14 waves - grygla public schoolthe bigger the wave is, the more energy it carries. a cruise ship...

452

C H A P T E R 14

WavesWaves

Chapter Preview

1 Types of WavesWhat Is a Wave?Vibrations and WavesTransverse and Longitudinal Waves

2 Characteristics of WavesWave PropertiesWave SpeedThe Doppler Effect

3 Wave InteractionsReflection, Diffraction, and RefractionInterferenceStanding Waves

Copyright © by Holt, Rinehart and Winston. All rights reserved.

ACTIVITYACTIVITYFocusFocus

A surfer takes advantageof the energy in oceanwaves. Energy travelsfrom the sun to Earth in the form of waves.

ACTIVITYACTIVITYFocusFocus

Background The energy in an ocean wave can lift a surfboardup into the air and carry the surfer into shore. Ocean waves getmost of their energy from the wind. A wave may start as a smallripple in a calm sea, then build up as the wind pushes it along.Waves that start on the coast of northern Canada may be verylarge by the time they reach a beach in the Hawaiian Islands.

The winds that create ocean waves are caused by convectioncurrents in the atmosphere, which are driven by energy from thesun. Energy travels across empty space from the sun to Earth—in the form of light waves.

Waves are all around us. As you read this book, you are de-pending on light waves. Light bounces off the pages and into youreyes. When you talk with a friend you are depending on soundwaves traveling through the air. Sometimes the waves can be gen-tle, such as those that rock a canoe in a pond. Other times wavescan be very destructive, such as those created by earthquakes.

Activity 1 Fill a long, rectangular pan with water. Experimentwith making waves in different ways. Try making waves by stick-ing the end of a pencil into the water, by moving a wide stick orboard back and forth, and by striking the side of the pan. Placewooden blocks or other obstacles into the pan, and watch howthe waves change when they encounter the obstacles.

Activity 2 With some of your classmates, practice the “wave” as is often performed by fans at football games. How does itresemble an ocean wave? How does it differ from other forms of motion?

Pre-Reading Questions1. What things do you do every day that

depend on waves? What kinds of wavesdo you think are involved?

2. What properties do you think these differ-ent kinds of waves have in common?

www.scilinks.orgTopic: Waves SciLinks code: HK4150

453Copyright © by Holt, Rinehart and Winston.All rights reserved.

Types of Waves> Recognize that waves transfer energy.> Distinguish between mechanical waves and

electromagnetic waves.> Explain the relationship between particle vibration

and wave motion.> Distinguish between transverse waves and

longitudinal waves.

When a stone is thrown into a pond, it creates ripples on thesurface of the water, as shown in Figure 1. If there is a leaf

floating on the water, the leaf will bob up and down and back andforth as each ripple, or wave, disturbs it. But after the waves pass,the leaf will almost return to its original position on the water.

What Is a Wave?Like the leaf, individual drops of water do not travel outwardwith a wave. They move only slightly from their resting place aseach ripple passes by. If drops of water do not move very far as awave passes, and neither does a leaf on the surface of the water,then what moves along with the wave? Energy does. A wave is notjust the movement of matter from one place to another. A is a disturbance that carries energy through matter or space.

wave

O B J E C T I V E S

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1

454 C H A P T E R 1 4

K E Y T E R M S

wavemediummechanical waveelectromagnetic wavetransverse wavelongitudinal wave

▲

wave a periodic disturbancein a solid, liquid, or gas asenergy is transmitted througha medium

▲

Figure 1A stone thrown into a pondcreates waves.


Most waves travel through a mediumThe waves in a pond are disturbances travelingthrough water. Sound also travels as a wave. Thesound from a stereo is a pattern of changes inthe air between the stereo speakers and yourears. Earthquakes create waves, called seismicwaves, that travel through Earth.

In each of these examples, the waves involvethe movement of some kind of matter. The mat-ter through which a wave travels is called the

In the example of the pond, the wateris the medium. For sound from a stereo, air isthe medium. And in earthquakes, Earth itself isthe medium.

Waves that require a medium are calledAlmost all waves are me-

chanical waves, with one important exception:light waves.

Light does not require a mediumLight can travel from the sun to Earth across theempty space between them. This is possiblebecause light waves do not need a mediumthrough which to travel. Instead, light wavesconsist of changing electric and magnetic fields in space. For thatreason, light waves are also called

Visible light waves are just one example of a wide range ofelectromagnetic waves. Radio waves, such as those that carry sig-nals to your radio or television, are also electromagnetic waves.Other kinds of electromagnetic waves will be introduced inSection 2. In this book, the terms light and light wave may referto any electromagnetic wave, not just visible light.

Waves transfer energyEnergy is the ability to exert a force over a certain distance. It isalso known as the ability to do work. We know that waves carryenergy because they can do work. For example, water waves cando work on a leaf, on a boat, or on a beach. Sound waves can dowork on your eardrum. Light waves can do work on your eye oron photographic film.

A wave caused by dropping a stone in a pond might carryenough energy to move a leaf up and down several centimeters.The bigger the wave is, the more energy it carries. A cruise shipmoving through water in the ocean could create waves bigenough to move a fishing boat up and down a few meters.

electromagnetic waves.

mechanical waves.

medium.

W A V E S 455

Connection toENGINEERINGENGINEERING

If you have ever been hit by an ocean wave atthe beach, you know these waves carry a lot

of energy. Could this energy be put to good use?Research is currently underway to find ways

to harness the energy of ocean waves. Somesmall floating navigation buoys, which shinelights to help ships find their way in the dark,obtain energy solely from the waves. A few largersystems are in place that harness wave energy toprovide electricity for small coastal communities.

Making the Connection1. In a library or on the Internet, research differ-

ent types of devices that harness waveenergy. How much power do some of thesedevices provide? Is that a lot of power?

2. Design a device of your own to capture theenergy from ocean waves. The device shouldtake the motion of waves and convert it intoa motion that could be used to drive amachine, such as a pump or a wheel.

medium a physical environ-ment in which phenomenaoccur

mechanical wave a wavethat requires a mediumthrough which to travel

electromagnetic wave awave that consists of oscillat-ing electric and magneticfields, which radiate outwardat the speed of light

▲▲

▲


Figure 2 shows a woodblock print of a tsunami, a huge oceanwave caused by earthquakes. A tsunami may be as high as 30 mwhen it reaches shore, taller than a 10-story building. Such wavescarry enough energy to cause a lot of damage to coastal townsand shorelines. Normal-sized ocean waves do work on the shore,too, breaking up rocks into tiny pieces to form sandy beaches.

Energy may spread out as a wave travelsIf you stand next to the speakers at a rock concert, the soundwaves may damage your ears. Likewise, if you look at a brightlight bulb from too close, the light may damage your eyes. But ifyou are 100 m away, the sound of the rock band or the light fromthe bulb is harmless. Why?

Think about waves created when a stone falls into a pond.The waves spread out in circles that get bigger as the waves movefarther from the center. Each of these circles, called a wave front,has the same amount of total energy. But as the circles get larger,the energy spreads out over a larger area.

When sound waves travel in air, the waves spread out inspheres, as shown in Figure 3. These spheres are similar to thecircular ripples on a pond. As they travel outward, the sphericalwave fronts get bigger, so the energy in the waves spreads outover a larger area. This is why large amplifiers and speakers areneeded to fill a concert hall with sound, even though the samemusic can sound just as loud if it is played on a portable radioand listened to with a small pair of headphones.

456 C H A P T E R 1 4

Figure 2 This portrait of a tsunami was created by the Japanese artistHokusai in 1830.

Figure 3 Sound waves from a stereospeaker spread out in sphericalwave fronts.


www.scilinks.orgTopic: Vibrations and

WavesSciLinks code: HK4145

Vibrations and WavesWhen a singer sings a note, vocal cords in the singer’s throatmove back and forth. That motion makes the air in the throatvibrate, creating sound waves that eventually reach your ears.The vibration of the air in your ears causes your eardrums tovibrate. The motion of the eardrum triggers a series of electricalpulses to your brain, and your brain interprets them as sounds.

Waves are related to vibrations. Most waves are caused by avibrating object. Electromagnetic waves may be caused byvibrating charged particles. In a mechanical wave, the particlesin the medium also vibrate as the wave passes through themedium.

Vibrations involve transformations of energyFigure 4 shows a mass hanging on a spring. If the mass is pulleddown slightly and released, it will begin to move up and downaround its original resting position. This vibration involves trans-formations of energy, much like those in a swinging pendulum.

When the mass is pulled away from its resting place, themass-spring system gains elastic potential energy. The springexerts a force that pulls the mass back to its original position.

As the spring moves back toward the original position, thepotential energy in the system changes to kinetic energy. Themass moves beyond its original resting position to the other side.

