tions - dearborn public schools...chalkboard. call attention to how frequently you tap and relate...
TRANSCRIPT
490
THE B
IGID
EA
........ VIBRA
TION
S A
ND
WAV
ES
All around
us we see thing
s that wig
gle and
jigg
le. Even thing
s too small to see, such as atom
s, are constantly w
igg
ling and
jigg
ling. A
repeating
, back-and
-forth m
otion about an eq
uilibrium
position is a vibration.
A vib
ration cannot exist in one instant. It needs
time to m
ove back and
forth. Strike a bell and
the vib
rations will continue for som
e time
before they d
ie dow
n.A
disturb
ance that is transmitted
pro-
gressively from
one place to the next
with no actual transp
ort of matter is
a w
ave. A w
ave cannot exist in one p
lace but m
ust extend from
one place
to another. Light and
sound are b
oth form
s of energy that m
ove through
space as w
aves. This chapter is ab
out vib
rations and w
aves, and the follow
-ing
chapters continue w
ith the study of
sound and
light.
Waves transm
it energy through space and tim
e.
5What A
re Standing
Waves?
1.Fill a foam
cup nearly to the top with w
ater. Place the cup on a sm
ooth, dry surface.2.
While applying a m
oderate downw
ard pres-sure, drag the cup across the surface.
3.A
djust the downw
ard pressure on the cup until a pattern of w
aves, called standing w
aves, appears on the surface of the water.
4.N
ow try to change the pattern by altering
both the speed of the cup and the downw
ard pressure.
Analyze and
Conclud
e1.
Observing D
escribe the patterns that you produced on the surface of the w
ater.2.
Predicting What do you think m
ight happen if you w
ere to drag the cup on a different kind of surface?
3.M
aking Generalizations D
o you think stand-ing w
aves can be produced in other media?
Explain.
disco
ver!
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49
0
V
IBR
ATIO
NS
AN
D W
AV
ESO
bje
ctive
s• D
escribe th
e perio
d o
f a p
end
ulu
m. (25.1)
• Describ
e the ch
aracteristics and
p
rop
erties of w
aves. (25.2)
• Describ
e wave m
otio
n. (25.3)
• Describ
e ho
w to
calculate th
e sp
eed o
f a wave. (25.4)
• Give exam
ples o
f transverse
waves. (25.5)
• Give an
examp
le of a
lon
gitu
din
al wave. (25.6)
• Explain
wh
at causes
interferen
ce pattern
s. (25.7)
• Describ
e ho
w a stan
din
g w
ave o
ccurs. (25.8)
• Describ
e ho
w th
e app
arent
frequ
ency o
f waves ch
ang
e as a w
ave sou
rce mo
ves. (25.9)
• Describ
e bo
w w
aves. (25.10)
• Describ
e son
ic bo
om
s. (25.11)
disco
ver!M
ATE
RIA
LS foam
cup
, water
EX
PE
CTE
D OU
TCO
ME R
egio
ns o
f still w
ater, no
des, an
d reg
ion
s o
f cho
pp
y water, an
tino
des,
sho
uld
be o
bservab
le. This
pattern
is the resu
lt of th
e in
terference o
f traveling
w
aves reflecting
from
the
vibratin
g w
alls of th
e cup
.
AN
ALY
ZE A
ND C
ON
CLU
DE
Stud
ents sh
ou
ld o
bserve
regio
ns o
f still water an
d
regio
ns o
f cho
pp
y water.
The p
attern ch
ang
es b
ecause th
e cup
vibrates
differen
tly on
differen
t su
rfaces.
Yes, b
ecause w
aves travel in
all med
ia and
interferen
ce is a ch
aracteristic of w
aves.
1.2.3.
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25.1 Vibration of a Pendulum
Suspend a stone at the end of a string and you have a simple pen-
dulum. Pendulum
s like the one in Figure 25.1 swing back and forth
with such regularity that they have long been used to control the
motion of clocks. G
alileo dis covered that the time a pendulum
takes to sw
ing back and forth through small angles depends only on the
length of the pendulum—
the mass has no effect. T
he time of a
back-and-forth swing of the pendulum
is called the period. T
he period of the pendulum depends only on the length of a
pendulum and the acceleration of gravity. 25.1
A long pendulum
has a longer period than a shorter pendulum;
that is, it swings back and forth m
ore slowly—
less frequently—than a
short pendulum. W
hen walking, w
e allow our legs to sw
ing with the
help of gravity, like a pendulum. In the sam
e way that a long pendu-
lum has a greater period, a person w
ith long legs tends to walk w
ith a slow
er stride than a person with short legs. T
his is most noticeable
in long-legged animals such as giraffes and horses, w
hich run with a
slower gait than do short-legged anim
als such as hamsters and m
ice.
CON
CEPT
CHECK
......What d
etermines the p
eriod of a p
endulum
?
25.2 Wave D
escriptionT
he back-and-forth vibratory motion (often called oscillatory
motion) of a sw
inging pendulum is called sim
ple harmonic
motion. 25.2 T
he pendulum bob filled w
ith sand in Figure 25.2 exhibits sim
ple harmonic m
otion above a conveyor belt. When the
conveyor belt is stationary, the sand traces out a straight line. More
interestingly, when the conveyor belt is m
oving at constant speed, the sand traces out a special curve know
n as a sine curve. A sine curve
is a pictorial representation of a wave.
