Ch16 sound and waves

SEMESTER 1: PHYSICS
Date/week
Learning unit
Theme/Topic Teaching Method
SEMESTER 1
1 -2
Learning unit 1
Dynamics of uniform circular motion ( Chapter 5) Lecture/ Question and answer/
Whole Class Discussions
3-4
Learning unit 2 Waves and sound (Chapter 16)
Lecture/ WCD/ CS/ Practical
5-6
Learning unit 3 Electromagnetic waves (Chapter 24)
7
Learning unit 4 Particles and waves (Chapter 29)
8-9
Learning unit 5 DC circuits (Chapter 20)
10-11
Learning unit 6 Magnetic Forces and Magnetic Fields (Chapter 21)
12-13
Learning unit 7 Electromagnetic Induction (Chapter 22)
MAY- JUNE EXAMINATIONS : PHYSICS

Sections to be covered
• Section 16.1: The nature of waves
• Section 16.2: Periodic waves
• Section 16.3: The speed of a wave on a string
• Section 16.4: Mathematical description of a wave
• Section 16.5: The nature of sound
• Section 16.6: The speed of sound
• Section 16.9: The Doppler Effect

16.1 The Nature of Waves
1. A wave is a traveling disturbance.
2. A wave carries energy from place to place.

longitudinal

Longitudinal Wave

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 harmonic
motion, provided the end of the slinky is moved in simple harmonic
motion.

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 from
the 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.
T
f
1

16.2 Periodic Waves
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 station
broadcasts 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
T
v
f
v

16.2 Periodic Waves
AM m244
Hz101230
sm1000.3
3
8
f
v
FM m26.3
Hz1091.9
sm1000.3
6
8
f
v

16.3 The 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
F
v
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 and
3.32 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.
sm826
m0.628kg100.208
N226
3-
Lm
F
v
sm207
m0.628kg103.32
N226
3-
Lm
F
v
High E
Low E

To think about
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?
The quantity in brackets is called the phase
angle measured in radians
A particle located at a distance x also exhibits the SHM but with phase angle given
by

Solution
SOLUTION The dimensionless term 2 f t in Equation 16.4 corresponds to the
term 8.2 t in the given wave equation. The time t is measured in seconds (s), so
in order for the quantity 8.2 t to be dimensionless, the units of the numerical
factor 8.2 must be s−1
= Hz, and we have that
Similarly, the dimensionless term 2 x/ in Equation 16.4 corresponds to the term
0.54 x in the mathematical description of this wave. Because x is measured in
meters (m), the term 0.54 x is dimensionless if the numerical factor 0.54 has
units of m−1
. Thus,

Tutorial Exercises 26 February 2013

16.5 The Nature of Sound Waves
LONGITUDINAL SOUND WAVES

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

THE FREQUENCY OF A SOUND WAVE
The frequency is the number of cycles
per second.
A sound with a single frequency is called
a pure tone.
The brain interprets the frequency in terms
of the subjective quality called pitch.

THE PRESSURE AMPLITUDE OF A SOUND WAVE
Loudness is an attribute of
a sound that depends primarily
on the pressure amplitude
of the wave.

16.6 The Speed of Sound
Sound travels through gases,
liquids, and solids at considerably
different 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
kT
v m
kT
vrms
3
KJ1038.1 23
k
gasesdiatomicidealfor
5
7
and
gasesidealmonoatomicidealfor
3
5
Do Example 4: The physics of ultrasonic Ruler

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 the
approximate distance (in miles) to the thunderstorm. Why does this
rule work?

LIQUIDS SOLID BARS
adB
v
Y
v
Where B and Y are Bulk and Young’s
modulus defined in section 10.7

16.9 The Doppler Effect
The Doppler effect is the
change in frequency or pitch
of the sound detected by
an observer because the sound
source and the observer have
different velocities with respect
to the medium of sound
propagation.

The Doppler effect is the apparent change in
frequency and wavelength of a wave when the
observer and the source of the wave move
relative to each other.
We experience the Doppler effect quite often in our
lives, without realizing that it is science taking
place.
For example, the changing sound of a taxi hooter
or ambulance as it drives past are the most
common examples.