At the top of its motion, the mass has lost all its kineticenergy. But the system now has both elastic potential energy andgravitational potential energy. The mass moves downward again,past the resting position, and back to the beginning of the cycle.

W A V E S 457

Figure 4When a mass hanging on a springis disturbed from rest, it starts tovibrate up and down around itsoriginal position.


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and the Consumerand the ConsumerScienceScience

Shock Absorbers: Why Are They Important?

Bumps in the road are certainly a nuisance, butwithout strategic use of damping devices, theycould also be very dangerous. To control a car

going 100 km/h (60 mi/h), a driver needs all thewheels of the vehicle on the ground. Bumps in the roadlift the wheels off the ground and may rob the driver ofcontrol of the car.

Springs Absorb EnergyTo solve this problem, cars are fitted with springs ateach wheel. When the wheel of a car goes over abump, the spring absorbs kinetic energy so that theenergy is not transferred to the rest of the car. The energy becomes elastic potential energy in the spring,which then allows the spring to push the wheel backdown onto the road.

Springs Alone Prolong VibrationsOnce a spring is set in motion, it tends to continue vibrating up and down in simple harmonic motion.This can create an uncomfortable ride, and it mayalso affect the driver’s control of the car. One way to cut down on unwanted vibrations is to use stiffsprings that compress only a few centimeters withthousands of newtons of force. However, the stifferthe spring is, the rougher the ride is and the morelikely the wheels are to come off the road.

Shock Absorbers Dampen VibrationsModern automobiles are fitted with devices knownas shock absorbers that absorb energy without pro-longing vibrations. Shock absorbers are fluid-filledtubes that turn the simple harmonic motion of thesprings into a damped harmonic motion. In adamped harmonic motion, each cycle of stretch andcompression of the spring is much smaller than theprevious cycle. Modern auto suspensions are set upso that all a spring’s energy is absorbed by the shockabsorbers in just one up-and-down cycle.

Shock Absorbers and Springs Come in Different Arrangements

Different types of springs and shock absorbers arecombined to give a wide variety of responses. For example, many passenger cars have coil springs with shock absorbers parallel to the springs, or eveninside the springs, as shown at near left. Some largervehicles have heavy-duty leaf springs made of stacksof steel strips. Leaf springs are stiffer than coilsprings, but they can bear heavier loads. In this typeof suspension system, the shock absorber is perpen-dicular to the spring, as shown at far left.

The stiffness of the spring can affect steering response time, traction, and the general feel of thecar. Because of the variety of combinations, your driving experiences can range from the luxurious“floating-on-air” ride of a limousine to the bone-rattling feel of a true sports car.

1. Making Decisions If you were going to haulheavy loads, would you look for a vehicle withcoil springs or leaf springs? Why?

2. Critical Thinking How do shock absorbersstop an automobile from continually bouncing?

Your Choice

Shock absorber Leaf spring

Coil spring

Shock absorber


Whenever the spring is expanded or compressed, it is exert-ing a force that pushes the mass back almost to the original rest-ing position. As a result, the mass will continue to bounce up anddown. This type of vibration is called simple harmonic motion.

A wave can pass through a series of vibrating objectsImagine a series of masses and springs tied together in a row, asshown in Figure 5. If you pull down on a mass at the end of therow, that mass will begin to vibrate up and down. As the mass onthe end moves, it pulls on the mass next to it, causing that massto vibrate. The energy in the vibration of the first mass, which isa combination of kinetic energy and elastic potential energy, istransferred to the mass-spring system next to it. In this way, thedisturbance that started with the first mass travels down the row.This disturbance is a wave that carries energy from one end ofthe row to the other.

If the first mass were not connected to the other masses, itwould keep vibrating up and down on its own. However, becauseit transfers its energy to the second mass, it slows down and thenreturns to its resting position. A vibration that fades out asenergy is transferred from one object to another is called dampedharmonic motion.

W A V E S 459

Figure 5 A wave can pass through a series of masses on springs. The massesact like the particles in a medium.


The motion of particles in a medium is like the motion ofmasses on springsIf you tie one end of a rope to a doorknob, pull it straight, andthen rapidly move your hand up and down once, you will gener-ate a single wave along the rope, as shown in Figure 6. A smallribbon tied to the middle of the rope can help you visualize themotion of a single particle of matter in the rope.

As the wave approaches, the ribbon moves up in the air, awayfrom its resting position. As the wave passes farther along therope, the ribbon drops below its resting position. Finally, afterthe wave passes by, the ribbon returns to its original starting

point. Like the ribbon, eachpart of the rope moves up anddown as the wave passes by.

The motion of each partof the rope is like the vibrat-ing motion of a mass hang-ing on a spring. As one partof the rope moves, it pulls onthe part next to it, transfer-ring energy. In this way, awave passes along the lengthof the rope.

Materials

How do particles move in a medium?

✔ long, flexible spring ✔ colored ribbon

1. Have two people each grab an end of the springand stretch it out along a smooth floor. Haveanother person tie a small piece of colored rib-bon to a coil near the middle of the spring.

2. Swing one end of the spring from side to side.This will start a wave traveling along the spring.Observe the motion of the ribbon as the wavepasses by.

3. Take a section of the spring and bunch ittogether as shown in the figure at right. Releasethe spring. This will create a different kind ofwave traveling along the spring. Observe themotion of the ribbon as this wave passes by.

Analysis1. How would you describe the motion of the

ribbon in step 2? How would you describe itsmotion in step 3?

2. How can you tell that energy is passing alongthe spring? Where does that energy come from?

460 C H A P T E R 1 4

Figure 6 As this wave passes along a rope,the ribbon moves up and downwhile the wave moves to the right.

Wave motion

Particle motion


Transverse and Longitudinal WavesParticles in a medium can vibrate either up and down or backand forth. Waves are often classified by the direction that the par-ticles in the medium move as a wave passes by.

Transverse waves have perpendicular motionWhen a crowd does “the wave” at a sporting event, people in thecrowd stand up and raise their hands into the air as the wavereaches their part of the stadium. The wave travels around the sta-dium in a circle, but the people move straight up and down. Thisis similar to the wave in the rope. Each particle in the rope movesstraight up and down as the wave passes by from left to right.

In these cases, the motion of the particles in the medium (inthe stadium, the people in the crowd) is perpendicular to themotion of the wave as a whole. Waves in which the motion of theparticles is perpendicular to the motion of the wave as a wholeare called

Light waves are another example of transverse waves. Thefluctuating electric and magnetic fields that make up a light waveare perpendicular to one another and are also perpendicular tothe direction the light travels.

Longitudinal waves have parallel motionSuppose you stretch out a long, flexible spring on a table or asmooth floor, grab one end, and move your hand back and forth,directly toward and directly away from the other end of thespring. You would see a wave travel along the spring as itbunches up in some spots and stretches in others, as shown inFigure 7.

As a wave passes along the spring, a ribbon tied to one of thecoils of the spring will move back and forth, parallel to the direc-tion that the wave travels. Waves that cause the particles in amedium to vibrate parallel tothe direction of wave motionare called

Sound waves are an exampleof longitudinal waves that weencounter every day. Soundwaves traveling in air compressand expand the air in bands. Assound waves pass by moleculesin the air move backward andforward parallel to the directionthat the sound travels.

longitudinal waves.

transverse waves.

W A V E S 461

transverse wave a wave in which the particles of themedium move perpendicularto the direction the wave istraveling

longitudinal wave a wavein which the particles of themedium vibrate parallel to thedirection of wave motion

▲▲

Quick

ACTIVITYACTIVITYQuickQuickQuick

Polarization

Polarizing filters block all lightexcept those waves that oscil-late in a certain direction.Look through two polarizingfilters at once. Then rotateone by 90° and look again.What do you observe?

Figure 7 As a longitudinal wave passesalong this spring, the ribbon tiedto the coils moves back and forth,parallel to the direction the waveis traveling.

Particle motion

Wave motion


In a surface wave, particles move in circlesWaves on the ocean or in a swimming pool are notsimply transverse waves or longitudinal waves.Water waves are an example of surface waves.Surface waves occur at the boundary between twodifferent mediums, such as between water and air.The particles in a surface wave move both per-pendicularly and parallel to the direction that thewave travels.

Follow the motion of the beach ball inFigure 8 as a wave passes by traveling from leftto right. At first, the ball is in a trough. As thecrest approaches, the ball moves to the left andupward. When the ball is very near the crest, itstarts to move to the right. Once the crest haspassed, the ball starts to fall back downward,then to the left. The up and down motions com-bine with the side to side motions to produce acircular motion overall.

The beach ball helps to make the motion ofthe wave more visible. Particles near the surface ofthe water also move in a similar circular pattern.