The source of all w
aves is som
ething that vibrates.
FIGU
RE 25.1 !
Two pendulum
s of the same
length have the same period
regardless of mass.
" FIG
URE 25.2
Frank Oppenheim
er, founder of the Exploratorium
® science m
useum in San Francisco, dem
on-strates that a pendulum
swinging
back and forth traces out a straight line over a stationary surface and a sine curve w
hen the surface moves
at constant speed.
What is the frequency in
vibrations per second of a 100-H
z wave?
Answer: 25.2.1
thin
k!
CH
APTER 25
VIBRATION
S AN
D W
AVES 491
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491
25.1 Vibration of a
PendulumK
ey
Term
sp
eriod
, vibratio
n, w
aves
# Teach
ing
Tip D
isting
uish
b
etween
a simp
le pen
du
lum
(the
bo
b is very sm
all com
pared
to th
e len
gth
of strin
g) an
d a p
hysical
pen
du
lum
(the stick m
akes up
a sig
nifican
t part o
f the m
ass). Exp
lain th
at their ro
tation
al in
ertias are differen
t.
Ask W
hat principle of m
echanics accounts for the different periods of pendulum
s of different lengths? R
otatio
nal
inertia
Attach
a small h
eavy weig
ht
to th
e end
of a p
iece of strin
g
abo
ut 1 m
lon
g. Sw
ing
it to
and
fro: th
is is a simp
le p
end
ulu
m. Id
entify freq
uen
cy an
d p
eriod
. Time h
ow
lon
g
the p
end
ulu
m takes to
make
10 com
plete cycles. R
epeat
to sh
ow
that th
e result d
oes
no
t chan
ge fro
m trial to
trial. D
ivide th
e time b
y 10 to g
et th
e perio
d. A
dd
mo
re mass to
th
e end
of th
e string
with
ou
t ch
ang
ing
the o
verall leng
th o
f th
e pen
du
lum
. Time 10 m
ore
cycles to sh
ow
that w
eigh
t d
oes n
ot affect th
e perio
d.
Th
e perio
d o
f the
pen
du
lum
dep
end
s o
nly o
n th
e leng
th o
f a pen
du
lum
an
d th
e acceleration
of g
ravity.
Te
ac
hin
g R
es
ou
rc
es
• Problem-Solving Exercises in
Physics 12-1, 12-2• Laboratory M
anual 68, 69• Probew
are Lab Manual 13
Dem
on
stratio
nD
em
on
stratio
n
CON
CEPT
CHECK
......
CON
CEPT
CHECK
......
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492
The Parts of a Wave
A w
eight attached to a spring undergoes vertical sim
ple harmonic m
otion as shown in Figure 25.3. A
marking
pen attached to the bob traces a sine curve on a sheet of paper that is m
oving horizontally at constant speed. Like a water w
ave, the high points on a w
ave are called crests. The low
points on a wave are
called troughs. T
he straight dashed line represents the “home” posi-
tion, or midpoint of the vibration. T
he term am
plitude refers to the distance from
the midpoint to the crest (or trough) of the w
ave. So the am
plitude equals the maxim
um displacem
ent from equilibrium
.T
he w
avelength of a wave is the distance from
the top of one crest to the top of the next one. O
r equivalently, the wavelength is the
distance between successive identical parts of the w
ave. The w
ave-lengths of w
aves at the beach are measured in m
eters, the wavelengths
of ripples in a pond in centimeters, and the w
avelengths of light in billionths of a m
eter (nanometers).
Frequency T
he number of vibrations an object m
akes in a unit of tim
e is an object’s frequency. The frequency of a vibrating pendu-
lum, or object on a spring, specifies the num
ber of back-and-forth vibrations it m
akes in a given time (usually one second). A
complete
back-and-forth vibration is one cycle. If it occurs in one second, the frequency is one vibration per second or one cycle per second. If tw
o vibrations occur in one second, the frequency is tw
o vibrations or tw
o cycles per second. The frequency of the vibrating source and the
frequency of the wave it produces are the sam
e.T
he unit of frequency is called the hertz (Hz). A
frequency of one cycle per second is 1 hertz, tw
o cycles per second is 2 hertz, and so on. H
igher frequencies are measured in kilohertz (kH
z—thou-
sands of hertz), and still higher frequencies in megahertz (M
Hz—
millions of hertz) or gigahertz (G
Hz—
billions of hertz). AM
radio w
aves are broadcast in kilohertz, while FM
radio waves are broadcast
in megahertz; radar and m
icrowave ovens operate at gigahertz. A
station at 960 kH
z broadcasts radio waves that have a frequency of
960,000 hertz. A station at 101 M
Hz broadcasts radio w
aves with a
frequency of 101,000,000 hertz. As Figure 25.4 show
s, these radio-w
ave frequencies are the frequencies at which electrons vibrate in the
transmitting antenna of a radio station.
FIGU
RE 25.3 !
A sine curve is a pictorial
representation of a wave.
FIGU
RE 25.4 "Electrons in the transm
itting antenna of a radio station at 960 kH
z on the AM
dial vibrate 960,000 tim
es each second and produce 960-kH
z radio waves.
