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Ch 16. Waves and Sound

The Nature of Waves

A wave is a traveling disturbance.A wave carries energy from place to place.

Longitudinal Wave

Transverse Wave

Water waves are partially transverse and partially longitudinal.

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Periodic Waves

In the drawing, one cycle is shaded in color.

Amplitude A is the maximum excursion of a particle of the medium fromthe particles undisturbed position.

wavelength is the horizontal length of one cycle of the wave.

period is the time required for one complete cycle.

frequency is related to the period and has units of Hz, or s-1. Tf

1

consist of cycles that are produced over and over again by the source.

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Periodic Waves

f

Tv

Example 1 The Wavelengths of Radio Waves

AM and FM radio waves are transverse waves consisting of electric and magnetic field disturbances traveling at a speed of 3.00x108m/s. A stationbroadcasts AM radio waves whose frequency is 1230x103Hz and an FM radio wave whose frequency is 91.9x106Hz. Find the distance between adjacent crests in each wave.

f

Tv

f

v

AM m 244Hz101230

sm1000.33

8

f

v

FM m 26.3Hz1091.9

sm1000.36

8

f

v

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Speed of a Wave on a String

The speed at which the wave moves to the right depends on how quickly one particle of the string is accelerated upward in response to the net pulling force.

Lm

Fv

tension

linear density

Example 2 Waves Traveling on Guitar Strings

Transverse waves travel on each string of an electric guitar after the string is plucked. The length of each string between its two fixed ends is 0.628 m, and the mass is 0.208 g for the highest pitched E string and3.32 g for the lowest pitched E string. Each string is under a tension of 226 N. Find the speeds of the waves on the two strings.

High E

sm826m 0.628kg100.208

N 2263-

Lm

Fv

Low E

sm207m 0.628kg103.32

N 2263-

Lm

Fv

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Speed of a Wave on a String

Conceptual Example 3 Wave Speed Versus Particle Speed

Is the speed of a transverse wave on a string the same as the speed at which a particle on the string moves?

Mathematical Description of a Wave

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16.5 The Nature of Sound Waves

LONGITUDINAL SOUND WAVES

The distance between adjacent condensations is equal to the wavelength of the sound wave.

Individual air molecules are not carried along with the wave.

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Nature of Sound Waves

THE FREQUENCY OF A SOUND WAVE

The frequency is the number of cyclesper second.

A sound with a single frequency is calleda pure tone.

The brain interprets the frequency in termsof the subjective quality called pitch.

THE PRESSURE AMPLITUDE OF A SOUND WAVE

Loudness is an attribute ofa sound that depends primarily on the pressure amplitudeof the wave.

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Speed of Sound

Sound travels through gases, liquids, and solids at considerablydifferent speeds.

In a gas, it is only when molecules collide that the condensations and rarefactions of a sound wave can move from place to place.

Ideal Gas

m

kTv

m

kTvrms

3

KJ1038.1 23k

5

7or

3

5

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16.6 The Speed of Sound

In a gas, it is only when molecules collide that the condensations andrerefactions of a sound wave can move from place to place.

Ideal Gas

m

kTv

m

kTvrms

3

KJ1038.1 23k

5

7or

3

5

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16.6 The Speed of Sound LIQUIDS SOLIDS

adBv

Y

v

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Sound Intensity

Sound waves carry energy.

The amount of energy transported per second is called the power of the wave.

The sound intensity is the power that passes perpendicularly through a surface divided by the area of that surface.

A

PI

Example 6 Sound Intensities

12x10-5W of sound power passed through the surfaces labeled 1 and 2. The areas of these surfaces are 4.0m2 and 12m2. Determine the sound intensity at each surface.

252

5

11 mW100.3

4.0m

W1012

A

PI

252

5

22 mW100.1

12m

W1012

A

PI

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16.7 Sound Intensity

24 r

PI

power of sound source

area of sphere

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Decibels

The decibel (dB) is a measurement unit used to two sound intensities. We use a logarithmic scale called the intensity level:

oI

IlogdB 10

212 mW1000.1 oI

Note that log(1)=0, so when the intensity of the sound is equal to the threshold of hearing, the intensity level is zero.

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Decibels

oI

I11 logdB 10

oI

I22 logdB 10

1

2

1

21212 logdB 10logdB 10logdB 10logdB 10

I

I

II

II

I

I

I

I

o

o

oo

1

2logdB 10dB 0.3I

I

0.210 30.0

1

2 I

I

1

2log0.30I

I

Example 9 Comparing Sound Intensities

Audio system 1 produces a sound intensity level of 90.0 dB, and system 2 produces an intensity level of 93.0 dB. Determine the ratio of intensities.

oI

IlogdB 10

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Doppler Effect

The Doppler effect is the change in frequency or pitchof the sound detected byan observer because the soundsource and the observer havedifferent velocities with respectto the medium of sound propagation.

Tvs

sssso fvfv

v

Tv

vvf

vv

ffs

so 1

1

MOVING SOURCE

vv

ffs

so 1

1source movingtoward a stationaryobserver

source movingaway from a stationaryobserver

vv

ffs

so 1

1

16

Doppler Effect

Example 10 The Sound of a Passing Train

A high-speed train is traveling at a speed of 44.7 m/s when the engineersounds the 415-Hz warning horn. The speed of sound is 343 m/s. What are the frequency and wavelength of the sound, as perceived by a personstanding at the crossing, when the train is (a) approaching and (b) leavingthe crossing?

vv

ffs

so 1

1

vv

ffs

so 1

1

Hz 4771

1Hz 415

sm343sm7.44

of

approaching

leaving

Hz 3671

1Hz 415

sm343sm7.44

of

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Doppler Effect MOVING OBSERVER

v

vf os 1

v

vff oso 1

v

vff oso 1

Observer movingtowards stationarysource

Observer movingaway from stationary source

s

os

oso f

vf

vff 1

vvvv

ffs

o

so

1

1

GENERAL CASE

Numerator: plus sign applies when observer moves towards the source

Denominator: minus sign applies when source moves towards the observer

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Applications of Sound in MedicineBy scanning ultrasonic waves across the body and detecting echoes from various locations, it is possible to obtain an image.

Ultrasonic sound waves causethe tip of the probe to vibrate at 23 kHz and shatter sections of the tumor that it touches.

When the sound is reflected from the red blood cells, its frequency is changed in a kind of Doppler effect because the cells are moving.

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16.11 The Sensitivity of the Human Ear