What is a Wave?A wave is a series of pulses or disturbances created in a medium from one location to another. To start a wave, the first particle is displaced or moved out of position. For example, a slinky is in equilibrium or rest position when you stretch it. The coils are equally spread out. But when a pulse occurs, the coils are unevenly spread and vibrate. After the pulses occur, the slinky eventually goes back to its original position. A medium is a substance or material that carries the wave. The news media refers to various institutions (newspaper offices, television stations, radio stations, etc.) within our society that carry the news from one location to another. The newsmoves throughthe media. The media doesn't make the news and the media isn't the same as the news. The news media is thethingthat carries the news from its source to various locations, just like how the medium carries the wave through the slinky.The medium is made of parts that are capable of interacting with each other. The interactions of one particle with the next particle allow the disturbance to travel through the medium.For example in the slinky, the first coil becomes disturbed and begins to push or pull on the second coil; this push or pull on the secondcoil will displace the second coil from its equilibrium position. As the second coil becomes displaced, it begins to push or pull on the third coil and so on. The particles apply force to the next particle. As a disturbance moves through a medium from one particle to the next particle, energy is being transported from one end of the medium to the other. In a slinky wave, a person gives energy to the first coil by doing work. When the first coil returns to its original position, it has the same amount of energy as it had before the pulse occurred. A wave transports its energy without transporting matter. Waves move through an ocean or lake and the water always returns to its rest position. Energy is transported through the medium, yet the water molecules are not transported. This is proof that there is still water in the middle of the ocean. The water has not moved from the middle of the ocean to the shore. In a stadium wave, the fans do not get out of their seats and walk around the stadium. It would be silly (and embarrassing) for any fan to do this. In a stadium wave, each fan rises up and returns to the original seat. The disturbance moves through the stadium, yet the fans are not transported.When a wave is present in a medium (that is, when there is a disturbance moving through a medium), the individual particles of the medium are only temporarily displaced from their rest position. There is always a force acting upon the particles that restores them to their original position. In a slinky wave, each coil of the slinky ultimately returns to its original position. In a water wave, each molecule of the water ultimately returns to its original position. And in astadium wave, each fan in the bleacher ultimately returns to its original position. It is for this reason, that a wave is said to involve the movement of a disturbance without the movement of matter. The particles of the medium (water molecules, slinky coils, stadium fans) simply vibrate about a fixed position as the pattern of the disturbance moves from one location to another location.Waves are said to be anenergy transport phenomenon. As a disturbance moves through a medium from one particle to its adjacent particle, energy is being transported from one end of the medium to the other. In a slinky wave, a person imparts energy to the first coil by doing work upon it. The first coil receives a large amount of energy that it subsequently transfers to the second coil. When the first coil returns to its original position, it possesses the same amount of energy as it had before it was displaced. The first coil transferred its energy to the second coil. The second coil then has a large amount of energy that it subsequently transfers to the third coil. When the second coil returns to its original position, it possesses the same amount of energy as it had before it was displaced. The third coil has received the energy of the second coil. This process of energy transfer continues as each coil interacts with its neighbor. In this manner, energy is transported from one end of the slinky to the other, from its source to another location.

Types of WavesAtransverse waveis a wave where particles of the medium move in a direction that isperpendicularto the direction that the wave moves. If a slinky is stretched out in a horizontal direction and 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. The particles of the medium move perpendicular to the direction that the pulse moves. This type of wave is a transverse wave. The particle motion of Transverse waves is always perpendicularto wave motion. Alongitudinal waveis a wave in which particles of the medium move in a directionparallelto 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 beingparallelto wave motion. These waves travel in depths of the ocean. The fans will need to sway side to side to move in stadium to produce a longitudinal wave. 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.The waves that travel along the surface of the oceans are surface waves. Asurface waveis a wave where 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.Anelectromagnetic waveis a wave that can transmit its energy through a vacuum (i.e., empty space). Electromagnetic waves are produced by the vibration of charged particles. Electromagnetic waves are produced on the sun after traveling to Earth through the vacuum of outer space. If electromagnetic waves could not travel to Earth through a vacuum, there would undoubtedly be no life on Earth. All light waves are examples of electromagnetic waves, including light waves and sound waves.Amechanical waveis a wave that cant transmit 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 cant travel through a vacuum. Slinky waves, water waves, stadium waves, andjump rope wavesare other examples that require 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.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 hasa crest and a troughand travels from one location to another. 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 afrontin 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. These mental pictures of water waves are useful for understanding the nature of a wave and will be revisited later when we begin our formal discussion of the topic. If you strike a horizontal rod vertically from above, what can be said about the waves created in the rod?The particles vibrate vertically, perpendicular to the direction of the rod. 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. Acompressionis 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. Ararefactionis 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.

Wavelength, AmplitudeA 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 tofreezethe 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 theequilibrium or rest positionof 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. Thecrestof 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 the wave. Thetroughof 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 amplitudeof 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 distancefrom 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. Thewavelengthof 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 awave 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.

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 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. The amplitude of the wave in the diagram above is given by letter D. The amplitude is the distance from rest to crest or from rest to trough.

3. Indicate the interval that represents one full wavelength.

Answer: C to G because 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.Frequency and PeriodSuppose 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. Thefrequencyof 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 "Howfrequentlydo you mow the lawn during the summer months?" Of course the question is an inquiry abouthow oftenthe 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 quantityfrequencywould have units of cycles/second, waves/second, vibrations/second, or something/second. Another unit for frequency is theHertz(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.Periodrefers to the time that it takes to do something. When an event occurs repeatedly, then we say that the event isperiodicand refer to the time for the event to repeat itself as the period. Theperiodof 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 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 a 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 symbolfis used for frequency and the symbolTis used for period, these equations are also expressed as:

1. A wave is introduced into a thin wire held tight at each end. It has 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.