462 C H A P T E R 1 4

S E C T I O N 1 R E V I E W

1. Identify the medium for the following waves:a. ripples on a pondb. the sound waves from a stereo speakerc. seismic waves

2. Name the one kind of wave that does not require a medium.

3. Describe the motion of a mass vibrating on a spring. Howdoes this relate to wave motion?

4. Explain the difference between transverse waves and longi-tudinal waves. Give an example of each type.

5. Describe the motion of a water molecule on the surface ofthe ocean as a wave passes by.

6. Critical Thinking Describe a situation that demonstrates thatwater waves carry energy.

S U M M A R Y

> A wave is a disturbancethat carries energy througha medium or through space.

> Mechanical waves require a medium through whichto travel. Light waves, alsocalled electromagneticwaves, do not require a medium.

> Particles in a medium mayvibrate perpendicularly toor parallel to the directiona wave is traveling.

Figure 8Ocean waves are surface waves at theboundary between air and water.


> Identify the crest, trough, amplitude, and wavelengthof a wave.

> Define the terms frequency and period.> Solve problems involving wave speed, frequency,

and wavelength.> Describe the Doppler effect.

Characteristics of Waves

If you have spent any time at the beach or on a boat, you haveprobably observed many properties of waves. Sometimes the

waves are very large; other times they are smaller. Sometimes theyare close together, and sometimes they are farther apart. How canthese differences be described and measured in more detail?

Wave PropertiesThe simplest transverse waves have somewhat similar shapes nomatter how big they are or what medium they travel through. Anideal transverse wave has the shape of a sine curve, such as thecurve on the graph in Figure 9A. A sine curve looks like an S lyingon its side. Sine curves can be used to represent waves and todescribe their properties.

Waves that have the shape of a sine curve, such as those onthe rope in Figure 9B, are called sine waves. Although manywaves, such as water waves, are not ideal sine waves, they canstill be modeled with the graph of a sine curve.

O B J E C T I V E S

SECTION

2

W A V E S 463

K E Y T E R M ScresttroughamplitudewavelengthperiodfrequencyDoppler effect

▲

Wavelength

Wavelength

Dis

plac

emen

t

Crest

Trough

Amplitude

This transverse wave on a ropeis a simple sine wave.B

Figure 9A sine curve can be used to demonstrate

the characteristics of waves.A


Amplitude measures the amount of particle vibrationThe highest points of a transverse wave are called Thelowest parts of a transverse wave are called The great-est distance that particles are displaced from their normal restingpositions because of a wave is called the The ampli-tude is also half the vertical distance between a crest and a trough.Larger waves have bigger amplitudes and carry more energy.

But what about longitudinal waves? These waves donot have crests and troughs because they cause particlesto move back and forth instead of up and down. If youmake a longitudinal wave in a spring, you will see amoving pattern of areas where the coils are bunched upalternating with areas where the coils are stretched out.The crowded areas are called compressions. Thestretched-out areas are called rarefactions. Figure 10Aillustrates these properties of a longitudinal wave.

Figure 10B shows a graph of a longitudinal wave.Density of the medium is plotted on the vertical axis; thehorizontal axis represents the distance along the spring.The result is a sine curve. The amplitude of a longitudi-nal wave is the maximum deviation from the normaldensity or pressure of the medium, which is shown bythe high and low points on the graph.

Wavelength measures the distance between two equivalentparts of a waveThe crests of ocean waves at a beach may be separated by severalmeters, while ripples in a pond may be only a few centimetersapart. Crests of a light wave may be separated by only billionthsof a meter.

The distance from one crest of a wave to the next crest, orfrom one trough to the next trough, is called the Ina longitudinal wave, the wavelength is the distance between twocompressions or between two rarefactions. The wavelength is thedistance between any two successive identical parts of a wave.

Not all waves have a single wavelength that is easy to measure.Most sound waves have a very complicated shape, so the wave-length may be difficult to determine. If the source of a wavevibrates in an irregular way, the wavelength may change over time.

When used in equations, wavelength is represented by theGreek letter lambda, l. Because wavelength is a distance meas-urement, it is expressed in the SI unit meters.

wavelength.

amplitude.

troughs.crests.

464 C H A P T E R 1 4

Den

sity

CompressionRarefaction

crest the highest point of a wave

trough the lowest point of a wave

amplitude the maximumdistance that the particles of a wave’s medium vibratefrom their rest position

wavelength the distancefrom any point on a wave to an identical point on thenext wave

▲▲

▲▲

Figure 10 A longitudinal wave has compressions

and rarefactions.

The high and low points of this sinecurve correspond to compressions and rarefactions in the spring.

B

A

A

B

Disc Two, Module 12:Frequency and WavelengthUse the Interactive Tutor to learn moreabout these topics.


The period measures how long it takes for waves to pass byIf you swim out into the ocean until your feet can no longer touchthe bottom, your body will be free to move up and down as wavescome into shore. As your body rises and falls, you can count offthe number of seconds between two successive wave crests.

The time required for one full wavelength of a wave to pass acertain point is called the of the wave. The period is alsothe time required for one complete vibration of a particle in amedium—or of a swimmer in the ocean. In equations, the periodis represented by the symbol T. Because the period is a timemeasurement, it is expressed in the SI unit seconds.

Frequency measures the rate of vibrationsWhile swimming in the ocean or floating in aninner tube, as shown in Figure 11, you couldalso count the number of crests that pass by ina certain time, say in 1 minute. The of a wave is the number of full wavelengths thatpass a point in a given time interval. The fre-quency of a wave also measures how rapidlyvibrations occur in the medium, at the sourceof the wave, or both.

The symbol for frequency is f. The SI unitfor measuring frequency is hertz (Hz), namedafter Heinrich Hertz, who in 1888 became thefirst person to experimentally demonstrate theexistence of electromagnetic waves. Hertz unitsmeasure the number of vibrations per second.One vibration per second is 1 Hz, two vibra-tions per second is 2 Hz, and so on. You canhear sounds with frequencies as low as 20 Hz and as high as 20000 Hz. When you hear a sound at 20 000 Hz, there are 20 000compressions hitting your ear every second.

The frequency and period of a wave are related. If more vibra-tions are made in a second, each one takes a shorter amount oftime. In other words, the frequency is the inverse of the period.

In the inner tube example, a wave crest passes the inner tubeevery 2 s, so the period is 2 s. The frequency can be found by usingthe frequency-period equation above. Because 0.5 (1/2) is theinverse of 2, the frequency is 0.5 Hz, or half a wave per second.

frequency

period

W A V E S 465

frequency = f =1�T

1�period

Frequency-Period Equation

t � 0 s

t � 1 s

t � 2 s

period the time that it takesa complete cycle or waveoscillation to occur

frequency the number ofcycles or vibrations per unit of time

▲▲

Figure 11 A person floating in an inner tubecan determine the period andfrequency of the waves by count-ing off the number of secondsbetween wave crests.


Light comes in a wide range of frequencies and wavelengthsOur eyes can detect light with frequencies ranging from about4.3 �1014 Hz to 7.5 �1014 Hz. Light in this range is called visiblelight. The differences in frequency in visible light account for thedifferent colors we see, as shown in Figure 12.

Electromagnetic waves also exist at other frequencies that wecannot see directly. The full range of light at different frequenciesand wavelengths is called the electromagnetic spectrum. Table 1lists several different parts of the electromagnetic spectrum,along with some real-world applications of the different kindsof waves.

466 C H A P T E R 1 4

Radio wave f < 1 × 109 Hz AM and FM radio; televisionλ > 30 cm broadcasting; radar; aircraft

navigation

Microwave 1 × 109 Hz < f < 3 × 1011 Hz Atomic and molecular research;30 cm > λ > 1 mm microwave ovens

Infrared (IR) wave 3 × 1011 Hz < f < 4.3 × 1014 Hz Infrared photography; remote-1 mm > λ > 700 nm control devices; heat radiation

Visible light 4.3 × 1014 Hz < f < 7.5 × 1014 Hz Visible-light photography; optical

700 nm (red) > λ > 400 nm (violet) microscopes; optical telescopes

Ultraviolet (UV) light 7.5 × 1014 Hz < f < 5 × 1015 Hz Sterilizing medical instruments;400 nm > λ > 60 nm identifying fluorescent minerals

X ray 5 × 1015 Hz < f < 3 × 1021 Hz Medical examination of bones,60 nm > λ > 1 × 10−4 nm teeth, and organs; cancer

treatments

Gamma ray 3 × 1018 Hz < f < 3 × 1022 Hz Food irradiation; studies of0.1 nm > λ > 1 × 10−5 nm structural flaws in thick materials

Type of wave Range of frequency and wavelength Applications

Table 1 The Electromagnetic Spectrum

Figure 12The part of the electromagneticspectrum that we can see is calledvisible light.

