Chapter 20. Traveling Waves - Physics & Astronomy - GSU...

Chapter 20. Traveling WavesChapter 20. Traveling Waves

You may not realize it, but you are surrounded by waves. The “waviness” of a water wave is readily apparent, from the ripples on a pond to ocean waves large

Copyright © 2008 Pearson Education, Inc., publishing as Pearson Addison-Wesley.

a pond to ocean waves large enough to surf. It’s less apparent that sound and light are also waves.

Chapter Goal: To learn thebasic properties of traveling waves.

Topics:

• The Wave Model

• One-Dimensional Waves

• Sinusoidal Waves

Chapter 20. Traveling WavesChapter 20. Traveling Waves


• Waves in Two and Three Dimensions

• Sound and Light

• Power, Intensity, and Decibels

• The Doppler Effect

Chapter 20. Reading Quizzes


Chapter 20. Reading Quizzes

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.


C. bar graph.

D. line graph.

E. composite graph.

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.


C. bar graph.

D. line graph.

E. composite graph.

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.


toward you.

D. the forces acting on a string that’s

under tension.

E. Wave front diagrams were not

discussed in this chapter.

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.


D. string, sound, and light waves.

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

Chapter 20. Basic Content and ExamplesChapter 20. Basic Content and Examples


Chapter 20. Basic Content and ExamplesChapter 20. Basic Content and Examples

Transverse and Longitudinal Waves


Wave Speed

The speed of transverse waves on a string stretched with

tension Ts is


where µ is the string’s mass-to-length ratio, also called the

linear density.

EXAMPLE 20.1 The speed of a wave pulse

QUESTION:


EXAMPLE 20.1 The speed of a wave pulse


One-Dimensional Waves

• To understand waves we must deal

with functions of two variables, position and

time.

• A graph that shows the wave’s displacement as

a function of position at a single instant of time


a function of position at a single instant of time

is called a snapshot graph. For a wave on a

string, a snapshot graph is literally a picture of

the wave at this instant.

• A graph that shows the wave’s displacement as

a function of time at a single position in space

is called a history graph. It tells the history of

that particular point in the medium.

EXAMPLE 20.2 Finding a history graph from a snapshot graph

QUESTION:


EXAMPLE 20.2 Finding a history graph from a snapshot graph


Sinusoidal Waves

• A wave source that oscillates with simple

harmonic motion (SHM) generates a sinusoidal wave.

• The frequency f of the wave is the frequency of

the oscillating source.

• The period T is related to the wave frequency f by


• The amplitude A of the wave is the maximum value

of the displacement. The crests of the wave

have displacement Dcrest = A and the troughs have

displacement Dtrough = −A.

Sinusoidal Waves


Sinusoidal Waves

• The distance spanned by one cycle of the motion is

called the wavelength λ of the wave. Wavelength is

measured in units of meters.

• During a time interval of exactly one period T, each

crest of a sinusoidal wave travels forward a distance of

exactly one wavelength λ.


exactly one wavelength λ.

• Because speed is distance divided by time, the

wave speed must be

or, in terms of frequency

Sinusoidal Waves

• The angular frequency of a wave is

• The wave number of a wave is


• The general equation for the displacement caused by a traveling sinusoidal wave is

This wave travels at a speed v = ω/k.

Waves in Two and Three Dimensions

• Suppose you were to take a photograph of ripples spreading on a pond. If you mark the location of the crests on the photo, these would be expanding concentric circles. The lines that locate the crests are called wave fronts, and they are spaced precisely one wavelength apart.


spaced precisely one wavelength apart.• Many waves of interest, such as sound waves or light waves, move in three dimensions. For example, loudspeakers and light bulbs emit spherical waves.• If you observe a spherical wave very, very far from its source, the wave appears to be a plane wave.