Answer:0.0195 secHere is an example of a problem with a lot of extraneous information. The period is simply the reciprocal of the frequency. In this case, the period is 1/(51.2 Hz) which is 0.0195 seconds.2. 2. Frieda the fly flaps its wings back and forth 121 times each second. The period of the wing flapping is ____ sec.

Answer: 0.00826 seconds. The quantity 121 times/second is the frequency. The period is the reciprocal of the frequency. T=1/(121 Hz) = 0.00826 seconds

3. A tennis coach paces back and forth along the sideline 10 times in 2 minutes. The frequency of her pacing is ________ Hz.

a. 5.0 b. 0.2 c. 0.12 d. 0.083Answer: D Frequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second. In this case, there are 10 cycles per 2 minutes (also known as 10 cycles per 120 seconds). So the frequency is f =10 cycles / 120 s = 0.0833 cycles/s

4. Non-digital clocks (which are becoming more rare) have a second hand that rotates around in a regular and repeating fashion. The frequency of rotation of a second hand on a clock is _______ Hz.a. 1/60b. 1/12c. 1/2

d. 1e. 60

Answer:AFrequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second. In this case, there is 1 cycle per 60 seconds. So the frequency isf = 1 cycle / (60 s) = (1 / 60) Hz5. Olive Udadi accompanies her father to the park for an afternoon of fun. While there, she hops on the swing and begins a motion characterized by a complete back-and-forth cycle every 2 seconds. The frequency of swing is _________.a. 0.5 Hzb. 1 Hzc. 2 Hz

Answer:AFrequency refers to the number of occurrences of a periodic event per time and is measured in cycles/second. In this case, there is 1 cycle per 2 seconds. So the frequency is 1 cycles/2 s = 0.5 Hz.

6. In problem #5, the period of swing is __________.a. 0.5 secondb. 1 secondc. 2 second

Answer:CPeriod refers to the time for something to happen. In this case, the period is the time for one complete swing - given as 2 seconds.

7. A period of 5.0 seconds corresponds to a frequency of ________ Hertz.a. 0.2b. 0.5c. 0.02

d. 0.05e. 0.002

Answer:AFrequency is the reciprocal of the period. The period is 5 seconds, so the frequency is 1/(5 s) = 0.20 Hz.8. A common physics lab involves the study of the oscillations of a pendulum. If a pendulum makes 33 complete back-and-forth cycles of vibration in 11 seconds, then its period is ______.Answer:0.33 secondPeriod refers to the time for something to happen and is measured in seconds/cycle. In this case, there are 11 seconds per 33 vibrational cycles. Thus the period is (11 s) / (33 cycles) = 0.33 seconds.

9. A child in a swing makes one complete back and forth motion in 3.2 seconds. This statement provides information about the child'sa. speedb. frequencyc. periodAnswer:B and CWe now know that the period is 3.2 seconds and that the frequency is 0.31 Hz.

10. The period of the sound wave produced by a 440 Hertz tuning fork is ___________.Answer:0.00227 secondsGIVEN: f = 440 HzFind TT = 1 / f = 1 / (440 HZ) = 0.00227 s11. As the frequency of a wave increases, the period of the wave ___________.a. decreasesb. increasesc. remains the sameAnswer:APeriod is the reciprocal of the frequency. So as f increases, 1 / f decreases.The Speed of a WaveAwave is a disturbancethat moves along a medium from one end to the other. If one watches an ocean wave moving along the medium (the ocean water), one can observe that the crest of the wave is moving from one location to another over a given interval of time. The crest is observed tocoverdistance. Thespeedof an object refers to how fast an object is moving and is usually expressed as the distance traveled per time of travel. In the case of a wave, the speed is the distance traveled by a given point on the wave (such as a crest) in a given interval of time. In equation form,

If the crest of an ocean wave moves a distance of 20 meters in 10 seconds, then the speed of the ocean wave is 2.0 m/s. On the other hand, if the crest of an ocean wave moves a distance of 25 meters in 10 seconds (the same amount of time), then the speed of this ocean wave is 2.5 m/s. The faster wave travels a greater distance in the same amount of time.he diagrams at the right show several "snapshots" of the production of a wave within a rope. The motion of the disturbance along the medium after every one-fourth of a period is depicted. Observe that in the time it takes from the first to the last snapshot, the hand has made one complete back-and-forth motion. Aperiodhas elapsed. Observe that during this same amount of time, the leading edge of the disturbance has moved a distance equal to one complete wavelength. So in a time of one period, the wave has moved a distance of one wavelength. Combining this information with the equation for speed (speed = distance/time), it can be said that the speed of a wave is also the wavelength/period.

Since the period is the reciprocal of the frequency, the expression 1/f can be substituted into the above equation for period. Rearranging the equation yields a new equation of the form:Speed = Wavelength FrequencyThe above equation is known as the wave equation. It states the mathematical relationship between the speed (v) of a wave and its wavelength () and frequency (f). Using the symbolsv, , andf, the equation can be rewritten asv = f

1. As the wavelength of a wave in a uniform medium increases, its speed will _____.a. decreaseb. increasec. remain the same

Answer:CIn rows 1 and 2, the wavelength was altered but the speed remained the same. The same can be said about rows 3 and 4 and rows 5 and 6. The speed of a wave is not affected by the wavelength of the wave.2. As the wavelength of a wave in a uniform medium increases, its frequency will _____.a. decreaseb. increasec. remain the same

Answer:AIn rows 1 and 2, the wavelength was increased and the frequency was decreased. Wavelength and frequency are inversely proportional to each other.