Be clear about the distinction betw
een frequency and speed.H
ow frequently a w
ave vibrates is altogether different from
how fast
it moves from
one loca-tion to another.
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49
2
25.2 Wave
Description
Ke
y Te
rms
simp
le harm
on
ic mo
tion
, sine
curve, crest, tro
ug
h, am
plitu
de,
wavelen
gth
, frequ
ency, h
ertz
! Teach
ing
Tip B
egin
by
tapp
ing
you
r lecture tab
le or th
e ch
alkbo
ard. C
all attentio
n to
ho
w
frequ
ently yo
u tap
and
relate th
is to th
e term freq
uen
cy. Call
attentio
n to
the tim
e interval
betw
een tap
s and
relate this
to th
e perio
d. Estab
lish th
e recip
rocal relatio
nsh
ip b
etween
freq
uen
cy and
perio
d.
! Teach
ing
Tip M
ove a p
iece of
chalk u
p an
d d
ow
n o
n th
e bo
ard,
tracing
and
retracing
a vertical straig
ht lin
e. Call atten
tion
to
ho
w “freq
uen
tly” you
oscillate
the ch
alk, again
tying
this to
th
e defin
ition
of freq
uen
cy. D
iscuss th
e idea o
f disp
lacemen
t an
d am
plitu
de (m
aximu
m
disp
lacemen
t). With
app
rop
riate m
otio
ns, sh
ow
differen
t freq
uen
cies and
differen
t am
plitu
des. Th
en d
o th
e same
wh
ile walkin
g acro
ss the fro
nt
of th
e bo
ard tracin
g o
ut a sin
e w
ave. Rep
eat sho
win
g w
aves of
differen
t wavelen
gth
s.
! Teach
ing
Tip Po
int o
ut th
at sin
ce a vibratio
n is also
called a
cycle, on
e hertz is also
on
e cycle p
er secon
d.
(1 kHz 5
103 cycles/s;
1 MH
z 5 10
6 cycles/s)
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If the frequency of a vibrating object is known, its period can be
calculated, and vice versa. Suppose, for example, that a pendulum
m
akes two vibrations in one second. Its frequency is 2 H
z. The tim
e needed to com
plete one vibration—that is, the period of vibration—
is 1/2 second. Or if the vibration period is 3 H
z, then the period is 1/3 second. A
s you can see below, frequency and period are inverses of
each other:
��
or periodfrequency
1period
1frequency
CON
CEPT
CHECK
......What is the source of all w
aves?
25.3 Wave M
otionM
ost of the information around us gets to us in som
e form of w
ave. Sound is energy that travels to our ears in the form
of a wave. Light is
energy that comes to our eyes in the form
of a different kind of wave
(an electromagnetic w
ave). The signals that reach our radio and tele-
vision sets also travel in the form of electrom
agnetic waves.
When energy is transferred by a w
ave from a vibrating source to a
distant receiver, there is no transfer of matter betw
een the two points.
To see this, think about the very simple w
ave produced when one end
of a horizontally stretched string is shaken up and down as show
n in Figure 25.5. A
fter the end of the string is shaken, a rhythmic dis-
turbance travels along the string. Each part of the string moves up
and down w
hile the disturbance moves horizontally along the length
of the string. It is the disturbance that moves along the length of the
string, not parts of the string itself.
FIGU
RE 25.5 !
When the string is shaken
up and down, a disturbance
moves along the string.
Noisy Bugs Big bum
blebees flap their w
ings at about 130 flaps per second, and produce sound of 130 H
z. A honeybee flaps its w
ings at 225 flaps per second and produces a higher-pitched sound of 225 H
z. The annoying high-pitched w
hine of a mosquito
results from its w
ings flapping at 600 Hz. These sounds are produced
by pressure variations in the air caused by vibrating wings.
Link
to E
NTO
MO
LOG
Y
CH
APTER 25
VIBRATION
S AN
D W
AVES 493
The Sears Tower in
Chicago sw
ays back and forth at a frequency of about 0.1 H
z. What is
its period of vibration? Answ
er: 25.2.2
thin
k!
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493
Th
e sou
rce of all
waves is so
meth
ing
th
at vibrates.
Te
ac
hin
g R
es
ou
rc
es
• Reading and Study W
orkbook • Transparency 50• Presentation
EXPR
ESS
• Interactive Textbook
25.3 Wave M
otionC
om
mo
n M
iscon
ceptio
nW
hen a wave travels in a m
edium,
the medium
moves w
ith the wave.
FAC
T As a w
ave travels thro
ug
h
a med
ium
, there is n
o tran
sfer of
matter.
" Teach
ing
Tip Po
int o
ut th
at if a leaf is flo
ating
in a p
on
d as
a wave p
asses, the leaf w
ill mo
ve u
p an
d d
ow
n w
ith th
e water
bu
t will n
ot m
ove alo
ng
with
th
e wave.
Have a stu
den
t ho
ld o
ne
end
of a stretch
ed sp
ring
or
a Slinky w
hile yo
u h
old
the
oth
er. Send
transverse p
ulses
alon
g it, stressin
g th
e idea
that th
e distu
rban
ce rather
than
the m
ediu
m m
oves alo
ng
th
e sprin
g. Sh
ake the sp
ring
an
d p
rod
uce a sin
e wave. Th
en
send
a stretch an
d sq
ueeze
(elon
gatio
n an
d co
mp
ression
) d
ow
n th
e sprin
g, sh
ow
ing
a lo
ng
itud
inal p
ulse. Sen
d a
sequ
ence o
f pu
lses and
you
h
ave a wave. A
fter som
e d
iscussio
n, p
rod
uce stan
din
g
waves.