MOVING SOURCE
Tvs
ssss
o
fvfv
v
Tv
vv
f
vv
ff
s
so
1
1

vv
ff
s
so
1
1source moving
toward a stationary
observer
source moving
away from a stationary
observer
vv
ff
s
so
1
1

Example 10 The Sound of a Passing Train
A high-speed train is traveling at a speed of 44.7 m/s when the engineer
sounds 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 person
standing at the crossing, when the train is (a) approaching and (b) leaving
the crossing?
vv
ff
s
so
1
1
vv
ff
s
so
1
1

Hz477
1
1
Hz415
sm343
sm7.44of
approaching
leaving
Hz367
1
1
Hz415
sm343
sm7.44of

MOVING OBSERVER
v
v
f
f
v
f
v
ff
o
s
s
o
s
o
so
1
1

v
v
ff o
so 1
v
v
ff o
so 1
Observer moving
towards stationary
source
Observer moving
away from
stationary source

v
v
v
v
ff
s
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 echoes
from various locations, it is possible to obtain an image.

Ultrasonic sound waves cause
the 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.

Class Exercises 28 02 2013
76. A bird is ﬂying directly toward a stationary bird-watcher and emits a frequency of 1500 Hz. The
bird-watcher, however, hears a frequency of 1560 Hz. What is the speed of the bird, expressed as
a percentage of the speed of sound?
REASONING:
• The observer of the sound (the bird-watcher) is stationary, while the source (the
bird) is moving toward the observer.
• Therefore, the Doppler-shifted observed frequency is given by Equation 16.11.
• This expression can be solved to give the ratio of the bird’s speed to the speed of
sound, from which the desired percentage follows directly.
• The observed frequency fo is related to the frequency fs of the source, and the
ratio of the speed of the source vs to the speed of sound v by:
Hence ,the ratio corresponds to 3.8 %

77. From a vantage point very close to the track at a stock car race, you hear the sound emitted by a
moving car. You detect a frequency that is 0.75 times as small as the frequency emitted by the car
when it is stationary. The speed of sound is 343 m/s. What is the speed of the car?
.
REASONING :
Since you detect a frequency that is smaller than that emitted by the car when the car is stationary, the car must be
moving away from you.
Therefore, according to Equation 16.12, the frequency fo heard by a stationary observer from a source moving away
from the observer is given by:
where fs is the frequency emitted from the source when it is stationary with respect to the observer, v is the speed of
sound, and vs is the speed of the moving source.
This expression can be solved for vs .
Solving for vs and noting that
We get

80. The security alarm on a parked car goes off and produces a frequency of 1000 Hz. The speed of sound is 343 m/s. As
you drive toward this parked car, pass it, and drive away, you observe the frequency to change by 100 Hz. At what speed
are you driving?
REASONING
The observed frequency changes because of the Doppler effect. As you drive toward the parked car (a stationary
source of sound), the Doppler effect is that given by Equation 16.13.
As you drive away from the parked car, Equation 16.14 applies.
o, toward s o o, away s o
Driving toward parked car Driving away from parked car
1 / and 1– /f f v v f f v v
 
Subtracting the equation on the right from the one on the left gives the change in the observed frequency
o, toward o, away s o– 2 /f f f v v
Solving for the observer’s speed (which is your speed), we obtain:
o, toward o, away
o
s
– 343 m/s 100 Hz
17 m/s
2 2 1000 Hz
v f f
v
f

78. Dolphins emit clicks of sound for communication and echolocation. A marine biologist is monitoring a
dolphin swimming in seawater where the speed of sound is 1522 m/s. When the dolphin is swimming
directly away at 10 m/s, the marine biologist measures the number of clicks occurring per second to be
at a frequency of 2300 Hz. What is the difference (in Hz) between this frequency and the number of
clicks per second actually emitted by the dolphin?REASONING
• The dolphin is the source of the clicks, and emits them at a frequency fs. The marine biologist measures a lower,
Doppler-shifted click frequency fo, because the dolphin is swimming directly away.
• The difference between the frequencies is the source frequency minus the observed frequency: fs − fo.
• We will use the equation :
o s
s
1
1
f f
v
v
where vs is the speed of the dolphin and v is the speed of
sound in seawater, to determine the difference between the
frequencies.
s
s o 1
v
f f
v
Solving for fs we get:
Therefore, the difference between the source and observed frequencies is:
s s
s o o o o
s
o
1 1 1
10.0 m/s
2300 Hz 15 Hz
1522 m/s
v v
f f f f f
v v
v
f
v
Tutorial Exercises Due on Monday: the 4th of March 2013
Chapter 16: Problem number, 81, 82, 86 and 87 :

Chapter 24
Electromagnetic
Waves

What are electromagnetic
waves
• Electromagnetic waves consist of a combination of
oscillating electrical and magnetic fields, perpendicular
to each other.
This is difficult to visualize, however the waveform has similar characteristics of
other types of waves.