3. The speed of a wave depends upon (i.e., is causally affected by) ...a. the properties of the medium through which the wave travelsb. the wavelength of the wave.c. the frequency of the wave.d. both the wavelength and the frequency of the wave.Answer:AWhenever the medium is the same, the speed of the wave is the same. However, when the medium changes, the speed changes. The speed of these waves were dependent upon the properties of the medium.The above example illustrates how to use the wave equation to solve mathematical problems. It also illustrates the principle thatwave speed is dependent upon medium propertiesand independent of wave properties. Even though the wave speed is calculated by multiplying wavelength by frequency, an alteration in wavelength does not affect wave speed. Rather, an alteration in wavelength affects the frequency in an inverse manner. A doubling of the wavelength results in a halving of the frequency; yet the wave speed is not changed.Check Your Understanding1. Two waves on identical strings have frequencies in a ratio of 2 to 1. If their wave speeds are the same, then how do their wavelengths compare?a. 2:1b. 1:2c. 4:1d. 1:4

Answer:BFrequency and wavelength are inversely proportional to each other. The wave with the greatest frequency has the shortest wavelength. Twice the frequency means one-half the wavelength. For this reason, the wavelength ratio is the inverse of the frequency ratio.

2. Mac and Tosh stand 8 meters apart and demonstrate the motion of a transverse wave on a snakey. The wave e can be described as having a vertical distance of 32 cm from a trough to a crest, a frequency of 2.4 Hz, and a horizontal distance of 48 cm from a crest to the nearest trough. Determine the amplitude, period, and wavelength and speed of such a wave.Amplitude = 16 cm(Amplitude is the distance from the rest position to the crest position which is half the vertical distance from a trough to a crest.)Wavelength = 96 cm(Wavelength is the distance from crest to crest, which is twice the horizontal distance from crest to nearest trough.)Period = 0.42 s(The period is the reciprocal of the frequency. T = 1 / f)Speed = 230 cm/s(The speed of a wave is calculated as the product of the frequency times the wavelength.)

3. Dawn and Aram have stretched a slinky between them and begin experimenting with waves. As the frequency of the waves is doubled,a. the wavelength is halved and the speed remains constantb. the wavelength remains constant and the speed is doubledc. both the wavelength and the speed are halved.d. both the wavelength and the speed remain constant.Answer:ADoubling the frequency will not alter the wave speed. Rather, it will halve the wavelength. Wavelength and frequency are inversely related.

4. A ruby-throated hummingbird beats its wings at a rate of about 70 wing beats per second.a. What is the frequency in Hertz of the sound wave?b. Assuming the sound wave moves with a velocity of 350 m/s, what is the wavelength of the wave?

Answer:f = 70 Hzand = 5.0 mThe frequency is given and the wavelength is the v/f ratio.

5. Ocean waves are observed to travel along the water surface during a developing storm. A Coast Guard weather station observes that there is a vertical distance from high point to low point of 4.6 meters and a horizontal distance of 8.6 meters between adjacent crests. The waves splash into the station once every 6.2 seconds. Determine the frequency and the speed of these waves.The wavelength is 8.6 meters and the period is 6.2 seconds.The frequency can be determined from the period. If T = 6.2 s, thenf =1 /T = 1 / (6.2 s)f = 0.161 HzNow find speed using the v = f equation.v = f = (0.161 Hz) (8.6 m)v = 1.4 m/s

6. Two boats are anchored 4 meters apart. They bob up and down, returning to the same up position every 3 seconds. When one is up the other is down. There are never any wave crests between the boats. Calculate the speed of the waves.The diagram is helpful. The wavelength must be 8 meters (see diagram).The period is 3 seconds so the frequency is 1 / T or 0.333 Hz.Now use speed = f wavelength Substituting and solving for v, you will get2.67 m/s.

Wave PhenomenonAs a wave travels through a medium, it will often reach the end of the medium and encounter an obstacle or perhaps another medium through which it could travel. Oneexampleof this has already been mentioned in Lesson 2. A sound wave is known to reflect off canyon walls and other obstacles to produce an echo. A sound wave traveling through air within a canyon reflects off the canyon wall and returns to its original source. What affect does reflection have upon a wave? Does reflection of a wave affect the speed of the wave? Does reflection of a wave affect the wavelength and frequency of the wave? Does reflection of a wave affect the amplitude of the wave? Or does reflection affect other properties and characteristics of a wave's motion? The behavior of a wave (or pulse) upon reaching the end of a medium is referred to asboundary behavior. When one medium ends, another medium begins; the interface of the two media is referred to as theboundaryand the behavior of a wave at that boundary is described as its boundary behavior. The questions that are listed above are the types of questions we seek to answer when we investigate the boundary behavior of waves.Fixed End ReflectionFirst consider an elastic rope stretched from end to end. One end will be securely attached to a pole on a lab bench while the other end will be held in the hand in order to introduce pulses into the medium. Because the right end of the rope is attached to a pole (which is attached to a lab bench) (which is attached to the floor that is attached to the building that is attached to the Earth), the lastparticleof the rope will be unable to move when a disturbance reaches it. This end of the rope is referred to as afixed end.If a pulse is introduced at the left end of the rope, it will travel through the rope towards the right end of the medium. This pulse is called theincident pulsesince it is incident towards (i.e., approaching) the boundary with the pole. When the incident pulse reaches the boundary, two things occur: A portion of the energy carried by the pulse is reflected and returns towards the left end of the rope. The disturbance that returns to the left after bouncing off the pole is known as thereflected pulse. A portion of the energy carried by the pulse istransmittedto the pole, causing the pole to vibrate.Because the vibrations of the pole are not visibly obvious, the energy transmitted to it is not typically discussed. The focus of the discussion will be on the reflected pulse. What characteristics and properties could describe its motion?When one observes the reflected pulse off the fixed end, there are several notable observations. First the reflected pulse isinverted. That is, if an upward displaced pulse is incident towards a fixed end boundary, it will reflect and return as a downward displaced pulse. Similarly, if a downward displaced pulse is incident towards a fixed end boundary, it will reflect and return as an upward displaced pulse.