CON
CEPT
CHECK
......
CON
CEPT
CHECK
......
Dem
on
stratio
nD
em
on
stratio
n
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494
Drop a stone in a quiet pond and you’ll produce a w
ave that m
oves out from the center in an expanding circle as show
n in Figure 25.6. It is the disturbance that m
oves, not the water, for after the dis-
turbance passes, the water is w
here it was before the w
ave passed.W
hen someone speaks to you from
across the room, the sound w
ave is a disturbance in the air that travels across the room
. The air m
olecules them
selves do not move along, as they w
ould in a wind. T
he air, like the rope and the w
ater in the previous examples, is the m
edium through
which w
ave energy travels. T
he energy transferred by a wave from
a vibrating source to a receiver is carried by a disturbance in a m
edium. Energy is not transferred by m
atter moving from
one place to another w
ithin the medium
.
CON
CEPT
CHECK
......How
does a w
ave transfer energy?
FIGU
RE 25.6 !A
circular water w
ave in a still pond m
oves out from the center
in an expanding circle.
Making
Waves
Part 11.
Oscillate a m
arking pen back and forth across a piece of paper as you slow
ly pull the paper in a direction perpendicular to your oscillation.
2.Repeat Step 1, but pull the paper faster this tim
e.3.
Think What happens to the w
avelength of the curves when you
pull the paper faster?
Part 21.
Repeatedly dip your finger into a wide pan of w
ater to make
circular waves on the surface.
2.Repeat Step 1, but dip your finger m
ore frequently.3.
Think What happens to the w
avelength of the waves w
hen you dip your finger m
ore frequently?
disco
ver!
For:Visit:W
eb Code: –
Links on wave m
otion
ww
w.SciLinks.org
csn
2503
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49
4
disco
ver!M
ATE
RIA
LS pen
, pap
er, wid
e p
an, w
ater
EX
PE
CTE
D OU
TCO
ME In
Part 1, stu
den
ts will create a p
ictorial
represen
tation
of a w
ave. Th
ey will o
bserve th
e same
pattern
as in Fig
ure 25.2. In
Part 2, stu
den
ts will actu
ally m
ake waves.
THIN
K, PA
RT 1 Th
e wavelen
gth
in
creases.
THIN
K, PA
RT 2 Th
e wavelen
gth
d
ecreases.
Th
e energ
y tran
sferred b
y a w
ave from
a vibratin
g so
urce
to a receiver is carried
by a
distu
rban
ce in a m
ediu
m.
Te
ac
hin
g R
es
ou
rc
es
• Reading and Study W
orkbook • Problem
-Solving Exercises in Physics 13-1
• PresentationEX
PRESS
• Interactive Textbook
CO
NCEP
TCH
ECK
......
CO
NCEP
TCH
ECK
......
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25.4 Wave Speed
The speed of a w
ave depends on the medium
through which the w
ave m
oves. Sound waves, for exam
ple, move at speeds of about
330 m/s to 350 m
/s in air (depending on temperature), and about four
times faster in w
ater. Whatever the m
edium, the speed, w
avelength, and frequency of the w
ave are related. Consider the sim
ple case of w
ater waves, as show
n in Figure 25.7. Imagine that you fix your eyes
at a stationary point on the surface of water and observe the w
aves passing by this point. If you observe the distance betw
een crests (the w
avelength) and also count the number of crests that pass each
second (the frequency), then you can calculate the horizontal distance a particular crest m
oves each second. For example, in
Figure 25.7, one crest passes by the bird every second. The w
aves therefore m
ove at 1 meter per second.
You can calculate the speed of a wave by m
ultiplying the w
avelength by the frequency. For example, if the w
avelength is 3 m
eters and if two crests pass a stationary point each second, then
3 meters !
2 waves pass by in 1 second. T
he waves therefore m
ove at 6 m
eters per second. In equation form, this relationship is w
ritten as
v�%f
where v
is wave speed, l (G
reek letter lambda) is w
avelength, and fis w
ave frequency. This relationship holds for all kinds of w
aves, w
hether they are water w
aves, sound waves, radio w
aves, or light waves.
FIGU
RE 25.7 !If the w
avelength is 1 meter, and one
wavelength per second passes the pole,
then the speed of the wave is 1 m
/s.
The equationv
�G
fm
akes sense: During
each vibration, a wave
travels a distance of one w
avelength.
CH
APTER 25
VIBRATION
S AN
D W
AVES 495
thin
k!
If a water w
ave vibrates up and down tw
o times each second and the
distance between w
ave crests is 1.5 m, w
hat is the frequency of the wave?
What is its w
avelength? What is its speed? Answ
er: 25.4.1
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25.4 Wave Speed
" Teach
ing
Tip Exp
lain th
at the
frequ
ency o
f a vibratin
g so
urce is
the sam
e as the freq
uen
cy of th
e w
ave it pro
du
ces.
