-rays are examples of electromagnetic waves.

Mechanical waves are often divided into three kinds of waves. The first type is the transverse wave. In this type of wave the particles in the medium vibrate in a perpendicular direction with respect to the forward motion of the wave. You can produce this type of wave along a rope or a spring. The second type of wave is the longitudinal wave. In this type of wave the particles in the medium tend to move parallel to the direction of the wave. These waves might be thought of as compression waves with the medium contracting and then expanding again as the wave passes through points in the medium. Sound waves are examples of this sort of wave. You can also produce this kind of wave along a stretched spring like a slinky by compressing several coils and then letting this wave of compressed coils move from one end of the spring to the other. The third type of waves is the surface wave. Water waves traveling along the surface of a body of water are examples of such a wave. As this wave travels across the surface of the medium the particles in the medium both move up and down and forwards and backwards as the wave passes by each position. If you track an individual particle as the wave passes by, it appears to travel in a circle, quickly returning to its starting position as the wave passes by. A single disturbance in a medium, usually thought of as a single wave by most people, is called a pulse. A periodic wave is a series of pulses generated in equal amounts of time, such that, wave pulse after wave pulse passes a certain point in equal intervals of time. If a continuing series of wave pulses are generated by a (simple harmonic motion, the waves produced are continuous periodic waves and form what is called a wave train.

Wave Characteristics: Regardless of the type of wave, all waves have certain characteristics in common. Throughout much of the information in these notes we will use a simple sine wave as the model for the wave being described. All waves have crests and troughs. A crest is the highest point in a wave pulse while the trough is the lowest point in a wave pulse. Waves have wavelength (symbol l , this is the Greek alphabet letter called lambda). This is the distance between any two identical points on two consecutive waves. Perhaps an easier way to remember this term is to describe it as the distance between two consecutive waves' crests. Wavelength is usually measured in meters. Waves have frequency (symbol f ). This is the number of wave pulses that pass by a specified point each second. Frequency is usually measured using the unit hertz. One hertz is equal to one wave per second. The reciprocal of frequency is the period (symbol T ). The period of a wave is the time for a single wave pulse to pass a specified point. It is usually expressed in seconds per wave. For example, if the period of a wave is known to be 0.5 seconds per wave, then the frequency of the wave is 1 / 0.5 seconds per wave, which equals 2 waves per second.

The velocity of a wave is the product of the wave's wavelength and its frequency. Using variable symbols the equation looks like v = f l. You should take notice of the fact that while velocity varies directly with either frequency or wavelength, frequency and wavelength vary inversely with respect to one another. Any of these relationships assumes that the third variable remains constant.

Amplitude of a Wave: When we study the model we are using for a wave, a sine wave, we notice that there is another measurement which we could call wave height that we have yet to describe or define. This measurement is formally called amplitude. The definition of amplitude is that it is the maximum displacement of the wave pulse with respect to some defined equilibrium position. This is sometimes also called a rest position. For example, visuallize a guitar string. If unplucked, the string remains motionless in its equilibrium or rest position. On the other hand, if the string is plucked, the string is pulled away from its rest position and then released. The string then vibrates back and forth slowly being dampened by the tension in the string. Without tension in the string, it would not vibrate back and forth. The greater the force used to pluck the string the further it is pulled back and the louder the sound will tend to be as it moves back and forth disturbing the air molecules around it. We associate the loudness of the string with the amplitude of the string's distortion upon being plucked. The more energy you put into generating a wave the greater the amplitude of the wave. A wave with a greater amplitude than another wave has more energy and therefore transmits more energy as it moves a long. A wave with more amplitude can do more work than a wave with less amplitude. As an example, visualize two water waves striking the shore. If one has a large amplitude while the other has a noticeably smaller amplitude, which one is "more capable" of knocking you down? In the case of mechanical waves the energy transmitted by the wave varies directly with square of the wave's amplitude.

Wave Speed in a Medium: The speed of a wave through a medium is usually described as being constant. A change in the wavelength or the frequency changes the other variable respectively but has no noticeable impact upon the speed of the wave. Amplitude is not figured into the speed of a wave, because it only affects how much energy the wave carries along and not how fast it is moving that energy.

(Behavior of Waves at Boundaries: You may be surprised to learn that the motion of a wave may be affected as it meets with or crosses over a boundary. When a wave meets a boundary, some of it, but not necessarily all of it, will be reflected. The amount that is reflected off of the boundary is dependent upon how different the two media that meet at the boundary. Also whether a wave is reflected back upwards (also called erect) or the wave is reflected back downwards (also called inverted) depends on how the two mediums characteristics compare. For example, if you attached a rope to a wall and stood with the rope stretched out with the other end in your hand, what would happen to a wave pulse you send towards the wall. You should expect to see almost 100% of the pulse reflecting back towards you and the returning pulse should be inverted. This would happen because the wall is very rigid, much like a medium is very dense, while the rope is not in anyway rigid, and by comparison to the wall it is not very dense at all.