What are electromagnetic
waves
• Although they seem different, radio waves, microwaves,
x-rays, and even visible light are all electromagnetic
waves. They are part of the electromagnetic spectrum,
and each has a different range of wavelengths, which
cause the waves to affect matter differently.
• The creation and detection of the wave depend much on
the range of wavelengths.

Questions you may have include:
• What is the electromagnetic spectrum?
• What are the characteristics of
electromagnetic waves?
• How are these waves created and
detected?

Electromagnetic spectrum
• The range of wavelengths for electromagnetic waves--from the very long to
the very short--is called the Electromagnetic Spectrum:

Electromagnetic Spectrum
• Radio and TV waves are the longest usable waves, having a wavelength of
1 mile (1.5 kilometer) or more.
• Microwaves are used in telecommunication as well as for cooking food.
• Infrared waves are barely visible. They are the deep red rays you get from
a heat lamp.
• Visible light waves are the radiation you can see with your eyes. Their
wavelengths are in the range of 1/1000 centimeter.
• Ultraviolet rays are what give you sunburn and are used in "black lights"
that make object glow.
• X-rays go through the body and are used for medical purposes.
• Gamma rays are dangerous rays coming from nuclear reactors and atomic
bombs. They have the shortest wavelength in the electromagnetic spectrum
of about 1/10,000,000 centimeter.

Properties
• They do not need a medium for transmission. Other
waves, such as sound waves, can not travel through a
vacuum. An electromagnetic wave is perfectly happy to
do that.
• Electromagnetic waves are transverse waves, similar to
water waves in the ocean or the waves seen on a guitar
string.
• The velocity of electromagnetic waves in a vacuum is
approximately 186,000 miles per second or 300,000
kilometers per second, the same as the speed of light.
When these waves pass through matter, they slow down
slightly, according to their wavelength.

The speed of light
• In 1865, Maxwell determined theoretically
that electromagnetic waves propagate
through a vacuum at a speed given by:

They all obey
• Electromagnetic waves are split into different categories based on
their frequency (or, equivalently, on their wavelength).
• In other words, we split up the electromagnetic spectrum based on
frequency.
• Visible light, for example, ranges from violet to red.
• Violet light has a wavelength of 400 nm, and a frequency of 7.5 x
1014 Hz.
• Red light has a wavelength of 700 nm, and a frequency of 4.3 x 1014
Hz.
• Any electromagnetic wave with a frequency (or wavelength)
between those extremes can be seen by humans.

Properties continued…
• An electromagnetic wave, although it
carries no mass, does carry energy. It also
has momentum, and can exert pressure
(known as radiation pressure)
• The energy carried by an electromagnetic
wave is proportional to the frequency of
the wave.

24.2 The Electromagnetic Spectrum
The Wavelength of Visible Light
Find the range in wavelengths for visible light in the frequency range
between 4.0x1014Hz and 7.9x1014Hz.
nm750m105.7
Hz104.0
sm1000.3 7
14
8
f
c
nm380m108.3
Hz107.9
sm1000.3 7
14
8
f
c

Creating an electromagnetic
wave
• From high school we already learned how moving charges (currents) produce magnetic
fields.
• A constant current produces a constant magnetic field, while a changing current produces a
changing field.
• We can go the other way, and use a magnetic field to produce a current, as long as the magnetic
field is changing.
• This is what induced emf is all about. A steadily-changing magnetic field can induce a constant
voltage, while an oscillating magnetic field can induce an oscillating voltage.
To Note:
• an oscillating electric field generates an oscillating magnetic field
• an oscillating magnetic field generates an oscillating electric field
• What this means in practice is that the source has created oscillating electric and
magnetic fields, perpendicular to each other, that travel away from the source.
• The E and B fields, along with being perpendicular to each other, are perpendicular
to the direction the wave travels, meaning that an electromagnetic wave The
energy of the wave is stored in the electric and magnetic fields

Energy in an electromagnetic wave
• The energy in an electromagnetic wave is tied up in the
electric and magnetic fields.
• In general, the energy per unit volume in an electric field
is given by:
And the magnetic energy density:
In an electromagnetic wave propagating through a vacuum or air, the electric field and the
magnetic field carry equal amounts of energy per unit volume of space.