" Teach
ing
Tip Exp
lain o
r d
erive wave sp
eed: Sp
eed 5
w
aveleng
th 3
frequ
ency.
Sup
po
rt this w
ith th
e freigh
t car exam
ple.
" Teach
ing
Tip H
ave stud
ents
calculate th
e wavelen
gth
s of
their favo
rite local rad
io statio
ns.
Wavelen
gth
5 sp
eed/freq
uen
cy. For exam
ple, 1000-kHz w
aves have w
avelengths 5 (3 3
108 m
/s)/(10
6 Hz) 5
300 m. Su
rprisin
gly
lon
g!
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496
Table 25.1 shows som
e wavelengths and corresponding frequen-
cies of sound in air at the same tem
perature. Notice that the product of
wavelength and frequency is the sam
e for each example—
340 m/s in this
case. During a concert, you do not hear the high notes in a chord before
you hear the low notes. T
he sounds of all instruments reach you at the
same tim
e. Notice that long w
avelengths have low frequencies, and short
wavelengths have high frequencies. W
avelength and frequency vary inversely to produce the sam
e wave speed for all sounds.
CON
CEPT
CHECK
......How
do you calculate the sp
eed of a w
ave?
If a train of freight cars, each 10 m
long, rolls b
y you at the rate of 2 cars each second
, what is the sp
eed of the train?
You can look at this problem in tw
o ways, the C
hapter 4 way and the
Chapter 25 w
ay.
From C
hapter 4 recall:
20 m/s
v�
dt2
�10 m
1 s�
�
Note that d is the length of that part of the train that passes you in
time
t.
Here in C
hapter 25 we com
pare the train to wave m
otion, w
here the wavelength corresponds to 10 m
, and the frequency is 2 H
z. Then
wave speed
�w
avelength�
frequency�
�(10 m
)�
(2 Hz)
�20 m
/s
O
ne of the nice things about physics is that different ways of
looking at things produce the same answ
er. When this doesn’t hap-
pen, and there is no error in computation, then the validity of one (or
both!) of those ways is suspect.
do
the
ma
th!
What is the w
avelength of a 340-H
z sound wave
when the speed of sound
in air is 340 m/s?
Answ
er: 25.4.2
thin
k!
Table 2
5.1
SoundW
aves
Wavelength (m
)Frequency (H
z)W
ave Speed (m/s)
2.13
1.29
0.86
0.64
160
264
396
528
340
340
340
340
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6
Be sure to distinguish electrom
agnetic waves from
longitudinal sound waves. Consider discussing Chapter 27 and Chapter 37 m
aterial here to lead into the fam
ily of electrom
agnetic waves. Show how electrom
agnetic waves are grouped according to their wavelengths and frequencies.
Y
ou
can calcu
late the
speed
of a w
ave by
mu
ltiplyin
g th
e wavelen
gth
by
the freq
uen
cy.
Te
ac
hin
g R
es
ou
rc
es
• Reading and Study W
orkbook • Presentation
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ESS
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NCEP
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ECK
......
CO
NCEP
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ECK
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25.5 Transverse Waves
Suppose you create a wave along a rope by shaking the free end up
and down, as show
n in Figure 25.8. The m
otion of the rope is at right angles to the direction in w
hich the wave is m
oving. Whenever the
motion of the m
edium is at right angles to the direction in w
hich a w
ave travels, the wave is a transverse w
ave. W
aves in the stretched strings of m
usical instruments and the electrom
agnetic w
aves that make up radio w
aves and light are transverse.
CON
CEPT
CHECK
......What are som
e examp
les of transverse waves?
25.6 Longitudinal Waves
Not all w
aves are transverse. Sometim
es the particles of the m
edium m
ove back and forth in the same direction in w
hich the w
ave travels. When the particles oscillate parallel to or along the
direction of the wave rather than at right angles to it, the w
ave is a
longitudinal wave.
Sound waves are longitudinal w
aves.B
oth transverse and longitudinal waves can be dem
onstrated with
a loosely-coiled spring, as shown in Figure 25.9. A
transverse wave is
demonstrated by shaking the end of a coiled spring up and dow
n. A
longitudinal wave is dem
onstrated by shaking the end of the coiled spring in and out. In this case w
e see that the medium
vibrates paral-lel to the direction of energy transfer.
CON
CEPT
CHECK
......What is an exam
ple of a long
itudinal w
ave?
! FIG
URE 25.9
Transverse and longitudi-nal w
aves transfer energy from
left to right. a. W
hen the end of a coiled spring is shaken up and dow
n, a transverse w
ave is produced. b.
When it is shaken in
and out, a longitudinal w
ave is produced.
! FIG
URE 25.8
A person creates a trans-
verse wave by shaking
the free end of a rope up and dow
n. The arrows
represent the motion of
the rope.
CH
APTER 25
VIBRATION
S AN
D W
AVES 497
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25.5 Transverse W
avesK
ey
Term
transverse w
ave
W
aves in th
e stretch
ed strin
gs
of m
usical in
strum
ents an
d th
e electro
mag
netic w
aves that
make u
p rad
io w
aves and
ligh
t are tran
sverse.