Transmitted Waves: As a wave passes from one medium into another, it changes speed. The frequency of the wave remains the same, but the wavelength changes. If the speed increases, the wavelength of the wave increases. If the speed of the wave decreases, the wavelength of the wave decreases.

Interference: If more than one wave is passing through a medium, they may vary likely intersect. At a point of intersection they will affect one another's amplitude by summation. This may result in a combined amplitude of greater or lesser value than the amplitude of either of the waves independent of each other. This addition of two or more waves to establish the position of the medium at a specified point is called the principle of superposition. This principle says that where two or more waves meet, the displacement of the medium is the sum of the displacements of the individual waves. When waves intersect traveling through the same medium they experience interference. Depending on how synchronized the waves are, the effect may be either result in constructive or destructive interference.

Nodes, Antinodes, and Standing Waves: Sometimes the interference caused by two waves passing through one another results in one or more points in the medium where the waves pass along through the medium without disturbing it. These points are called nodes. At a node the medium remains undisturbed, even though on either side of the node the medium is moving up and down as wave pulses pass by. A node is the result of destructive interference. Sometimes the interference has the opposite effect and the amplitude of the combined waves reaches a maximum. Any points at which the displacement of combined waves is at its maximum possible value are called antinodes. Try to visualize a string attached to a stationary platform, such as a wall, heavy table, etc.. Now imagine the rope is pulled out straight with the unattached end in your hand. Now imagine that you are producing a succession of identical wave pulses. Very soon you will have these wave pulses moving away from you and the reflection of these waves moving back along the rope towards you. If very little resistance force is present the two oncoming wave trains will move towards and through each other with equal frequencies, wavelengths, and amplitudes. If these two waves are in phase they will produce a standing wave. This sort of wave makes the string appear to vibrate in sections between the nodes that have formed. In this situation the nodes and antinodes remain stationary making the waves appear to be standing still. They are not, however, and if you stop generating waves, the rope becomes stationary once again without any wave trains.

The Law of Reflection: The law of reflection states that when waves are reflected from a barrier, the angle of reflection is equal to the angle of incident. Both angles are measured from the normal (which is an imaginary line perpendicular to the surface of the barrier at the point where the wave strikes the barrier.

Refraction of Waves: Refraction is the change in direction of a wave at the boundary between two media. This apparent bending occurs if the angle of incident measured off of the normal (see the definition above) is greater than zero.

Diffraction and Interference of Waves: Diffraction is the bending of a wave around an obstacle placed in its path. Water waves are seen to bend around breakwaters that are used around harbors. Light and sound waves are seen and heard respectively around corners. When waves such as water waves are sent through openings narrower then their own wavelengths, the diffraction they experience as they emerge on the other side of the slit (opening) results in the wave moving outwards as a circular wave emitted from the slit. When two such waves pass through one another interference patterns form as a result of constructive and destructive interference. The anitnodal points line up in the interference pattern and form what are called nodal lines. This pattern can be easily seen in photographs taken of ripple tanks where the surface water waves are passing through a double slit apparatus producing two interfering circular waves. What do you think this might mean for the design of the seating arrangement in a theater, if such nodal lines appear in diffracted sound waves?

Vocabulary: wave, wave pulse, continuous wave, transverse wave, longitudinal wave, surface wave, trough, crest, wavelength, frequency, incident wave, reflective wave, principle of superposition, interference, destructive interference, node, constructive interference, antinode, standing wave, law of reflection, refraction, diffraction

Skills to be learned:

Describe wave phenomena and wave concepts

Solve wave problems involving velocity, period, frequency and wavelength.

Describe the behavior of reflected waves given information about the wave pulse(s) and

the media through which the wave travels and / or reflects off of.

Describe the phenomena of reflection, refraction and diffraction.

Assignments:

Textbook: Read / Study / Learn Chapter 14, sections 14.1 and 14.2

WB Exercise(s): PS#14-1

Activities: TBA

Resources:

This Handout and the Overhead and Board Notes discussed in class

Textbook: Chapter 14

WB Lessons and Problem Set(s)

- “Waves Phenomena and Energy”

( / Wave Phenomena and Energy

( / Wave Phenomena and Energy

( / Wave Phenomena and Energy

( / Wave Phenomena and Energy

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