The inversion of the reflected pulse can be explained by returning to our conceptions of the nature of a mechanical wave. When a crest reaches the end of a medium ("medium A"), the last particle of the medium A receives an upward displacement. This particle is attached to the first particle of the other medium ("medium B") on the other side of the boundary. As the last particle of medium A pulls upwards on the first particle of medium B, the first particle of medium B pulls downwards on the last particle of medium A. This is merely Newtons. For every action, there is an equal and opposite reaction. The upward pull on the first particle of medium B has little effect upon this particle due to the large mass of the pole and the lab bench to which it is attached. The effect of the downward pull on the last particle of medium A (a pull that is in turn transmitted to the other particles) results in causing the upward displacement to become a downward displacement. The upward displaced incident pulse thus returns as a downward displaced reflected pulse. It is important to note that it is theheavinessof the pole and the lab bench relative to the rope that causes the rope to become inverted upon interacting with the wall. When two media interact by exerting pushes and pulls upon each other, the most massive mediumwins the interaction. Just like in arm wrestling, the medium that loses receives a change in its state of motion.Other notable characteristics of the reflected pulse include: The speed of the reflected pulse is the same as the speed of the incident pulse. The wavelength of the reflected pulse is the same as the wavelength of the incident pulse. The amplitude of the reflected pulse is less than the amplitude of the incident pulse.Of course, it is not surprising that the speed of the incident and reflected pulse are identical since the two pulses are traveling in the same medium. Since the speed of a wave (or pulse) is dependent upon the medium through which it travels,two pulses in the same medium will have the same speed. A similar line of reasoning explains why the incident and reflected pulses have the same wavelength. Every particle within the rope will have the same frequency. Being connected to one another, they must vibrate at the same frequency. Since the wavelength of a wave depends upon the frequency and the speed, two waves having the same frequency and the same speed must also have the same wavelength. Finally, the amplitude of the reflected pulse is less than the amplitude of the incident pulse since some of the energy of the pulse was transmitted into the pole at the boundary. The reflected pulse is carrying less energy away from the boundary compared to the energy that the incident pulse carried towards the boundary. Since the amplitude of a pulse is indicative of the energy carried by the pulse, the reflected pulse has a smaller amplitude than the incident pulse.Free End ReflectionNow consider what would happen if the end of the rope were free to move. Instead of being securely attached to a lab pole, suppose it is attached to a ring that is loosely fit around the pole. Because the right end of the rope is no longer secured to the pole, the lastparticleof the rope will be able to move when a disturbance reaches it. This end of the rope is referred to as afree end.Once more if a pulse is introduced at the left end of the rope, it will travel through the rope towards the right end of the medium. When the incident pulse reaches the end of the medium, the last particle of the rope can no longer interact with the first particle of the pole. Since the rope and pole are no longer attached and interconnected, they will slide past each other. So when a crest reaches the end of the rope, the last particle of the rope receives the same upward displacement; only now there is no adjoining particle to pull downward upon the last particle of the rope to cause it to be inverted. The result is that the reflected pulse is not inverted. When an upward displaced pulse is incident upon a free end, it returns as an upward displaced pulse after reflection. And when a downward displaced pulse is incident upon a free end, it returns as a downward displaced pulse after reflection. Inversion is not observed in free end reflection.

Transmission of a Pulse Across a Boundary from Less to More DenseLet's consider a thin rope attached to a thick rope, with each rope held at opposite ends by people. And suppose that a pulse is introduced by the person holding the end of the thin rope. If this is the case, there will be an incident pulse traveling in the less dense medium (the thin rope) towards the boundary with a more dense medium (the thick rope).

Upon reaching the boundary, the usual two behaviors will occur. A portion of the energy carried by the incident pulse is reflected and returns towards the left end of the thin rope. The disturbance that returns to the left after bouncing off the boundary is known as thereflected pulse. A portion of the energy carried by the incident pulse is transmitted into the thick rope. The disturbance that continues moving to the right is known as thetransmitted pulse.The reflected pulse will be found to be inverted in situations such as this. During the interaction between the two media at the boundary, the first particle of the more dense medium overpowers the smaller mass of the last particle of the less dense medium. This causes an upward displaced pulse to become a downward displaced pulse. The more dense medium on the other hand was at rest prior to the interaction. The first particle of this medium receives an upward pull when the incident pulse reaches the boundary. Since the more dense medium was originally at rest, an upward pull can do nothing but cause an upward displacement. For this reason, the transmitted pulse is not inverted. In fact, transmitted pulses can never be inverted. Since the particles in this medium are originally at rest, any change in their state of motion would be in the same direction as the displacement of the particles of the incident pulse.TheBeforeandAftersnapshots of the two media are shown in the diagram below.