25.6 Longitudinal W
avesK
ey
Term
lon
gitu
din
al wave
" Teach
ing
Tip A
llow
stu
den
ts to p
lay with
large
sprin
gs o
r Slinkys u
ntil th
ey can
dem
on
strate and
explain
the
differen
ce betw
een tran
sverse an
d lo
ng
itud
inal w
aves.
Ask W
ith respect to the direction of the w
ave’s motion,
how do the directions of
vibrations differ for transverse and longitudinal w
aves? Perp
end
icular fo
r transverse;
parallel fo
r lon
gitu
din
al
So
un
d w
aves are lo
ng
itud
inal w
aves.
Te
ac
hin
g R
es
ou
rc
es
• Reading and Study W
orkbook • Transparency 51• Presentation
EXPR
ESS
• Interactive Textbook
CON
CEPT
CHECK
......
CON
CEPT
CHECK
......
CON
CEPT
CHECK
......
CON
CEPT
CHECK
......
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25.7 InterferenceA
material object such as a rock w
ill not share its space with another
rock. But m
ore than one vibration or wave can exist at the sam
e tim
e in the same space. If you drop tw
o rocks in water, the w
aves produced by each can overlap and form
an interference pattern. A
n interference pattern is a regular arrangement of places w
here w
ave effects are increased, decreased, or neutralized. Interference
patterns occur when w
aves from different sources arrive at the
same point—
at the same tim
e.In constructive interference, the crest of one w
ave overlaps the crest of another and their individual effects add together. T
he result is a w
ave of increased amplitude. A
s Figure 25.10a shows, this is
called reinforcement. In destructive interference, the crest of one
wave overlaps the trough of another and their individual effects are
reduced. The high part of one w
ave simply fills in the low
part of another. A
s Figure 25.10b shows, this is called cancellation.
FIGU
RE 25.10 !There are tw
o types of wave
interference. a. In construc-tive interference, the w
aves reinforce each other to pro-duce a w
ave of increased am
plitude.b. In destructive interference, the w
aves can-cel each other and no w
ave is produced.
Sound, a longitudinal w
ave, requires a medium
. It can’t travel in a vacuum
because there’s nothing to com
press and stretch.
Seismologist
When an earthquake occurs, the sudden release of energy produces
waves. Seis m
ologists study and interpret those waves in order to
determine the strength and location of the earthquake. They com
pare the speed, am
plitude, and reception of primary longitudinal w
aves w
ith secondary transverse waves. Because they understand how
waves
travel and the materials through w
hich they pass, seismologists are
able to describe earthquakes, learn about the composition of Earth,
and possibly predict future earthquakes. Seismologists conduct
research from university and governm
ent facilities, such as the National
Earthquake Information Service (N
EIS) in Colorado.
Ph
ysics o
n th
e Jo
b
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8
25.7 InterferenceK
ey
Term
sin
terference p
attern,
con
structive in
terference,
destru
ctive interferen
ce, ou
t of
ph
ase, in p
hase
! Teach
ing
Tip D
escribe
interferen
ce by d
rawin
g
Figu
re 25.10 on
the b
oard
. If yo
u h
ave a ripp
le tank, sh
ow
th
e overlap
pin
g o
f water w
aves an
d in
terference.
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Wave interference is easiest to see in w
ater. Figure 25.11a shows
the interference pattern made w
hen two vibrating objects touch the
surface of water. T
he gray “spokes” are regions where w
aves cancel each other out. A
t points along these regions, the waves from
the two
objects arrive “out of step,” or out of phase, with one another. W
hen w
aves are out of phase, the crests of one wave overlap the troughs
of another to produce regions of zero amplitude. T
he dark and light-striped regions are w
here the waves are “in step,” or in phase, w
ith each other. W
hen waves are in phase, the crests of one w
ave overlap the crests of the other, and the troughs overlap as w
ell.Interference patterns are nicely illustrated by
the overlapping of concentric circles printed on a pair of clear sheets, as show
n in Figures 25.11b and 25.12. W
hen the sheets overlap with their centers
slightly apart, a so-called moiré pattern is form
ed that is very sim
ilar to the interference pattern of w
ater waves (or any kind of w
aves). A slight shift
in either of the sheets produces noticeably differ-ent patterns. If a pair of such sheets is available, be sure to try this and see the variety of patterns for yourself.
Interference is characteristic of all wave
motion, w
hether the waves are w
ater waves, sound
waves, or light w
aves. The interference of sound is
discussed in the next chapter, and the interference of light in C
hapter 31.
CON
CEPT
CHECK
......What causes interference p
atterns?
! FIG
URE 25.11
a. Two overlapping w
ater w
aves produce an interfer-ence pattern. b. O
verlapping concentric circles produce a pictorial representation of an interfer-ence pattern.
FIGU
RE 25.12 "
A m
oiré pattern is very similar
to an interference pattern.
ab
CH
APTER 25
VIBRATION
S AN
D W
AVES 499
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499
# Teach
ing
Tip M
ake a pair
of tran
sparen
cies of co
ncen
tric circles. Su
perim
po
se them
on
yo
ur o
verhead
pro
jector an
d
sho
w th
e variety of in
terference
pattern
s that resu
lt wh
en th
eir cen
ters are disp
laced. O
ne
examp
le is sho
wn
in Fig
ure 25.12.
