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Chapter 20: Traveling Waves

20.1 The wave model

20.2 One-dimensional waves

20.3 Sinusoidal waves

20.4 Waves in 2- & 3-dimensions

20.5 Sound and Light Waves

20.6 Power and Intensity

20.7 Doppler Effect

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What is the essence of waviness?

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The Wave Model

What is a wave?

… a disturbance that moves through a medium (or vacuum).

Types of waves:

1. Mechanical waves: water waves and sound waves

2. Electromagnetic waves: light waves including radio waves, x-rays, etc

3. Matter waves: electrons and atoms show wave-like characteristics

Wave

Continuous, nonlocalized, collective

Particles

discrete, localized, individual

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Waves: examples

1. Ripples on a pond …

Think of a leaf, or a cork on the water …

… this leaf (or water) “bobs” up and down,

but the disturbance, i. e. the ripples,

moves to the edge of the pond.

2. Slinky …

the disturbance, red-dot moves back and forth…,

but the wave moves from one end to the other.

A wave transfers energy, but no material or substance from the source.

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Waves: examples

3. Cornfield…

As the wind blows across the field, observe one stalk ...the disturbance,

ear of corn, moves side to side, but the wave across the field.

4. Waves on a string or a rope- example of one dimensional waves

up/down

motion of wave at speed v

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Waves on a string

Wave speed: v = √√√√Ts/µµµµ

Ts = tension,

µµµµ = linear density

= mass/length

Does v depend on size of the wave?

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Wave speed, wavelength, time period and frequency

t

Wavelength = distance from one crest to the next

Frequency (f) = number of cycles (ups and downs) per second

Period = time for one complete cycle (up-down-up) = 1/f

Amplitude = Height of a crest

Speed (v) = wavelength/period

= frequency x wavelength 8

Two types of wave motion: transverse and longitudinal

Transverse waves: … the disturbance is perpendicular to the

direction of the wave. Examples?

Longitudinal waves: …the disturbance is parallel to the wave.

slinky Sound wave, speed = 1100ft/s (approx)

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Electromagnetic spectrum

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Chapter 20. Reading Quizzes

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A graph showing wave displacement versus position at a specific instant of time is called a

A. snapshot graph.

B. history graph.

C. bar graph.

D. line graph.

E. composite graph.

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A graph showing wave displacement versus position at a specific instant of time is called a

A. snapshot graph.

B. history graph.

C. bar graph.

D. line graph.

E. composite graph.

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A graph showing wave displacement versus time at a specific point in space is called a

A. snapshot graph.

B. history graph.

C. bar graph.

D. line graph.

E. composite graph.

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A graph showing wave displacement versus time at a specific point in space is called a

A. snapshot graph.

B. history graph.

C. bar graph.

D. line graph.

E. composite graph.

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A wave front diagram shows

A. the wavelengths of a wave.

B. the crests of a wave.

C. how the wave looks as it moves

toward you.

D. the forces acting on a string that’s

under tension.

E. Wave front diagrams were not

discussed in this chapter.

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A wave front diagram shows

A. the wavelengths of a wave.

B. the crests of a wave.

C. how the wave looks as it moves

toward you.

D. the forces acting on a string that’s

under tension.

E. Wave front diagrams were not

discussed in this chapter.

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The waves analyzed in this chapter are

A. string waves.

B. sound and light waves.

C. sound and water waves.

D. string, sound, and light waves.

E. string, water, sound, and light waves.

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The waves analyzed in this chapter are

A. string waves.

B. sound and light waves.

C. sound and water waves.

D. string, sound, and light waves.

E. string, water, sound, and light waves.

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Sine-function: mathematical representation of a wave

x

0( ) sin 2

xE x E π ϕπ ϕπ ϕπ ϕ

λλλλ

= += += += +

λλλλ 2λλλλ 3λλλλ

( )E x

0EAmplitude

Amplitude Phase (initial)

0ϕϕϕϕ ====

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Sinusoidal Waves are periodic both in time and space

Source of

the WaveTime

Distribution of waves in

space at different time

x

v

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Phase difference

Phase =

Phase difference:

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Waves in Two and Three Dimensions

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Power and Intensity

Power (P) = the rate of energy transfer

from the source (J/sec)

Intensity = P/area = Power-to-area ratio

∝∝∝∝ Amplitude2

Sound intensity level:

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Doppler Effect: observed frequency shift due to motion

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Doppler Effect …

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Doppler Effect …

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EXAMPLE 20.11 How fast are the police traveling?

QUESTION:

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EXAMPLE 20.11 How fast are the police traveling?

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EXAMPLE 20.11 How fast are the police traveling?

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Chapter 20. Summary SlidesChapter 20. Summary Slides

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General Principles

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General Principles

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Important Concepts

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Important Concepts

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Applications

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Applications

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Applications

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Chapter 20. MultipleChapter 20. Multiple--Choice Choice

QuestionsQuestions

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Which of the following actions would make a pulse travel faster down a stretched string?

A. Use a heavier string of the same length, under the same tension.

B. Use a lighter string of the same length, under the same tension.

C. Move your hand up and down more quickly as you generate the pulse.

D. Move your hand up and down a larger distance as you generate the pulse.

E. Use a longer string of the same thickness, density, and tension.

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Which of the following actions would make a pulse travel faster down a stretched string?

A. Use a heavier string of the same length, under the same tension.

B. Use a lighter string of the same length, under the same tension.

C. Move your hand up and down more quickly as you generate the pulse.

D. Move your hand up and down a larger distance as you generate the pulse.

E. Use a longer string of the same thickness, density, and tension.

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What is the

frequency of this

traveling wave?

A. 0.1 Hz

B. 0.2 Hz

C. 2 Hz

D. 5 Hz

E. 10 Hz

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A. 0.1 Hz

B. 0.2 Hz

C. 2 Hz

D. 5 Hz

E. 10 Hz

What is the

frequency of this

traveling wave?

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What is the phase difference between the crest of a wave and the adjacent trough?

A. 0

B. π

C. π /4

D. π /2

E. 3 π /2

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What is the phase difference between the crest of a wave and the adjacent trough?

A. 0

B. π

C. π /4

D. π /2

E. 3 π /2

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A light wave travels through three transparent materials of equal thickness. Rank in order, from the largest to smallest, the indices of refraction n1, n2, and n3.

A. n1 > n2 > n3

B. n2 > n1 > n3

C. n3 > n1 > n2

D. n3 > n2 > n1

E. n1 = n2 = n3 46

A light wave travels through three transparent materials of equal thickness. Rank in order, from the largest to smallest, the indices of refraction n1, n2, and n3.

A. n1 > n2 > n3

B. n2 > n1 > n3

C. n3 > n1 > n2

D. n3 > n2 > n1

E. n1 = n2 = n3

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Amy and Zack are both listening to the source of sound waves that is moving to the right. Compare the frequencies each hears.

A. fAmy > fZack

B. fAmy < fZack

C. fAmy = fZack

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Amy and Zack are both listening to the source of sound waves that is moving to the right. Compare the frequencies each hears.

A. fAmy > fZack

B. fAmy < fZack

C. fAmy = fZack