Comparisons can also be made between the characteristics of the transmitted pulse and those of the reflected pulse. Once more there are several noteworthy characteristics. The transmitted pulse (in the more dense medium) is traveling slower than the reflected pulse (in the less dense medium). The transmitted pulse (in the more dense medium) has a smaller wavelength than the reflected pulse (in the less dense medium). The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse.One goal of physics is to use physical models and ideas to explain the observations made of the physical world. So how can these three characteristics be explained? First recall fromLesson 2that the speed of a wave is dependent upon the properties of the medium. In this case, the transmitted and reflected pulses are traveling in two distinctly different media. Waves always travel fastest in the least dense medium. Thus, the reflected pulse will be traveling faster than the transmitted pulse. Second, particles in the more dense medium will be vibrating with the same frequency as particles in the less dense medium. Since the transmitted pulse was introduced into the more dense medium by the vibrations of particles in the less dense medium, they must be vibrating at the same frequency. So the reflected and transmitted pulses have the different speeds but the same frequency. Since the wavelength of a wave depends upon the frequency and the speed, the wave with the greatest speed must also have the greatest wavelength. Finally, the incident and the reflected pulse share the same medium. Since the two pulses are in the same medium, they will have the same speed. Since the reflected pulse was created by the vibrations of the incident pulse, they will have the same frequency. And two waves with the same speed and the same frequency must also have the same wavelength.Transmission of a Pulse Across a Boundary from More to Less DenseFinally, let's consider a thick rope attached to a thin rope, with the incident pulse originating in the thick rope. If this is the case, there will be an incident pulse traveling in the more dense medium (thick rope) towards the boundary with a less dense medium (thin rope). Once again there will be partial reflection and partial transmission at the boundary. The reflected pulse in this situation will not be inverted. Similarly, the transmitted pulse is not inverted (as is always the case). Since the incident pulse is in a heavier medium, when it reaches the boundary, the first particle of the less dense medium does not have sufficient mass to overpower the last particle of the more dense medium. The result is that an upward displaced pulse incident towards the boundary will reflect as an upward displaced pulse. For the same reasons, a downward displaced pulse incident towards the boundary will reflect as a downward displaced pulse.TheBeforeandAftersnapshots of the two media are shown in the diagram below.

Comparisons between the characteristics of the transmitted pulse and the reflected pulse lead to the following observations. The transmitted pulse (in the less dense medium) is traveling faster than the reflected pulse (in the more dense medium). The transmitted pulse (in the less dense medium) has a larger wavelength than the reflected pulse (in the more dense medium). The speed and the wavelength of the reflected pulse are the same as the speed and the wavelength of the incident pulse.These three observations are explained using the same logic as usedabove.

Check Your UnderstandingCase 1: A pulse in a more dense medium is traveling towards the boundary with a less dense medium.

1. The reflected pulse in medium 1 ________ (will, will not) be inverted because _______.2. The speed of the transmitted pulse will be ___________ (greater than, less than, the same as) the speed of the incident pulse.3. The speed of the reflected pulse will be ______________ (greater than, less than, the same as) the speed of the incident pulse.4. The wavelength of the transmitted pulse will be ___________ (greater than, less than, the same as) the wavelength of the incident pulse.5. The frequency of the transmitted pulse will be ___________ (greater than, less than, the same as) the frequency of the incident pulse.Answers1. will not... because the reflection occurs for a wave in a more dense medium heading towards a less dense medium.2. faster3. the same as4. greater than5. the same asCase 2: A pulse in a less dense medium is traveling towards the boundary with a more dense medium.

6. The reflected pulse in medium 1 ________ (will, will not) be inverted because _____________.7. The speed of the transmitted pulse will be ___________ (greater than, less than, the same as) the speed of the incident pulse.8. The speed of the reflected pulse will be ______________ (greater than, less than, the same as) the speed of the incident pulse.9. The wavelength of the transmitted pulse will be ___________ (greater than, less than, the same as) the wavelength of the incident pulse.10. The frequency of the transmitted pulse will be ___________ (greater than, less than, the same as) the frequency of the incident pulse.Answers6. will... because the reflection occurs for a wave in a less dense medium heading towards a more dense medium.7. less than8. the same as9. less than10. the same as