Ask Can w
aves overlap in such a w
ay as to produce a zero am
plitude? Yes, th
at is th
e destru
ctive interferen
ce ch
aracteristic of all w
aves.
In
terference p
atterns
occu
r wh
en w
aves fro
m d
ifferent so
urces arrive at
the sam
e po
int—
at the sam
e tim
e.
Te
ac
hin
g R
es
ou
rc
es
• Reading and Study W
orkbook • Laboratory M
anual 71• Presentation
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ESS
• Interactive Textbook
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CEPT
CHECK
......
CON
CEPT
CHECK
......
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25.8 Standing Waves
If you tie a rope to a wall and shake the free end up and dow
n, you w
ill produce a wave in the rope. T
he wall is too rigid to shake, so
the wave is reflected back along the rope to you. B
y shaking the rope just right, you can cause the incident (original) and reflected w
aves to form
a standing wave. A
standing wave is a w
ave that appears to stay in one place—
it does not seem to m
ove through the medium
. C
ertain parts of a standing wave rem
ain stationary. Nodes are the
stationary points on a standing wave.
Interestingly enough, you could hold your fingers on either side of the rope at a node, and the rope w
ould not touch them. O
ther parts of the rope w
ould make contact w
ith your fingers. The posi-
tions on a standing wave w
ith the largest amplitudes are know
n as
antinodes. Antinodes occur halfw
ay between nodes.
Standing waves are the result of interference. W
hen two w
aves of equal am
plitude and wavelength pass through each other in opposite
directions, the waves are alw
ays out of phase at the nodes. As Figure
25.13 shows, the nodes are stable regions of destructive interference.
FIGU
RE 25.13 !The incident and reflected w
aves interfere to produce a standing w
ave. The nodes are places that rem
ain stationary.
thin
k!
Is it possible for one wave
to cancel another wave so
that the combined am
pli-tude is zero? Explain your answ
er. Answ
er: 25.8
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0
25.8 Standing W
avesK
ey
Term
sstan
din
g w
ave, no
de, an
tino
de
" Teach
ing
Tip Em
ph
asize that
a stand
ing
wave is th
e result o
f in
terference.
" Teach
ing
Tip U
se a lon
g th
in
sprin
g o
r a rop
e to d
emo
nstrate
stand
ing
waves. H
ave stud
ents
iden
tify the n
od
es and
com
e up
clo
se to in
spect th
em. C
han
ge
the freq
uen
cy and
sho
w th
at on
ly sp
ecific frequ
encies allo
w th
e creatio
n o
f stand
ing
waves.
" Teach
ing
Tidb
it Figu
re 25.14a sh
ow
s the lo
west
frequ
ency o
f vibratio
n o
f a stan
din
g w
ave—th
e fun
dam
ental
frequ
ency.
" Teach
ing
Tip Po
int o
ut th
at fo
r a string
free at on
e end
and
a tu
be o
pen
at on
e end
and
closed
at th
e oth
er end
, stand
ing
waves
form
wh
en o
dd
integ
er mu
ltiples
of q
uarter w
aveleng
ths fit in
to
the vib
rating
med
ium
. A so
da-
po
p b
ottle is an
examp
le of a
tub
e op
en at o
ne en
d an
d clo
sed
at the o
ther en
d.
A
stand
ing
wave
form
s on
ly if half a
wavelen
gth
or a m
ultip
le of h
alf a w
aveleng
th fits exactly in
to th
e len
gth
of th
e vibratin
g m
ediu
m.
Te
ac
hin
g R
es
ou
rc
es
• Reading and Study W
orkbook • Problem
-Solving Exercises in Physics 13-3
• Transparency 52• Presentation
EXPR
ESS
• Interactive Textbook• N
ext-Time Q
uestion 25-1
CO
NCEP
TCH
ECK
......
CO
NCEP
TCH
ECK
......
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You can produce a variety of standing waves by shaking the rope
at different frequencies. Once you find a frequency that produces a
standing wave, doubling or tripling the frequency w
ill also produce a standing w
ave. A
standing wave form
s only if half a wavelength
or a multiple of half a w
avelength fits exactly into the length of the vibrating m
edium. In Figure 25.14a, the rope length equals half a
wavelength. In Figure 25.14b, the rope length equals one w
avelength. In Figure 25.14c, the rope length equals one and one-half w
ave-lengths. If you keep increasing the frequency, you’ll produce m
ore interesting w
aves.
Standing waves are set up in the strings of m
usical instruments that
are struck. They are set up in the air in an organ pipe and the air of a
soda-pop bottle when air is blow
n over the top. Standing waves can be
produced in either transverse or longitudinal waves.
CON
CEPT
CHECK
......At w
hat waveleng
ths can a standing
w
ave form in a vib
rating m
edium
?
25.9 The Doppler Effect
Imagine a bug jiggling its legs and bobbing up and dow
n in the m
iddle of a quiet puddle, as shown in Figure 25.15. Suppose the bug
is not going anywhere but is m
erely treading water in a fixed posi-
tion. The crests of the w
ave it makes are concentric circles, because
the wave speed is the sam
e in all directions. If the bug bobs in the w
ater at a constant frequency, the distance between w
ave crests (the w
avelength) will be the sam
e for all successive waves. W
aves encounter point A
as frequently as they encounter point B. T
his means that the
frequency of wave m
otion is the same at points A
and B, or anyw
here in the vicinity of the bug. T
his wave frequency is the sam
e as the bob-bing frequency of the bug.