Infrared Red

700

5.0 6.0 7.5

600 500 400Orange Yellow Green Blue Violet

Ultraviolet

4.3

Wavelength (nm)

Frequency (�1014 Hz)


Wave SpeedImagine watching as water waves move past a post at a pier suchas the one in Figure 13. If you count the number of crests passingthe post for 10 s, you can determine the frequency of the wavesby dividing the number of crests you count by 10 s. If you meas-ure the distance between crests, you can find the wavelength ofthe wave. But how fast are the water waves moving?

Wave speed equals frequency times wavelengthThe speed of a moving object is found by dividing the distancethe object travels by the time it takes to travel that distance.Speed can be calculated using the speed equation:

speed =

v =

If SI units are used for measuring distance and time, speed isexpressed as meters per second (m/s). The wave speed is simplyhow fast a wave moves. Finding the speed of a wave is just likefinding the speed of a moving object: you need to measure howfar the wave travels in a certain amount of time.

For a wave, it is most convenient to use the wavelength as thedistance traveled. The amount of time it takes the wave to travela distance of one wavelength is the period. Substituting theseinto the speed equation gives an equation that can be used to cal-culate the speed of a wave.

speed =

v =

Because the period is the inverse of the frequency, dividing bythe period is equivalent to multiplying by the frequency.Therefore, the speed of a wave can also be calculated by multi-plying the wavelength by the frequency.

Suppose that waves passing by a post at a pier have a wave-length of 10 m, and two waves pass by in 5 s. The period is there-fore 2.5 s, and the frequency is the inverse of 2.5 s, or 0.4 Hz. Thewaves in this case travel with a wave speed of 4 m/s.

l�T

wavelength��

period

d�t

distance�

time

W A V E S 467

wave speed = frequency × wavelengthv = f × l

Wave Speed Equation

Figure 13 By observing the frequency andwavelength of waves passing apier, you can calculate the speedof the waves.

EARTH SCIENCEEarthquakes createwaves, called seismicwaves, that travelthrough Earth. There

are two main types of seismicwaves, P waves (primarywaves) and S waves (second-ary waves).

P waves travel faster than S waves, so the P waves arriveat a given location first. P wavesare longitudinal waves that tendto shake the ground from sideto side.

S waves move more slowlythan P waves but also carrymore energy. S waves aretransverse waves that shakethe ground up and down, oftendamaging buildings and roads.


Math SkillsMath Skills

Wave Speed The string of a piano that produces the note mid-dle C vibrates with a frequency of 264 Hz. If the sound wavesproduced by this string have a wavelength in air of 1.30 m,what is the speed of sound in air?

List the given and unknown values.Given: frequency, f = 264 Hz

wavelength, l = 1.30 mUnknown: wave speed, v = ? m/s

Write the equation for wave speed.v = f × l

Insert the known values into the equation, and solve.v = 264 Hz × 1.30 m = 264 s−1 × 1.30 mv = 343 m/s

3

2

1

PracticePractice

Wave Speed1. The average wavelength in a series of ocean waves is 15.0 m.

A wave crest arrives at the shore on average every 10.0 s, so thefrequency is 0.100 Hz. What is the average speed of the waves?

2. An FM radio station broadcasts electromagnetic waves at a frequency of 94.5 MHz (9.45 × 107 Hz). These radio waves havea wavelength of 3.17 m. What is the speed of the waves?

3. Green light has a wavelength of 5.20 × 10−7 m. The speed oflight is 3.00 × 108 m/s. Calculate the frequency of green lightwaves with this wavelength.

4. The speed of sound in air is about 340 m/s. What is the wavelength of a sound wave with a frequency of 220 Hz (on a piano, the A below middle C)?

The speed of a wave depends on the mediumSound waves can travel through air. If they couldn’t, you wouldnot be able to have a conversation with a friend or hear musicfrom a radio across the room. Because sound travels very fast inair (about 340 m/s), you don’t notice a time delay in most normalsituations.

If you swim with your head underwater, you may hear certainsounds very clearly. Sound waves travel better—and three to fourtimes faster—in water than in air. Dolphins, such as those inFigure 14, use sound waves to communicate with one anotherover long distances underwater. Sound waves travel even fasterin solids than in air or in water. Sound waves have speeds 15 to20 times faster in rock or metal than in air.

468 C H A P T E R 1 4

PracticeHINT

> When a problem requires youto calculate wave speed, youcan use the wave speed equa-tion on the previous page.

> The wave speed equation canalso be rearranged to isolatefrequency on the left in thefollowing way:

v = f × lDivide both sides by l.

=

f =

You will need to use this form of the equation in Practice Problem 3.

> In Practice Problem 4, youwill need to rearrange theequation to isolate wave-length on the left.

v�l

f × l�

l

v�l


Quick

ACTIVITYACTIVITYQuickQuickQuick

If someone strikes a long steel rail witha hammer at one end and you listen for thesound at the other end, you might hear twobangs. The first sound comes through thesteel rail itself and reaches you shortlybefore the second sound, which travelsthrough the air.

The speed of a wave depends on themedium. In a given medium, though, thespeed of waves is constant; it does notdepend on the frequency of the wave. Nomatter how fast you shake your hand upand down to create waves on a rope, thewaves will travel the same speed. Shakingyour hand faster just increases the fre-quency and decreases the wavelength.

Kinetic theory explains differences in wave speedThe arrangement of particles in a medium determines how wellwaves travel through it. The different states of matter are due todifferent degrees of organization at the particle level.

In gases, the molecules are far apart and move around ran-domly. A molecule must travel through a lot of empty spacebefore it bumps into another molecule. Waves don’t travel as fastin gases.

In liquids, such as water, the molecules are much closertogether. But they are also free to slide past one another. As aresult, vibrations are transferred more quickly from one mole-cule to the next than they are in a gas. This situation can be com-pared to vibrating masses on springs that are so close togetherthat the masses rub against each other.

In a solid, molecules are not only closer together but alsotightly bound to each other. The effect is like having vibratingmasses that are glued together. When one mass starts to vibrate,all the others start to vibrate almost immediately. As a result,waves travel very quickly through most solids.

Light has a finite speedWhen you flip a light switch, light seems to fill the room instantly.However, light does take time to travel from place to place. Allelectromagnetic waves in empty space travel at the same speed,the speed of light, which is 3.00 � 108 m/s (186 000 mi/s). Thespeed of light in empty space is a constant that is often representedby the symbol c. Light travels slower when it has to pass througha medium such as air or water.

W A V E S 469

Figure 14 Dolphins use sound waves tocommunicate with one another.Sound travels three to four timesfaster in water than in air.

Wave Speed1. Place a rectangular pan

on a level surface, andfill the pan with water toa depth of about 2 cm.

2. Cut a wooden dowel (3cm in diameter orthicker) to a lengthslightly less than thewidth of the pan, andplace the dowel in oneend of the pan.

3. Move or roll the dowelslowly back and forth,and observe the lengthof the wave generated.

4. Now move the dowelback and forth faster(increased frequency).How does that affect thewavelength?

5. Do the waves alwaystravel the same speed inthe pan?


The Doppler EffectImagine that you are standing on a corner as an ambulancerushes by. As the ambulance passes, the sound of the sirenchanges from a high pitch to a lower pitch. Why? Do the soundwaves produced by the siren change as the ambulance goes by?How does the motion of the ambulance affect the sound?

Pitch is determined by the frequency of sound wavesThe pitch of a sound, how high or low it is, is determined by thefrequency at which sound waves strike the eardrum in your ear.A higher-pitched sound is caused by sound waves of higher fre-quency. As you know from the wave speed equation, frequencyand wavelength are also related to the speed of a wave.

Suppose you could see the sound waves from the ambulancesiren when the ambulance is at rest. You would see the soundwaves traveling out from the siren in circular wave fronts, asshown in Figure 15A. The distance between two successive wavefronts shows the wavelength of the sound waves. When the soundwaves reach your ears, they have a frequency equal to the num-ber of wave fronts that strike your eardrum each second. Thatfrequency determines the pitch of the sound that you hear.

470 C H A P T E R 1 4

ObserverA

ObserverB

Figure 15

When an ambulance is not moving, the soundwaves produced by the siren spread out in circles.The frequency of the waves is the same at anylocation.

A When an ambulance is moving, the sound wavesproduced by the siren are closer together in frontand farther apart behind. Observer A hears ahigher-pitched sound than Observer B hears.

