Chapter 16

Waves and Sound

16.1 The Nature of Waves

1. A wave is a traveling disturbance.

2. A wave carries energy from place to place.

16.1 The Nature of Waves

Transverse Wave

16.1 The Nature of Waves

Longitudinal Wave

16.1 The Nature of Waves

Water waves are partially transverse and partially longitudinal.

16.2 Periodic Waves

Periodic waves consist of cycles or patterns that are produced over and over again by the source.

In the figures, every segment of the slinky vibrates in simple harmonicmotion, provided the end of the slinky is moved in simple harmonicmotion.

16.2 Periodic Waves

In the drawing, one cycle is shaded in color.

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

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

The period is the time required for one complete cycle.

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

Tf 1=

16.2 Periodic Waves

λλ fT

v ==

16.2 Periodic Waves

Example 1 The Wavelengths of Radio Waves

AM and FM radio waves are transverse waves consisting of electric andmagnetic 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.

λλ fT

v ==

fv

=λ

16.2 Periodic Waves

AM m 244Hz101230

sm1000.33

8

=××

==fvλ

FM m 26.3Hz1091.9

sm1000.36

8

=××

==fvλ

16.3 The Speed of a Wave on a String

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

LmFv =

tension

linear density

16.3 The Speed of a Wave on a String

Example 2 Waves Traveling on Guitar Strings

Transverse waves travel on each string of an electric guitar after thestring is plucked. The length of each string between its two fixed endsis 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.

16.3 The Speed of a Wave on a String

High E

( ) ( ) sm826m 0.628kg100.208N 226

3- =×==

LmFv

Low E

( ) ( ) sm207m 0.628kg103.32N 226

3- =×==

LmFv

16.3 The 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?

16.4 The Mathematical Description of a Wave

What is the displacement y at time t of a particle located at x?

16.5 The Nature of Sound Waves

LONGITUDINAL SOUND WAVES

16.5 The Nature of Sound Waves

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

16.5 The Nature of Sound Waves

Individual air molecules are not carried along with the wave.

16.5 The 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.

16.5 The Nature of Sound Waves

THE PRESSURE AMPLITUDE OF A SOUND WAVE

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

16.6 The Speed of Sound

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

16.6 The Speed of Sound

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

Ideal GasmkTv γ=

mkTvrms

3=

KJ1038.1 23−×=k

57or

35

=γ

16.6 The Speed of Sound

Conceptual Example 5 Lightning, Thunder, and a Rule of Thumb

There is a rule of thumb for estimating how far away a thunderstorm is.After you see a flash of lighting, count off the seconds until the thunder is heard. Divide the number of seconds by five. The result gives theapproximate distance (in miles) to the thunderstorm. Why does thisrule work?

16.6 The Speed of Sound

LIQUIDS SOLID BARS

ρadBv =

ρYv =

16.7 Sound Intensity

Sound waves carry energy that can be used to do work.

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

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

API =

16.7 Sound Intensity

Example 6 Sound Intensities

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

16.7 Sound Intensity

252

5

11 mW100.34.0m

W1012 −− ×=×==API

252

5

22 mW100.112m

W1012 −− ×=×==API

16.7 Sound Intensity

For a 1000 Hz tone, the smallest sound intensity that the human earcan detect is about 1x10-12W/m2. This intensity is called the thresholdof hearing.

On the other extreme, continuous exposure to intensities greater than 1W/m2 can be painful.

If the source emits sound uniformly in all directions, the intensity dependson the distance from the source in a simple way.

16.7 Sound Intensity

24 rPIπ

=

power of sound source

area of sphere

16.7 Sound Intensity

Conceptual Example 8 Reflected Sound and Sound Intensity

Suppose the person singing in the shower produces a sound power P.Sound reflects from the surrounding shower stall. At a distance r in front of the person, does the equation for the intensity of sound emitted uniformlyin all directions underestimate, overestimate, or give the correct sound intensity?