Reflection, Refraction, DefractionA linear object attached to an oscillator bobs back and forth within the water, it becomes a source ofstraightwaves. These straight waves have alternating crests and troughs. As viewed on the sheet of paper below the tank, the crests are the dark lines stretching across the paper and the troughs are the bright lines.These waves will travel through the water until they encounter an obstacle - such as the wall of the tank or an object placed within the water. The diagram at the right depicts a series of straight waves approaching a long barrier extending at an angle across the tank of water. The direction that these wavefronts (straight-line crests) are traveling through the water is represented by the blue arrow. The blue arrow is called arayand is drawn perpendicular to the wavefronts. Upon reaching the barrier placed within the water, these waves bounce off the water and head in a different direction. The diagram below shows the reflected wavefronts and the reflected ray. Regardless of the angle at which the wavefronts approach the barrier, one general law of reflection holds true: the waves will always reflect in such a way that the angle at which they approach the barrier equals the angle at which they reflect off the barrier. This is known as thelaw of reflection. The discussion above pertains to the reflection of waves off of straight surfaces. But what if the surface is curved, perhaps in the shape of a parabola? What generalizations can be made for the reflection of water waves off parabolic surfaces? Suppose that a rubber tube having the shape of a parabola is placed within the water. The diagram at the right depicts such a parabolic barrier in the ripple tank. Several wavefronts are approaching the barrier; the ray is drawn for these wavefronts. Upon reflection off the parabolic barrier, the water waves will change direction and head towards a point. This is depicted in the diagram below. It is as though all the energy being carried by the water waves is converged at a single point - the point is known as the focal point. After passing through the focal point, the waves spread out through the water. Refraction of WavesReflection involves a change in direction of waves when they bounce off a barrier.Refractionof waves involves a change in the direction of waves as they pass from one medium to another. Refraction, or the bending of the path of the waves, is accompanied by a change in speed and wavelength of the waves. InLesson 2, it was mentioned that the speed of a wave is dependent upon the properties of the medium through which the waves travel. So if the medium (and its properties) is changed, the speed of the waves is changed. The most significant property of water that would affect the speed of waves traveling on its surface is the depth of the water. Water waves travel fastest when the medium is the deepest. Thus, if water waves are passing from deep water into shallow water, they will slow down. And as mentioned inthe previous section of Lesson 3, this decrease in speed will also be accompanied by a decrease in wavelength. So as water waves are transmitted from deep water into shallow water, the speed decreases,the wavelength decreases, and the direction changes.This boundary behavior of water waves can be observed in a ripple tank if the tank is partitioned into a deep and a shallow section. If a pane of glass is placed in the bottom of the tank, one part of the tank will be deep and the other part of the tank will be shallow. Waves traveling from the deep end to the shallow end can be seen to refract (i.e., bend), decrease wavelength (the wavefronts get closer together), and slow down (they take a longer time to travel the same distance). When traveling from deep water to shallow water, the waves are seen to bend in such a manner that they seem to be traveling more perpendicular to the surface. If traveling from shallow water to deep water, the waves bend in the opposite direction. Diffraction of WavesReflection involves a change in direction of waves when they bounce off a barrier;refractionof wavesinvolves a change in the direction of waves as they pass from one medium to another; anddiffractioninvolves a change in direction of waves as they pass through an opening or around a barrier in their path. Water waves have the ability to travel around corners, around obstacles and through openings. This ability is most obvious for water waves with longer wavelengths. Diffraction can be demonstrated by placing small barriers and obstacles in a ripple tank and observing the path of the water waves as they encounter the obstacles. The waves are seen to pass around the barrier into the regions behind it; subsequently the water behind the barrier is disturbed. The amount of diffraction (the sharpness of the bending) increases with increasing wavelength and decreases with decreasing wavelength. In fact, when the wavelength of the waves is smaller than the obstacle, no noticeable diffraction occurs.Diffraction of water waves is observed in a harbor as waves bend around small boats and are found to disturb the water behind them. The same waves however are unable to diffract around larger boats since their wavelength is smaller than the boat. Diffraction of sound waves is commonly observed; we notice sound diffracting around corners, allowing us to hear others who are speaking to us from adjacent rooms. Many forest-dwelling birds take advantage of the diffractive ability of long-wavelength sound waves. Owls for instance are able to communicate across long distances due to the fact that their long-wavelengthhootsare able to diffract around forest trees and carry farther than the short-wavelengthtweetsof songbirds. Diffraction is observed of light waves but only when the waves encounter obstacles with extremely small wavelengths (such as particles suspended in our atmosphere).Reflection, refraction and diffraction are all boundary behaviors of waves associated with the bending of the path of a wave. The bending of the path is an observable behavior when the medium is a two- or three-dimensional medium. Reflection occurs when there is a bouncing off of a barrier. Reflection of waves off straight barriers follows the law of reflection. Reflection of waves off parabolic barriers results in the convergence of the waves at a focal point. Refraction is the change in direction of waves that occurs when waves travel from one medium to another. Refraction is always accompanied by a wavelength and speed change. Diffraction is the bending of waves around obstacles and openings. The amount of diffraction increases with increasing wavelength.Constructive Interference and Destructive InterferenceWhat is Interference?Wave interferenceis the phenomenon that occurs when two waves meet while traveling along the same medium. The interference of waves causes the medium to take on a shape that results from the net effect of the two individual waves upon the particles of the medium. To begin our exploration of wave interference, consider two pulses of the same amplitude traveling in different directions along the same medium. Let's suppose that each displaced upward 1 unit at its crest and has the shape of a sine wave. As the sine pulses move towards each other, there will eventually be a moment in time when they are completely overlapped. At that moment, the resulting shape of the medium would be an upward displaced sine pulse with an amplitude of 2 units. The diagrams below depict the before and during interference snapshots of the medium for two such pulses. The individual sine pulses are drawn in red and blue and the resulting displacement of the medium is drawn in green.

Constructive InterferenceThis type of interference is sometimes called constructive interference.Constructive interferenceis a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the same direction. In this case, both waves have an upward displacement; consequently, the medium has an upward displacement that is greater than the displacement of the two interfering pulses. Constructive interference is observed at any location where the two interfering waves are displaced upward. But it is also observed when both interfering waves are displaced downward. This is shown in the diagram below for two downward displaced pulses.

In this case, a sine pulse with a maximum displacement of -1 unit (negative means a downward displacement) interferes with a sine pulse with a maximum displacement of -1 unit. These two pulses are drawn in red and blue. The resulting shape of the medium is a sine pulse with a maximum displacement of -2 units.

Destructive InterferenceDestructive interferenceis a type of interference that occurs at any location along the medium where the two interfering waves have a displacement in the opposite direction. For instance, when a sine pulse with a maximum displacement of +1 unit meets a sine pulse with a maximum displacement of -1 unit, destructive interference occurs. This is depicted in the diagram below.

In the diagram above, the interfering pulses have the same maximum displacement but in opposite directions. The result is that the two pulses completely destroy each other when they are completely overlapped. At the instant of complete overlap, there is no resulting displacement of the particles of the medium. This "destruction" is not a permanent condition. In fact, to say that the two waves destroy each other can be partially misleading. When it is said that the two pulsesdestroy each other, what is meant is that when overlapped, the effect of one of the pulses on the displacement of a given particle of the medium isdestroyedor canceled by the effect of the other pulse. Recall fromLesson 1that waves transport energy through a medium by means of each individual particle pulling upon its nearest neighbor. When two pulses with opposite displacements (i.e., one pulse displaced up and the other down) meet at a given location, the upward pull of one pulse is balanced (canceled or destroyed) by the downward pull of the other pulse. Once the two pulses pass through each other, there is still an upward displaced pulse and a downward displaced pulse heading in the same direction that they were heading before the interference. Destructive interference leads to only a momentary condition in which the medium's displacement is less than the displacement of the largest-amplitude wave.The two interfering waves do not need to have equal amplitudes in opposite directions for destructive interference to occur. For example, a pulse with a maximum displacement of +1 unit could meet a pulse with a maximum displacement of -2 units. The resulting displacement of the medium during complete overlap is -1 unit.