B


www.scilinks.orgTopic: Doppler EffectSciLinks code: HK4032

Frequency changes when the source of waves is movingIf the ambulance is moving toward you, the sound waves fromthe siren are compressed in the direction of motion, as shown inFigure 15B. Between the time that one sound wave and the nextsound wave are emitted by the siren, the ambulance moves ashort distance. This shortens the distance between wave fronts,while the wave speed remains the same. As a result, the soundwaves reach your ear at a higher frequency.

Because the waves now have a higher frequency, you hear ahigher-pitched sound than you would if the ambulance were atrest. Similarly, if the ambulance were moving away from you, thefrequency at which the waves reached your ear would be lessthan if the ambulance were at rest, and you would hear the soundof the siren at a lower pitch. This change in the observed fre-quency of a wave resulting from the motion of the source orobserver is called the The Doppler effect occursfor light and other types of waves as well.

Doppler effect.

W A V E S 471


1. Draw a sine curve, and label a crest, a trough, and theamplitude.

2. State the SI units used for wavelength, period, frequency,and wave speed.

3. Describe how the frequency and period of a wave are related.

4. Explain why sound waves travel faster in liquids or solidsthan in air.

5. Critical Thinking What happens to the wavelength of a wavewhen the frequency of the wave is doubled but the wavespeed stays the same?

6. Critical Thinking Imagine you are waiting for a train to pass ata railroad crossing. Will the train whistle have a higher pitchas the train approaches you or after it has passed you by?

7. A wave along a guitar string has a frequency of 440 Hz anda wavelength of 1.5 m. What is the speed of the wave?

8. The speed of sound in air is about 340 m/s. What is thewavelength of sound waves produced by a guitar stringvibrating at 440 Hz?

9. The speed of light is 3 � 108 m/s. What is the frequency ofmicrowaves with a wavelength of 1 cm?

S U M M A R Y

> The highest points of atransverse wave are calledcrests; the lowest parts arecalled troughs.

> The amplitude of a trans-verse wave is half the verti-cal distance between acrest and a trough.

> The wavelength is the dis-tance between two identi-cal parts of a wave.

> The period of a wave is thetime it takes a wavelengthto pass a certain point.

> The frequency of a wave isthe number of vibrationsthat occur in a givenamount of time. (1 Hz �1 vibration/s)

> The speed of a waveequals the frequency timesthe wavelength. (v � f � l)

PracticePractice

Doppler effect an observedchange in the frequency of awave when the source orobserver is moving

▲


Disc Two, Module 13: ReflectionUse the Interactive Tutor to learn moreabout this topic.

O B J E C T I V E S

SECTION

3

472 C H A P T E R 1 4

Wave Interactions

> Describe how waves behave when they meet an obstacleor pass into another medium.

> Explain what happens when two waves interfere.> Distinguish between constructive interference and

destructive interference.> Explain how standing waves are formed.

When waves are simply moving through a medium orthrough space, they may move in straight lines like waves

on the ocean, spread out in circles like ripples on a pond, orspread out in spheres like sound waves in air. But what happenswhen a wave meets an object or another wave in the medium?And what happens when a wave passes into another medium?

Reflection, Diffraction, and RefractionYou probably already know what happens when light wavesstrike a shiny surface: they reflect off the surface. Other wavesreflect, too. Figure 16 shows two ways that a wave on a rope maybe reflected. is simply the bouncing back of a wavewhen it meets a surface or boundary.

Reflection

K E Y T E R M S

reflectiondiffractionrefractioninterferenceconstructive interferencedestructive interferencestanding wave

▲

reflection the bouncingback of a ray of light, sound,or heat when the ray hits asurface that it does not gothrough

▲

Figure 16If the end of a rope is

free to slide up and downa post, a wave on therope will reflect from theend.

If the end of the ropeis fixed, the reflectedwave is turned upsidedown.

B

A

Original wave Original wave

Reflectedwave

Reflectedwave

A B


www.scilinks.orgTopic: Reflection, Refrac-

tion, DiffractionSciLinks code: HK4119

Waves reflect at a free boundaryFigure 16A shows the reflection of a single wave traveling on arope. The end of the rope is free to move up and down on a post.When the wave reaches the post, the loop on the end moves upand then back down. This is just what would happen if someonewere shaking that end of the rope to create a new wave. Thereflected wave in this case is exactly like the original wave exceptthat the reflected wave is traveling in the opposite direction tothe direction of the original wave.

At a fixed boundary, waves reflect and turn upside downFigure 16B shows a slightly different situation. In this case, theend of the rope is not free to move because it is attached to a wall.When the wave reaches the wall, the rope exerts an upward forceon the wall. The wall is too heavy to move, but it exerts an equaland opposite downward force on the rope, following Newton’sthird law. The force exerted by the wall causes another wave tostart traveling down the rope. This reflected wave travels in theopposite direction and is turned upside down.

Diffraction is the bending of waves around an edgeIf you stand outside the doorway of a classroom, youmay be able to hear the sound of voices inside the room.But if the sound waves cannot travel in a straight line toyour ear, how are you able to hear the voices?

When waves pass the edge of an object or passthrough an opening, such as an open window or a door,they spread out as if a new wave were created there. Ineffect, the waves seem to bend around an object oropening. This bending of waves as they pass an edge iscalled

Figure 17A shows waves passing around a block in atank of water. Before they reach the block, the wavestravel in a straight line. After they pass the block, thewaves near the edge bend and spread out into the spacebehind the block. Diffraction is the reason that shadowsnever have perfectly sharp edges.

The tank in Figure 17B contains two blocks placedend to end with a small gap in between. In this case,waves bend around two edges and spread out as theypass through the opening. Sound waves passingthrough a door behave the same way. Because soundwaves spread out into the space beyond the door, a per-son near the door on the outside can hear sounds frominside the room.

diffraction.

W A V E S 473

diffraction a change in thedirection of a wave when thewave finds an obstacle or anedge, such as an opening

▲

Figure 17Waves bend when they pass the edge of

an obstacle.

When they pass through an opening,waves bend around both edges.B

A

A

B


Waves can also bend by refractionFigure 18 shows a spoon in a glass of water. Why does the spoonlook like it is broken into two pieces? This strange sight resultsfrom light waves bending, but not because of diffraction. Thistime, the waves are bending because of Refraction isthe bending of waves when they pass from one medium intoanother. All waves are refracted when they pass from onemedium to another at an angle.

Light waves from the top of the spoon handle pass straightthrough the air and the glass from the spoon to your eyes. But thelight waves from the rest of the spoon start out in the water, thenpass into the glass, then into the air. Each time the waves enter anew medium, they bend slightly because of a change in speed. Bythe time those waves reach your eyes, they are coming from a dif-ferent angle than the waves from the top of the spoon handle. Butyour eyes just see that one set of light waves are coming from onedirection, and another set of waves are coming from a differentdirection. As a result, the spoon appears to be broken.

InterferenceWhat would happen if you and another person tried to walkthrough the exact same place at the same time? You would runinto each other. Material objects, such as a human body, cannotshare space with other material objects. More than one wave,however, can exist in the same place at the same time.

Waves in the same place combine to producea single waveWhen several waves are in the same location,the waves combine to produce a single, newwave that is different from the original waves.This is called Figure 19 showsinterference occurring as water waves passthrough each other. Once the waves havepassed through each other and moved on, theyreturn to their original shape.

You can show the interference of two wavesby drawing one wave on top of another on agraph, as in Figure 20. The resulting wave canbe found by adding the height of the waves ateach point. Crests are considered positive, andtroughs are considered negative. This methodof adding waves is sometimes known as theprinciple of superposition.

interference.

refraction.

Figure 18Because light waves bend whenthey pass from one medium toanother, this spoon looks like itis in two pieces.

474 C H A P T E R 1 4

Figure 19Water waves passing through each other produceinterference patterns.

refraction the bending of a wavefront as the wavefrontpasses between two sub-stances in which the speed of the wave differs

interference the combina-tion of two or more waves ofthe same frequency that resultsin a single wave

▲▲


Disc Two, Module 14: RefractionUse the Interactive Tutor to learn moreabout this topic.

Constructive interference increases amplitudeWhen the crest of one wave overlaps the crest of another wave,the waves reinforce each other, as shown in Figure 20A. Thinkabout what happens at the particle level. Suppose the crest of onewave would move a particle up 4 cm from its original position,and another wave crest would move the particle up 3 cm.

When both waves hit at the same time, the particle moves up 4 cm due to one wave and 3 cm due to the other for a total of 7 cm. The result is a wave whose amplitude is the sum of the amplitudes of the two individual waves. This is called

Destructive interference decreases amplitudeWhen the crest of one wave meets the trough of another wave,the resulting wave has a smaller amplitude than the larger of the two waves, as shown in Figure 20B. This is called

To understand how this works, imagine again a single parti-cle. Suppose the crest of one wave would move the particle up 4cm, and the trough of another wave would move it down 3 cm. Ifthe waves hit the particle at the same time, the particle wouldmove in response to both waves, and the new wave would havean amplitude of just 1 cm. When destructive interference occursbetween two waves that have the same amplitude, the waves maycompletely cancel each other out, as shown in Figure 20C.

destructive interference.

constructive interference.