Waves in Two and Three Dimensions


Sound Waves


Sound Waves

• For air at room temperature (20°C), the speed of sound is vsound = 343 m/s.• Your ears are able to detect sinusoidal sound waves with frequencies between about 20 Hz and about 20,000 Hz, or 20 kHz. • Low frequencies are perceived as “low pitch” bass notes, while high frequencies are heard as “high


bass notes, while high frequencies are heard as “high pitch” treble notes.• Sound waves exist at frequencies well above 20 kHz, even though humans can’t hear them. These are called ultrasonic frequencies. • Oscillators vibrating at frequencies of many MHz generate the ultrasonic waves used in ultrasound medical imaging.

EXAMPLE 20.6 Sound wavelengths

QUESTION:


EXAMPLE 20.6 Sound wavelengths


Electromagnetic Waves

• A light wave is an electromagnetic wave, an oscillation of the electromagnetic field.• Other electromagnetic waves, such as radio waves, microwaves, and ultraviolet light, have the same physical characteristics as light waves even though we cannot sense them with our eyes.


we cannot sense them with our eyes.• All electromagnetic waves travel through vacuum with the same speed, called the speed of light. The value of the speed of light is c = 299,792,458 m/s.• At this speed, light could circle the earth 7.5 times in a mere second—if there were a way to make it go in circles!

The Index of Refraction

• Light waves travel with speed c in a vacuum, but they slow down as they pass through transparent materials such as water or glass or even, to a very slight extent, air. • The speed of light in a material is characterized by the material’s index of refraction n, defined as


Power and Intensity


EXAMPLE 20.9 The intensity of a laser beam

QUESTION:


EXAMPLE 20.9 The intensity of a laser beam


Intensity and Decibels

• Human hearing spans an extremely wide range of intensities, from the threshold of hearing at ≈ 1 ×10−12 W/m2 (at midrange frequencies) to the threshold of pain at ≈ 10 W/m2. • If we want to make a scale of loudness, it’s convenient and logical to place the zero of our scale at the threshold of hearing.


the threshold of hearing. • To do so, we define the sound intensity level, expressed in decibels (dB), as

where I0 = 1 × 10−12 W/m2.

Intensity and Decibels


The Doppler Effect

• An interesting effect occurs when you are in motion relative to a wave source. It is called the Doppler effect. • You’ve likely noticed that the pitch of an ambulance’s siren drops as it goes past you.


an ambulance’s siren drops as it goes past you. A higher pitch suddenly becomes a lower pitch.• As a wave source approaches you, you will observe a frequency f+ which is slightly higher than f0, the natural frequency of the source.• As a wave source recedes away from you, you will observe a frequency f− which is slightly lower than f0, the natural frequency of the source.

The Doppler Effect

The frequencies heard by a stationary observer when the sound source is moving at speed v0 are


The frequencies heard by an observer moving at speed v0 relative to a stationary sound source emitting frequency f0 are

EXAMPLE 20.11 How fast are the police traveling?

QUESTION:


EXAMPLE 20.11 How fast are the police traveling?


Chapter 20. Summary SlidesChapter 20. Summary Slides


Chapter 20. Summary SlidesChapter 20. Summary Slides

General Principles


Important Concepts


Applications


Chapter 20. QuestionsChapter 20. Questions


Chapter 20. QuestionsChapter 20. Questions

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.


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.

The graph at the top is the history graph at x = 4 m of a wave traveling to the right


at x = 4 m of a wave traveling to the right at a speed of 2 m/s. Which is the history graph of this wave at x = 0 m?

The graph at the top is the history graph at x = 4 m of a wave traveling to the right at a speed of 2 m/s. Which is the history


at a speed of 2 m/s. Which is the history graph of this wave at x = 0 m?

What is the

frequency of this

traveling wave?

A. 0.1 Hz


A. 0.1 Hz

B. 0.2 Hz

C. 2 Hz

D. 5 Hz

E. 10 Hz

A. 0.1 Hz

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

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

A. 0

B. π


B. π

C. π /4

D. π /2

E. 3 π /2

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

Four trumpet players are playing the same note. If three of them suddenly stop, the sound intensity level decreases by

A. 4 dB

B. 6 dB


B. 6 dB

C. 12 dB

D. 40 dB

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

Chapter 20. Traveling Waves - Physics & Astronomy - GSU...

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