This is still destructive interference since the two interfering pulses have opposite displacements. In this case, the destructive nature of the interference does not lead to complete cancellation.Interestingly, the meeting of two waves along a medium does not alter the individual waves or even deviate them from their path. This only becomes an astounding behavior when it is compared to what happens when two billiard balls meet or two football players meet. Billiard balls might crash and bounce off each other and football players might crash and come to a stop. Yet two waves will meet, produce a net resulting shape of the medium, and then continue on doing what they were doing before the interference.

The Doppler EffectSuppose that there is a happy bug in the center of a circular water puddle. The bug is periodically shaking itslegs 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'sshaking 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 atthe 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 away from whom the bug is moving observes a frequency that is less than 2 disturbances/second. This effect is known as theDoppler effect.

What is the Doppler Effect?The Doppler Effect is observed whenever the source of waves is moving with respect to an observer. The Doppler effectcan 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 anactualchange 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 in AstronomyThe 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 (ared 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 (ablue shift) of such observed radiation if the star is rotating in a direction that is towards the Earth.

Standing WaveIt is however possible to have a wave confined to a given space in a medium and still produce a regular wave pattern that is readily discernible amidst the motion of the medium. For instance, if an elastic rope is held end-to-end and vibratedat just the right frequency, a wave pattern would be produced that assumes the shape of a sine wave and is seen to change over time. The wave pattern is only produced when one end of the rope is vibrated at just the right frequency. When the proper frequency is used, the interference of the incident wave and the reflected wave occur in such a manner that there are specific points along the medium that appear to be standing still. Because the observed wave pattern is characterized by points that appear to be standing still, the pattern is often called astanding wave pattern. There are other points along the medium whose displacement changes over time, but in a regular manner. These points vibrate back and forth from a positive displacement to a negative displacement; the vibrations occur at regular time intervals such that the motion of the medium is regular and repeating. A pattern is readily observable.The diagram at the right depicts a standing wave pattern in a medium. A snapshot of the medium over time is depicted using various colors. Note that point A on the medium moves from a maximum positive to a maximum negative displacement over time. The diagram only shows one-half cycle of the motion of the standing wave pattern. The motion would continue and persist, with point A returning to the same maximum positive displacement and then continuing its back-and-forth vibration between the up to the down position. Note that point B on the medium is a point that never moves. Point B is a point of no displacement. Such points are known asnodes. The standing wave pattern that is shown at the right is just one of many different patterns that could be produced within the rope. What are Nodes and Antinodes?One characteristic of every standing wave pattern is that there are points along the medium that appear to be standing still. These points, sometimes described as points of no displacement, are referred to asnodes. There are other points along the medium that undergo vibrations between a large positive and large negative displacement. These are the points that undergo the maximum displacement during each vibrational cycle of the standing wave. In a sense, these points are the opposite of nodes, and so they are calledantinodes. A standing wave pattern always consists of an alternating pattern of nodes and antinodes. The animation shown below depicts a rope vibrating with a standing wave pattern. The nodes and antinodes are labeled on the diagram. When a standing wave pattern is established in a medium, the nodes and the antinodes are always located at the same position along the medium; they arestanding still. It is this characteristic that has earned the pattern the namestanding wave.Standing Wave DiagramsThe positioning of the nodes and antinodes in a standing wave pattern can be explained by focusing on the interference of the two waves. The nodes are produced at locations where destructive interference occurs. For instance, nodes form at locations where a crest of one wave meets a trough of a second wave; or ahalf-crestof one wave meets ahalf-troughof a second wave; or aquarter-crestof one wave meets aquarter-troughof a second wave; etc. Antinodes, on the other hand, are produced at locations where constructive interference occurs. For instance, if a crest of one wave meets a crest of a second wave, a point of large positive displacement results. Similarly, if a trough of one wave meets a trough of a second wave, a point of large negative displacement results. Antinodes are always vibrating back and forth between these points of large positive and large negative displacement; this is because during a complete cycle of vibration, a crest will meet a crest; and then one-half cycle later, a trough will meet a trough. Because antinodes are vibrating back and forth between a large positive and large negative displacement, a diagram of a standing wave is sometimes depicted by drawing the shape of the medium at an instant in time and at an instant one-half vibrational cycle later. This is done in the diagram below.

Nodes and antinodes should not be confused with crests and troughs. When the motion of atraveling waveis discussed, it is customary to refer to a point of large maximum displacement as acrestand a point of large negative displacement as atrough. These represent pointsof the disturbancethat travel from one location to another through the medium. An antinode on the other hand is a pointon the mediumthat is staying in the same location. Furthermore, an antinode vibrates back and forth between a large upward and a large downward displacement. And finally, nodes and antinodes are not actually part of a wave. Recall that a standing wave is not actually a wave but rather a pattern that results from the interference of two or more waves. Since a standing wave is not technically a wave, an antinode is not technically a point on a wave. The nodes and antinodes are merely unique points on the medium that make up the wave pattern.Check Your Understanding1. Suppose that there was arideat an amusement park that was titledThe Standing Wave. Which location - node or antinode - on the ride would give the greatest thrill?Answer:The antinodeThe antinode is continually vibrating from a high to a low displacement - now that would be a ride.