W A V E S 475

Figure 20Constructive and DestructiveInterference

When two waves line up sotheir crests overlap, they addtogether to make a larger wave.

When the crest of a largewave overlaps with the trough of a smaller wave, subtractionoccurs.

Two waves of the same sizemay completely cancel each otherout.

C

B

A

First wave

Second wave

Resulting wave

First wave

Resulting wave

Second wave

First wave

Resulting wave

Second wave

constructive interferenceany interference in whichwaves combine so that theresulting wave is bigger thanthe original waves

destructive interferenceany interference in whichwaves combine so that theresulting wave is smaller thanthe largest of the original waves

▲▲

A

B

C


Interference of light waves creates colorful displaysThe interference of light waves often produces colorful displays.You can see a rainbow of colors when oil is spilled onto a waterysurface. Soap bubbles, like the ones shown in Figure 21, havereds, blues, and yellows on their surfaces. The colors in theseexamples are not due to pigments or dyes. Instead, they are dueto the interference of light.

When you look at a soap bubble, some light waves bounce offthe outside of the bubble and travel directly to your eye. Otherlight waves travel into the thin shell of the bubble, bounce off theinner side of the bubble’s shell, then travel back through the shell,into the air and to your eye. Those waves travel farther than thewaves reflected directly off the outside of the bubble. At times thetwo sets of waves are out of step with each other. The two sets ofwaves interfere contructively at some frequencies (colors) anddestructively at other frequencies (colors). The result is a swirlingrainbow effect.

Interference of sound waves produces beatsThe sound waves from two tuning forks of slightly different frequencies will interfere with each other as shown in Figure 22A.Because the frequencies of the tuning forks are different, thecompressions arrive at your ear at different rates.

When the compressions from the two tuning forks arrive atyour ear at the same time, constructive interference occurs, andthe sound is louder. A short time later, the compression from oneand the rarefaction from the other arrive together. When thishappens, destructive interference occurs, and a softer sound isheard. After a short time, the compressions again arrive at thesame time, and again a loud sound is heard. Overall, you hear aseries of loud and soft sounds called beats.

476 C H A P T E R 1 4

Figure 21 The colorful swirls on a bubbleresult from the constructiveinterference of some colors andthe destructive interference ofother colors.

Figure 22When two waves of slightly

different frequencies interfere witheach other, they produce beats.

A piano tuner can listen forbeats to tell if a string is out of tune.

B

A

Destructiveinterference

Destructiveinterference

Constructiveinterference

t1 t2 t3

A B


Figure 22B shows a piano tuner tuning astring. Piano tuners listen for beats between atuning fork of known frequency and a string ona piano. By adjusting the tension in the string,the tuner can change the pitch (frequency) ofthe string’s vibration. When no beats are heard,the string is vibrating with the same frequencyas the tuning fork. In that case, the string is saidto be in tune.

Standing WavesWaves can also interfere in another way.Suppose you send a wave through a rope tied toa wall at the other end. The wave is reflectedfrom the wall and travels back along the rope.If you continue to send waves down the rope,the waves that you make will interfere withthose waves that reflect off the wall and travelback toward you.

Interference can cause standing wavescan form when a wave is

reflected at the boundary of a medium. In astanding wave, interference of the originalwave with the reflected wave causes themedium to vibrate in a stationary pattern thatresembles a loop or a series of loops. Althoughit appears as if the wave is standing still, in real-ity waves are traveling in both directions.

Standing waves have nodes and antinodesEach loop of a standing wave is separated from the next loop bypoints that have no vibration, called nodes. Nodes lie at thepoints where the crests of the original waves meet the troughs ofthe reflected waves, causing complete destructive interference.

One of the nodes on a fixed rope lies at the point of reflection,where the rope cannot vibrate. Another node is near your hand.If you shake the rope up and down at the right frequency, you cancreate standing waves with several nodes along the length of thestring.

Midway between the nodes lie points of maximum vibration,called antinodes. Antinodes form where the crests of the originalwaves line up with the crests of the reflected waves so that com-plete constructive interference occurs.

Standing waves

W A V E S 477

standing wave a pattern ofvibration that simulates a wavethat is standing still

▲

Connection toARCHITECTUREARCHITECTUREARCHITECTUREARCHITECTUREARCHITECTUREARCHITECTURE

You might have experienced destructive inter-ference in an auditorium or a concert hall.

As sound waves reflect from the walls, there areplaces, known as dead spots, where the wavesinterfere destructively and cancel out.

Dead spots are produced by the interferenceof sound waves coming directly from the stageand waves reflected off the walls. For this reason,architects design concert halls so that the dimen-sions are not simple multiples of each other.They also try to avoid smooth, parallel walls inthe design. Irregularities in the wall and ceilingcontribute to reducing the direct reflections ofwaves and the possible resulting interference.

Making the Connection1. With a friend, go to a square or rectangular

room with walls made of brick, cinder block,or concrete. Have one person talk or singloudly while the other person moves aroundthe room to locate dead spots.

2. Draw an overhead view of the room, andmark the locations of the dead spots. Why doyou think the dead spots are in those places?

3. Write a short paragraph explaininghow the room could be changedto reduce or eliminate the deadspots.

WRITINGS K I L L


Standing waves can have only certain wavelengthsFigure 23 shows several different possible stand-ing waves on a string fixed at both ends. Only afew waves with specific wavelengths can formstanding waves in any given string.

The simplest standing waves occur when thewavelength of the waves is twice the length of thestring. In that case, it just looks like the entirestring is shaking up and down. The only nodesare on the two ends of the string.

If the string vibrates with a higher frequency,the wavelength becomes shorter. At a certain fre-quency, the wavelength is exactly equal to thelength of the string. In the middle of the string,complete destructive interference occurs, pro-ducing a node.

In general, standing waves can exist whenevera multiple of half-wavelengths will fit exactly inthe length of the string. It is even possible forstanding waves of more than one wavelength toexist on a string at the same time.

478 C H A P T E R 1 4


1. Describe what may happen when ripples on a pondencounter a large rock in the water.

2. Explain why you can hear two people talking even after theywalk around a corner.

3. Name the conditions required for two waves to interfereconstructively.

4. Explain why colors appear on the surface of a soap bubble.

5. Draw a standing wave, and label the nodes and antinodes.

6. Critical Thinking What conditions are required for twowaves on a rope to interfere completely destructively?

7. Critical Thinking Imagine that you and a friend are trying totune the lowest strings on two different guitars to the samepitch. Explain how you could use beats to determine if thestrings are tuned to the same frequency.

8. Critical Thinking Determine the longest possible wavelengthof a standing wave on a string that is 2 m long.

S U M M A R Y

> Waves bouncing off a sur-face is called reflection.

> Diffraction is the bendingof waves as they pass anedge or corner.

> Refraction is the bending ofwaves as they pass fromone medium to another.

> Interference results whentwo waves exist in thesame place and combineto make a single wave.

> Interference may causestanding waves.

Figure 23 These photos of standing waves were capturedusing a strobe light that flashes different colors at different times.


G R A P H I N G S K I L L S 479

Interpreting Graphs

The graphs above show the behavior of a single transverse wave. Study the graphs, andanswer the following questions.

What types of graphs are these?

What variable is described in the x-axis of the firstgraph? What variable is described in the x-axis of the second graph?

What information about the wave is indicated by thefirst graph? What information is indicated by the sec-ond graph?

Determine from the graphs the period, amplitude,and wavelength of the wave.

Using the frequency-period equation, calculate thefrequency of the wave. Use the wave speed equationto calculate the speed of the wave.

Why are both graphs needed to provide completeinformation about the wave?

Plot the data given in the table to the right. From thegraph, calculate the wavelength and amplitude of thewave.

7

6

5

4

3

2

1

Graphing SkillsGraphing SkillsGraphing Skills

x-axis (cm) y-axis (cm)

0 0.93

0.25 2.43

0.50 3.00

0.75 2.43

1.00 0.93

1.25 –0.93

1.50 –2.43

1.75 –3.00

2.00 –2.43

2.25 –0.93

2.50 0.93

2.75 2.43

3.00 3.00

Dis

plac

emen

t (c

m) 5

-5

0.005 0.01 0.015 0.02 0.025 0.03

Time (s)

Dis

plac

emen

t (c

m) 5

-5

10 20 30 40 50 60

Distance (cm)


8. In an ocean wave, the molecules of watera. move perpendicular to the direction of

wave travel.b. move parallel to the direction of wave

travel.c. move in circles.d. don’t move at all.