24.5 The Doppler Effect and Electromagnetic Waves
Electromagnetic waves also can exhibit a Doppler effect, but it
differs for two reasons:
a) Sound waves require a medium, whereas electromagnetic
waves do not.
b) For sound, it is the motion relative to the medium that is important.
For electromagnetic waves, only the relative motion of the source
and observer is important.
cv
c
v
ff so rel
rel
if1

Sign Conventions for Relative Motion
Plus Sign (source and observer come
together)
Minus sign (source and observer move
apart)
1. The source is catching up with the
observer
2. The observer is catching up with the
source
3. The source and the observer move
toward one another
1. The source is pulling away from the
observer
2. The observer is pulling away from the
source
3. The source and the observer both
move away from one another

Focus on Concepts Problem 6
The drawing shows four situations—A, B, C, and D—in which an observer and a source
of electromagnetic waves can move along the same line. In each case the source emits a
wave of the same frequency, and in each case only the source or the observer is moving.
The arrow in each situation denotes the velocity vector, which has the same magnitude in
each situation. When there is no arrow, the observer or the
source is stationary. Rank the frequencies of the observed electromagnetic waves in
descending order (largest ﬁrst) according to magnitude.
(a) A and B (a tie), C and D (a tie)
(b) C and D (a tie), A and B (a tie)
(c) A and D (a tie), B and C (a tie)
(d) B and D (a tie), A and C (a tie)
(e) B and C (a tie), A and D (a tie)

Problem 1
Theelapsedtimetis giveninhours,soitmustbeconvertedtoseconds:
Thedistance,then,betweenearthandtheprobeis

Problem 9
2d
(1)
2d (1)
Solving c f (Equation16.1)forfyields c
f
(2)

Problem 38
Reasoning part:
The observed frequency is given by:
In situations A and B the observer and the source move
away from each other, and the minus sign in Equation 24.6
applies. In situation C the observer and the source move
toward each other, and the plus sign applies. Thus, the
observed frequency is largest in C.
[Situation A, minus sign in Equation 24.6]

Calculation part
[Situation A, minus sign in Equation 24.6]
rel
6
14 14rel
o s s 8
2
1.50 10 m/s
1 1 4.57 10 Hz 1 4.55 10 Hz
3.00 10 m/s
v v v v
v v
f f f
c c
[Situation B, minus sign in Equation 24.6]
rel
6
14 14rel
o s s 8
2 3
3 1.50 10 m/s3
1 1 4.57 10 Hz 1 4.50 10 Hz
3.00 10 m/s
v v v v
v v
f f f
c c
[Situation C, plus sign in Equation 24.6]
rel
6
14 14rel
o s s 8
2
2 1.50 10 m/s2
1 1 4.57 10 Hz 1 4.62 10 Hz
3.00 10 m/s
v v v v
v v
f f f
c c

Your Chance: Study Example: Radar Guns and Speed Traps
Police use radar guns and the Doppler effect to catch speeders.
A moving car approaches a stationary police car. A radar gun emits an
electromagnetic waves that reflects form the oncoming car. The reflected
Wave returns to the police car with a frequency measured by on-board
equipment that is different from the emitted frequency. One such radar
emits a wave whose frequency is 8.0x109Hz. When the speed is 39m/s
and the approach is essentially head on, what is the difference between
the frequency of the wave returning to the police car and that emitted
by the radar gun
.

1 rel
c
v
ff so
1 rel
c
v
ff oo
frequency “observed”
by speeding car
frequency observed
by police car
soso f
c
v
fff rel
1
c
v
fff sso
rel
2
ss f
c
v
c
v
f relrel
11
ss f
c
v
f rel2
1
c
v
c
v
fs
relrel
2
c
vrel
2

C Y U 7 page 24.5
• An astronomer measures a Doppler change in frequency for light reaching
the earth from a distant star, from this measurement, can the astronomer
tell whether the star is moving away from the earth or the earth moving
away from the star?
• Answer: No The same Doppler change results when the star moves away
from the earth and when the earth moves away from the star

Ch16 sound and waves

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