2. A standing wave is formed when ____.a. a wave refracts due to changes in the properties of the medium.b. a wave reflects off a canyon wall and is heard shortly after it is formed.c. red, orange, and yellow wavelengths bend around suspended atmospheric particles.d. two identical waves moving different directions along the same medium interfere.Answer:D3. The number of nodes in the standing wave shown in the diagram at the right is ____.a. 6b. 7

c. 8d. 14

Answer:C (8 nodes)There are eight positions along the medium which have no displacement. Be sure to avoid the common mistake of not counting the end positions.

4. The number of antinodes in the standing wave shown in the diagram above right is ____.a. 6b. 7c. 8d. 14

Answer:B (7 antinodes)There are seven positions along the medium which have vibrate between a large positive and a large negative displacement.Be sure to avoid the common mistake of counting the antinodal positions twice. An antinode is simply a point along a medium which undergoes maximum displacement above and below the rest position. Do not count these positions twice.

Consider the standing wave pattern at the right in answering these next two questions.5. The number of nodes in the entire pattern is ___.a. 7b. 8

c. 9d. 16

Answer:C (9 nodes)There are nine positions along the medium which have no displacement. (Be sure to avoid the common mistake of not counting the end positions.)

6. Of all the labeled points, destructive interference occurs at point(s) ____.a. B, C, and Db. A, E, and Fc. A only

d. C onlye. all points

Answer:ADestructive interference has occurred at points B, C and D to produce the nodes which are seen at these pointsFirst Harmonic Standing Wave Pattern Second Harmonic Standing Wave Pattern

Third Harmonic Standing Wave PatternOne full wave equals two loops. So then each loop is equal one half a wave length.

n represents the number of antinodes in a standing waveThe Electromagnetic and Visible SpectraElectromagnetic wavesare waves that are capable of traveling through a vacuum. Unlikemechanical wavesthat require a medium in order to transport their energy, electromagnetic waves are capable of transporting energy through the vacuum of outer space. Electromagnetic waves are produced by a vibrating electric charge and as such, they consist of both an electric and a magnetic component. The precise nature of such electromagnetic waves is not discussed in The Physics Classroom Tutorial. Nonetheless, there are a variety of statements that can be made about such waves.Electromagnetic waves exist with an enormous range of frequencies. This continuous range of frequencies is known as theelectromagnetic spectrum. The entire range of the spectrum is often broken into specific regions. The subdividing of the entire spectrum into smaller spectra is done mostly on the basis of how each region of electromagnetic waves interacts with matter. The diagram below depicts the electromagnetic spectrum and its various regions. The longer wavelength, lower frequency regions are located on the far left of the spectrum and the shorter wavelength, higher frequency regions are on the far right. Two very narrow regions within the spectrum are the visible light region and the X-ray region. You are undoubtedly familiar with some of the other regions of the electromagnetic spectrum.

Visible Light SpectrumThe focus of Lesson 2 will be upon the visible light region - the very narrow band of wavelengths located to the right of the infrared region and to the left of the ultraviolet region. Though electromagnetic waves exist in a vast range of wavelengths, our eyes are sensitive to only a very narrow band. Since this narrow band of wavelengths is the means by which humans see, we refer to it as thevisible light spectrum. Normally when we use the term "light," we are referring to a type of electromagnetic wave that stimulates the retina of our eyes. In this sense, we are referring to visible light, a small spectrum from the enormous range of frequencies of electromagnetic radiation. This visible light region consists of a spectrum of wavelengths that range from approximately 700 nanometers (abbreviated nm) to approximately 400 nm. Expressed in more familiar units, the range of wavelengths extends from 7 x 10-7meter to 4 x 10-7meter. This narrow band of visible light is affectionately known asROYGBIV.Each individual wavelength within the spectrum of visible light wavelengths is representative of a particular color. That is, when light of that particular wavelength strikes the retina of our eye, we perceivethat specific color sensation. Isaac Newton showed thatlight shining through a prism will be separated into its different wavelengthsand will thus show the various colors that visible light is comprised of. The separation of visible light into its different colors is known asdispersion. Each color is characteristic of a distinct wavelength; and different wavelengths of light waves will bend varying amounts upon passage through a prism. For these reasons, visible light is dispersed upon passage through a prism. Dispersion of visible light produces the colors red (R), orange (O), yellow (Y), green (G), blue (B), and violet (V). It is because of this that visible light is sometimes referred to as ROY G. BIV.(Incidentally, the indigo is not actually observed in the spectrum but is traditionally added to the list so that there is a vowel in Roy's last name.) The red wavelengths of light are the longer wavelengths and the violet wavelengths of light are the shorter wavelengths. Between red and violet, there is a continuous range or spectrum of wavelengths.The visible light spectrum is shown in the diagram below.

When all the wavelengths of the visible light spectrum strike your eye at the same time, white is perceived. The sensation of white is not the result of a single color of light. Rather, the sensation of white is the result of a mixture of two or more colors of light. Thus, visible light - the mix of ROYGBIV - is sometimes referred to as white light. Technically speaking, white is not a color at all - at least not in the sense that there is a light wave with a wavelength that is characteristic of white. Rather, white is the combination of all the colors of the visible light spectrum. If all the wavelengths of the visible light spectrum give the appearance of white, then none of the wavelengths would lead to the appearance of black. Once more, black is not actually a color. Technically speaking, black is merely the absence of the wavelengths of the visible light spectrum. So when you are in a room with no lights and everything around you appears black, it means that there are no wavelengths of visible light striking your eye as you sight at the surroundings.