9. Half the vertical distance between the crestand trough of a wave is called the a. frequency. c. wavelength.b. crest. d. amplitude.

10. The number of waves passing a given pointper unit of time is called the a. frequency. c. wavelength.b. wave speed. d. amplitude.

11. The Doppler effect of a passing siren resultsfrom an apparent change ina. loudness. c. frequency.b. wave speed. d. interference.

12. The combining of waves as they meet isknown asa. a crest. c. interference.b. noise. d. the Doppler effect.

13. Waves bend when they pass through anopening. This is called a. interference. c. refraction.b. diffraction. d. the Doppler effect.

14. Refraction occurs whenevera. a wave passes from one medium to

another at an angle.b. two waves interfere with one another.c. a wave is reflected at a free boundary.d. standing waves occur.

15. The Greek letter l is often used to representa wave’s a. period. c. frequency.b. wavelength. d. amplitude.

Chapter HighlightsBefore you begin, review the summaries of thekey ideas of each section, found at the end ofeach section. The key vocabulary terms arelisted on the first page of each section.

1. A wave is a disturbance that transmits a. matter. c. energy.b. particles. d. a medium.

2. Electromagnetic waves a. are transverse waves.b. require a medium.c. are mechanical waves.d. are longitudinal waves.

3. The speed of a wave depends on the a. medium. c. amplitude.b. frequency. d. wavelength.

4. Waves that need a medium in which totravel are called a. longitudinal waves.b. transverse waves.c. mechanical waves.d. All of the above.

5. Most waves are caused by a. velocity. c. a vibration.b. amplitude. d. earthquakes.

6. For which type of waves do particles in themedium vibrate perpendicular to the direc-tion in which the waves are traveling?a. transverse wavesb. longitudinal wavesc. P wavesd. none of the above

7. A sound wave is an example of a. an electromagnetic wave.b. a transverse wave.c. a longitudinal wave.d. a surface wave.

UNDERSTANDING CONCEPTSUNDERSTANDING CONCEPTS

480 C H A P T E R 1 4

R E V I E WC H A P T E R 14


16. How would you describe the amplitude of a wave using the words crest and trough?

17. Explain the difference between waves bend-ing due to refraction and diffraction.

18. Imagine you are shaking the end of a ropeto create a series of waves. What will youobserve if you begin shaking the rope morequickly? Use the terms wave speed, frequency,and wavelength in your answer.

19. Describe the changes in elastic potentialenergy and kinetic energy that occur whena mass vibrates on a spring.

20. Use the kinetic theory to explain the differ-ence in wave speed in solids, liquids, andgases.

21. Why is the reflection of a wave at a freeboundary different from reflection at a fixed boundary?

22. How do beats help determine whether two sound waves are of the same frequency?Use the terms constructive interference anddestructive interference in your answer.

23. How is an electromagnetic wave differentfrom a mechanical wave?

24. You have a long metal rod and a hammer.How would you hit the metal rod to create a longitudinal wave? How would you hit it to create a transverse wave?

25. Identify each of the following as a distancemeasurement, a time measurement, or neither.a. amplitude d. frequencyb. wavelength e. wave speedc. period

26. Explain the difference between constructiveinterference and destructive interference.

27. Imagine a train approaching a crossing whereyou are standing safely behind the gate. Ex-plain the changes in sound of the horn thatyou may hear as the train passes. Use thefollowing terms in your answer: frequency,wavelength, wave speed, and Doppler effect.

28. Draw a picture of a standing wave, and labela node and an antinode.

29. Wave Speed Suppose you tie one end of a rope to a doorknob and shake the otherend with a frequency of 2 Hz. The wavesyou create have a wavelength of 3 m. Whatis the speed of the waves along the rope?

30. Wave Speed Ocean waves are hitting abeach at a rate of 2.0 Hz. The distancebetween wave crests is 1.5 m. Calculate the speed of the waves.

31. Wavelength All electromagnetic waves have the same speed in empty space, 3.00 � 108 m/s. Using that speed, find thewavelengths of the electromagnetic waves at the following frequencies:a. radio waves at 530 kHzb. visible light at 6.0 � 1014 Hzc. X rays at 3.0 � 1018 Hz

32. Frequency Microwaves range in wavelengthfrom 1 mm to 30 cm. Calculate their rangein frequency. Use 3.00 � 108 m/s as thespeed of electromagnetic waves.

33. Wavelength The frequency of radio wavesrange from about 3.00 � 105 Hz to 3.00 �107 Hz. What is the range of frequenciesof these waves? Use 3.00 � 108 m/s as thespeed of electromagnetic waves.

34. Frequency The note A above middle C on apiano emits a sound wave with wavelength0.77 m. What is the frequency of the wave?Use 340 m/s as the speed of sound in air.

W A V E S 481

USING VOC ABULARYUSING VOC ABULARY

BUILDING MATH SKILLSBUILDING MATH SKILLS


41. Interpreting Graphics Draw the wave thatresults from interference between the twowaves shown below.

42. Understanding Systems An orchestra isplaying in a huge outdoor amphitheater, andthousands of listeners are sitting on a hill-side far from the stage. To help those listen-ers hear the concert, the amphitheater hasspeakers halfway up the hill. How could youimprove this system? A computer delays thesignal to the speakers by a fraction of a sec-ond. Why is this computer used? Explainwhat might happen if the signal were notdelayed at all.

43. Applying Knowledge Dolphins use soundwaves to detect other organisms close by.How can a dolphin use the Doppler effect todetermine whether an organism is movingtowards it? (Hint: the sound waves dolphinsuse can reflect off objects in the water andcreate an echo.)

44. Applying Knowledge Describe how youinteract with waves during a typical schoolday. Document the types of waves youencounter. Document also how often youinteract with each type of wave. Decidewhether one type of wave is more importantin your life than the other types of waves.

45. Applying Technology With yourteacher’s help, use a microphoneand an oscilloscope or a CBLinterface to obtain an image of a sound.Determine the frequency and wavelength ofthe sound.

35. Graphing Draw a sine curve, and label a crest, a trough, and the amplitude.

36. Interpreting Graphics The wave shown inthe figure below has a frequency of 25.0 Hz.Find the following values for this wave:a. amplitude c. speedb. wavelength d. period

37. Understanding Systems A friend standing2 m away strikes two tuning forks at thesame time, one at a frequency of 256 Hz and the other at 240 Hz. Which sound willreach your ear first? Explain.

38. Applying Knowledge When you are watch-ing a baseball game, you may hear the crackof the bat a short time after you see the bat-ter hit the ball. Why does this happen?(Hint: Consider the relationship betweenthe speed of sound and the speed of light.)

39. Understanding Systems You are standingon a street corner, and you hear a fire truckapproaching. Does the pitch of the sirenstay constant, increase, or decrease as itapproaches you? Explain.

40. Applying Knowledge If you yell or clap yourhands while standing at the edge of a largerock canyon, you may hear an echo a fewseconds later. Explain why this happens.

482 C H A P T E R 1 4

R E V I E WC H A P T E R 14

THINKING CR ITIC ALLYTHINKING CR ITIC ALLY

b.a.

DEVELOPING LI FE/WORK SKILLSDEVELOPING LI FE/WORK SKILLS

COMPUTERS K I L L

18 cm

10.0 cm

BUILDING GR APHING SKILLSBUILDING GR APHING SKILLS


46. Making Decisions A new car is advertised ashaving antinoise technology. The manufac-turer claims that inside the car any soundsare negated. Evaluate the possibility of sucha claim. What would have to be created tocause destructive interference with anysound in the car? Do you believe that themanufacturer is correct in its statement?

47. Working Cooperatively Work with otherclassmates to research architecturalacoustics that would affect a restaurant.Investigate acoustics problems in placeswhere many people gather. How do odd-shaped ceilings, decorative panels, and glasswindows affect echoes? Prepare a model ofyour school cafeteria showing what changesyou would make to reduce the level of noise.

48. Applying Knowledge A piano tuner listensto a tuning fork vibrating at 440 Hz to tunethe string of a piano. He hears beats betweenthe tuning fork and the piano string. Is thestring in tune? Explain your answer.

49. Connection to Space Science The Dopplereffect occurs for light waves as well as forsound waves. Research some of the waysin which the Doppler effect has helpedastronomers understand the motion of dis-tant galaxies and other objects in deep space.

50. Connection to Earth Science What is themedium for seismic waves?

51. Connection to Architecture Explore anddescribe research on earthquake-proofbuildings and materials. Evaluate theimpact of this research on society in termsof building codes and architectural styles inearthquake-prone areas such as Los Angeles,San Francisco, and Tokyo.