24 rPIπ

=

16.8 Decibels

The decibel (dB) is a measurement unit used when comparing two soundintensities.

Because of the way in which the human hearing mechanism responds tointensity, it is appropriate to use a logarithmic scale called the intensitylevel:

( )

=

oIIlogdB 10β

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.

16.8 Decibels

( )

=

oIIlogdB 10β 212 mW1000.1 −×=oI

16.8 Decibels

Example 9 Comparing Sound Intensities

Audio system 1 produces a sound intensity level of 90.0 dB, and system2 produces an intensity level of 93.0 dB. Determine the ratio of intensities.

( )

=

oIIlogdB 10β

16.8 Decibels

( )

=

oIIlogdB 10β

( )

=

oII1

1 logdB 10β ( )

=

oII2

2 logdB 10β

( ) ( ) ( ) ( )

=

=

−

=−

1

2

1

21212 logdB 10logdB 10logdB 10logdB 10 I

IIIII

II

II

o

o

oo

ββ

( )

=

1

2logdB 10dB 0.3II

0.210 30.01

2 ==II

=

1

2log0.30II

16.9 The 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.

16.9 The Doppler Effect

MOVING SOURCE

Tvs−=′ λλ

sssso fvfv

vTv

vvf−

=−

=′

=λλ

−

=vv

ffs

so 11

16.9 The Doppler Effect

−

=vv

ffs

so 11source movingtoward a stationary

observer

source movingaway from a stationaryobserver

+

=vv

ffs

so 11

16.9 The 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 11

+

=vv

ffs

so 11

16.9 The Doppler Effect

( ) Hz 4771

1Hz 415sm343sm7.44 =

−=of

approaching

leaving

( ) Hz 3671

1Hz 415sm343sm7.44 =

+=of

16.9 The Doppler Effect

MOVING OBSERVER

+=

+=+=

vvf

fvfvff

os

s

os

oso

1

1λλ

16.9 The Doppler Effect

+=

vvff oso 1

−=

vvff oso 1

Observer movingtowards stationarysource

Observer movingaway from stationary source

16.9 The Doppler Effect

±=

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

16.10 Applications of Sound in Medicine

By scanning ultrasonic waves across the body and detecting the echoesfrom various locations, it is possible to obtain an image.

16.10 Applications of Sound in Medicine

Ultrasonic sound waves causethe tip of the probe to vibrate at23 kHz and shatter sections ofthe tumor that it touches.

16.10 Applications of Sound in Medicine

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

16.11 The Sensitivity of the Human Ear

Chapter 1616.1 The Nature of Waves16.1 The Nature of Waves16.1 The Nature of Waves16.1 The Nature of Waves16.2 Periodic Waves16.2 Periodic Waves16.2 Periodic Waves16.2 Periodic Waves16.2 Periodic Waves16.3 The Speed of a Wave on a String16.3 The Speed of a Wave on a String16.3 The Speed of a Wave on a String16.3 The Speed of a Wave on a String16.4 The Mathematical Description of a Wave16.5 The Nature of Sound Waves16.5 The Nature of Sound Waves16.5 The Nature of Sound Waves16.5 The Nature of Sound Waves16.5 The Nature of Sound Waves16.6 The Speed of Sound16.6 The Speed of Sound16.6 The Speed of Sound16.6 The Speed of Sound16.7 Sound Intensity16.7 Sound Intensity16.7 Sound Intensity16.7 Sound Intensity16.7 Sound Intensity16.7 Sound Intensity16.8 Decibels16.8 Decibels16.8 Decibels16.8 Decibels16.9 The Doppler Effect16.9 The Doppler Effect16.9 The Doppler Effect16.9 The Doppler Effect16.9 The Doppler Effect16.9 The Doppler Effect16.9 The Doppler Effect16.9 The Doppler Effect16.10 Applications of Sound in Medicine16.10 Applications of Sound in Medicine16.10 Applications of Sound in Medicine16.11 The Sensitivity of the Human Ear