52. Concept Mapping Copy the unfinishedconcept map below onto a sheet of paper.Complete the map by writing the correctword or phrase in the lettered boxes.

W A V E S 483

INTEGR ATING CONCEPTSINTEGR ATING CONCEPTS

and caneither be

in whichparticlesvibrate

are either

transversewaves

a. electromagneticwaves

b.

Waves

f.

c.

through

or g.matter

d.

in whichparticlesvibrate

e.

require a mediumin which to travel

or

or

whichwhich carry

Art Credits: Fig. 4-5, Uhl Studios, Inc.; Fig. 8, Uhl Studios, Inc.; Fig. 9, Mark Schroeder; Fig. 11, Uhl Studios, Inc.; Fig. 16, Mark Schroeder; Fig. 20, Uhl Studios, Inc.

Photo Credits: Chapter Opener image of surfer, International Stock Photography; sunset overbeach, Bill Brooks/Masterfile; Fig. 1, SuperStock; Fig. 2, Art Resource, NY; Fig. 3, “Quick Lab,” Fig. 6-7, Peter Van Steen/HRW; Fig. 13, Joe Devenney/Getty Images/The Image Bank; Fig. 14, Jeff Hunter/Getty Images/The Image Bank; Fig. 15, Peter Van Steen/HRW; Fig. 17, E. R.Degginger/Color-Pic, Inc.; Fig. 18, Peter Van Steen/HRW; Fig. 19, E. R. Degginger/Color-Pic, Inc.; Fig. 21, Michael Freeman/Bruce Coleman, Inc.; Fig. 22, Neil Nissing/Getty Images/FPG International;Fig. 23, Richard Megna/Fundamental Photographs; “Skills Practice Lab,” Sam Dudgeon/HRW;“Career Link,” Peter Van Steen/HRW.

www.scilinks.orgTopic: Seismic Waves SciLinks code: HK4126


Introduction

Objectives

Materials

484 C H A P T E R 1 4

Modeling TransverseWaves

� Procedure

Making Sine Curves with a Sand Pendulum 1. Review the discussion in Section 2 on the use of sine

curves to represent transverse waves.

2. On a blank sheet of paper, prepare a table like theone shown at right.

3. Use a nail to puncture a small hole in the bottom ofa paper cup. Also punch two holes on opposite sidesof the cup near the rim. Tie strings of equal lengththrough the upper holes. Make a pendulum by tyingthe strings from the cup to a ring stand or other sup-port. Clamp the stand down at the end of a table, asshown in the photograph at right. Cover the bottomhole with a piece of tape, then fill the cup with sand.SAFETY CAUTION Wear gloves while handling the nails and punching holes.

4. Unroll some of the paper, and mark off a length of 1 m using two dotted lines.Then roll the paper back up, and position the paperunder the pendulum, as shown in the photograph atright.

5. Remove the tape over the hole. Start the pendulumswinging as your lab partner pulls the paper perpen-dicular to the cup’s swing. Another lab partner shouldloosely hold the paper roll. Try to pull the paper in astraight line with a constant speed. The sand shouldtrace a sine curve on the paper, as in the photographat right.

6. As your partner pulls the paper under the pendulum,start the stopwatch when the sand trace reaches thefirst dotted line marking the length of 1 m. When thesand trace reaches the second dotted line, stop thewatch. Record the time in your table.

7. When you are finished making a curve, stop the pen-dulum and cover the hole in the bottom of the cup.Be careful not to jostle the paper; if you do, your tracemay be erased. You may want to tape the paper down.

When a transverse wave model is cre-ated with a sand pendulum, what wavecharacteristics can you measure?

> Create sine curves by pulling paperunder a sand pendulum.

> Measure the amplitude, wavelength,and period of transverse waves usingsine curves as models.

> Form ahypothesis about how changes tothe experiment may change theamplitude and wavelength.

> Calculate frequency and wave speedusing your measurements.

colored sandmasking tapemetersticknailpaper or plastic-foam cupring stand or other supportrolls of white paper, about 30 cm widestopwatchstring and scissors

USING SCIENTIFIC METHODS


W A V E S 485

8. For the part of the curve between the dotted lines, mea-sure the distance from the first crest to the last crest, thendivide that distance by the total number of crests. Recordyour answer in the table under “Average wavelength.”

9. For the same part of the curve, measure the vertical distance between the first crest and the first trough,between the second crest and the second trough, andso on. Add the distances together, then divide by thenumber of distances you measured. Record your answerin the table under “Average amplitude.”

Designing Your Experiment 10. With your lab partners, form a hypothesis about how to make two additional sine

curve traces, one with a different average wavelength than the first trace and onewith a different average amplitude.

11. In your lab report, write down your plan for changing these two factors. Before youcarry out your experiment, your teacher must approve your plan.

Performing Your Experiment12. After your teacher approves your plan, carry out your experiment. For each curve,

measure and record the time, the average wavelength, and the average amplitude.

13. After each trace, return the sand to the cup and roll the paper back up.

� Analysis 1. For each of your three curves, calculate the average speed at which the paper was

pulled by dividing the length of 1 m by the time measurement. This is equivalentto the speed of the wave that the curve models or represents.

2. For each curve, use the wave speed equation to calculate average frequency.

� Conclusions3. What factor did you change to alter the average wavelength of the curve? Did your

plan work? If so, did the wavelength increase or decrease?

4. What factor did you change to alter the average amplitude? Did your plan work?

average frequency = f = v�l

average wave speed��average wavelength

Length along Time (s) Average Average paper = 1 m wavelength (m) amplitude (m)

Curve 1

Curve 2

Curve 3


486 C A R E E R L I N K

Most people have seen a sonogram showing anunborn baby inside its mother’s womb. Ultrasoundtechnologists make these images with an ultrasound machine, which sends harmless, high-frequency sound waves into the body. Ultra-sonographers work in hospitals, clinics, and doctors’ offices. Besides checking on the health of unborn babies, ultrasonographersuse their tools to help diagnose cancer, heart disease, and otherhealth problems. To find out moreabout this career, read this inter-view with Estela Zavala, a registered diagnostic medical sonographer who works at Austin Radiological Association in Austin, Texas.

Ultrasonographer

What does an ultrasonographer do?

We scan various organs of the body with anultrasound machine to see if there are anyabnormalities. For example, we can check a gallbladder to see if there are any stonesin it. We already know what healthy organslook like, so anything unusual shows up inthese pictures. This can help a doctor makea diagnosis.

How does the ultrasoundmachine make pictures?

The machine creates high-frequency soundwaves. When the sound waves reflect off of the organs in the body, the waves strikea piezoelectric crystal in the detector. Piezoelectric crystals can convert the pres-sure energy from the ultrasound wave intoan electrical signal. The ultrasound systemprocesses the signal to create an image.

What part of your job doyou find most satisfying?

I like helping people find out what is wrongwith them in a noninvasive way. Beforeultrasound, invasive surgery was often theonly option.

What is challenging aboutyour job?

The technology is constantly changing. Weare using ultrasound in more ways thanever before. For example, we can now cre-ate images of veins and arteries.

What skills does an ultrasonographer need?

First you need excellent hand-eye coordina-tion, so you can move the equipment overthe parts of the body you need to image.You also have to know a lot about all of theorgans in the body. It is very important to be able to work quickly, because some-times patients are uncomfortable.

Estela Zavala uses anultrasound machineto check this man’skidneys.

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“Ultrasound is ahelpful diagnostictool that allowsyou to see insidethe body withoutthe use of X rays.”

CareerLinkCareerLinkCareerLinkCareerLinkCareerLink


How much training and education did you receivebefore becoming an ultrasonographer?

After graduating from high school, I went to an X-ray school to be licensed as an X-ray technolo-gist. A medical background like this is necessaryfor entering ultrasound training. First I went toan intensive 1-month training program, whichinvolved 2 weeks of hands-on work and 2 weeks of classwork. After that, I worked for alicensed radiologist for about a year. Finally, Iattended an accredited year-long ultrasound program at a local community college beforebecoming fully licensed.

What part of your education do you think was the mostvaluable?

The best part was the on-the-job training thatwas involved. You need to do a lot of ultra-sounds before you can become proficient.

“I’ve seen many changes and innovations in ultrasound since I began. Because of this, the job always seems new.”

—Estela Zavala

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487

www.scilinks.orgTopic: UltrasoundSciLinks code: HK4143

Would you recommend ultra-sound technology as a career to students?

Yes, I would recommend it. Just remember thatyou must have some medical experience first,such as being a nurse or an X-ray technician, ifyou want to continue into other areas of radiol-ogy, like ultrasound.

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14 waves - grygla public schoolthe bigger the wave is, the more energy it carries. a cruise ship...

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