! FIG
URE 25.14
You can produce a variety of standing w
aves. a. Shake the rope until you set up a standing w
ave of ! 12 ! w
avelength. b. Shake w
ith twice the frequency
and produce a standing wave of
1 wavelength.
c. Shake with three tim
es the fre-quency and produce a standing w
ave of 1! 12 ! w
avelengths.
CH
APTER 25
VIBRATION
S AN
D W
AVES 501
For:Visit:W
eb Code: –
Doppler Effect activity
ww
w.PHSchool.com
csp
4259
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25.9 The Doppler
EffectK
ey
Term
sD
op
pler effect, b
lue sh
ift, red
shift
Co
mm
on
Misco
ncep
tion
Changes in w
ave speed cause the D
oppler effect.
FAC
T The D
op
pler effect is an
ap
paren
t chan
ge in
frequ
ency
du
e to th
e mo
tion
of th
e sou
rce.
" Teach
ing
Tip Place an
electro
nic w
histle th
at emits a
sou
nd
of ab
ou
t 3000 Hz in
to a
spo
ng
e, rub
ber, o
r foam
ball.
Intro
du
ce the D
op
pler effect b
y th
row
ing
the b
all arou
nd
the
roo
m. A
sk stud
ents to
describ
e w
hat th
ey hear as th
e ball m
oves
thro
ug
h th
e air. Then
ask if the
frequ
ency o
f the so
un
d th
at the
wh
istle emits actu
ally chan
ges.
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502
Suppose the jiggling bug moves across the w
ater at a speed less than the w
ave speed. In effect, the bug chases part of the crests it has produced. T
he wave pattern is distorted and is no longer concentric,
as shown in Figure 25.16. T
he center of the outer crest was m
ade w
hen the bug was at the center of that circle. T
he center of the next sm
aller crest was m
ade when the bug w
as at the center of that circle, and so forth. T
he centers of the circular crests move in the direction
of the swim
ming bug. A
lthough the bug maintains the sam
e bob-bing frequency as before, an observer at B
would encounter the crests
more often. T
he observer would encounter a higher frequency. T
his is because each successive crest has a shorter distance to travel so they arrive at B
more frequently than if the bug w
ere not moving tow
ard B.
An observer at A
, on the other hand, encounters a lower fre-
quency because of the longer time betw
een wave-crest arrivals. To
reach A, each crest has to travel farther than the one ahead of it due
to the bug’s motion.
As a w
ave source approaches, an observer encounters w
aves with a higher frequency. A
s the wave source
moves aw
ay, an observer encounters waves w
ith a lower frequency.
This apparent change in frequency due to the m
otion of the source (or receiver) is called the D
oppler effect (after the Austrian scientist
Christian D
oppler, 1803–1853). The greater the speed of the source,
the greater will be the D
oppler effect.W
ater waves spread over the flat surface of the w
ater. Sound and light w
aves, on the other hand, travel in three-dimensional space in
all directions like an expanding balloon. Just as circular wave crests
are closer together in front of the swim
ming bug, spherical sound or
light wave crests ahead of a m
oving source are closer together than those behind the source and encounter a receiver m
ore frequently.
FIGU
RE 25.15 !
A stationary bug jiggling
in still water produces a
circular water w
ave.
FIGU
RE 25.16 !
A bug sw
imm
ing in still w
ater produces a wave
pattern that is no longer concentric.
Police Offi cer
Police officers are responsible for protecting people. While that
involves catching criminals and solving crim
es, it also requires that police officers prevent drivers from
speeding. In this way, police
officers protect pedestrians and people in vehicles. One w
ay that police officers prevent speeding is by using radar equipm
ent. Radar equipm
ent sends waves tow
ard a moving vehicle and uses the
Doppler effect to determ
ine the speed of the vehicle. By knowing
how to operate the device, police officers can determ
ine when a
driver is not obeying the speed limit.
Ph
ysics o
n th
e Jo
b
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50
2
" Teach
ing
Tip D
escribe th
e p
attern th
at a station
ary bu
g
jigg
ling
in still w
ater makes as
sho
wn
in Fig
ure 25.15. D
raw
circles to sh
ow
the to
p view
of
circular rip
ples m
ade b
y a bu
g
bo
bb
ing
in th
e water. Stress
that w
ave speed
, wavelen
gth
, an
d freq
uen
cy are the sam
e in
all directio
ns, as sh
ow
n b
y the
circular sh
ape.
" Teach
ing
Tip N
ow
con
sider
a mo
ving
bu
g an
d th
e pattern
it m
akes (Figu
re 25.16). Explain
h
ow
the freq
uen
cy of w
aves is in
creased in
fron
t of th
e bu
g;
waves w
ou
ld b
e enco
un
tered
mo
re often
(mo
re frequ
ently) b
y yo
ur h
and
placed
in th
e water in
fro
nt o
f the b
ug
. (The o
bserver
wo
uld
also en
cou
nter a sh
orter
wavelen
gth
; since v is a co
nstan
t fo
r a given
med
ium
, then
as f in
creases, l decreases.) Sim
ilarly w
aves wo
uld
be en
cou
ntered
less o
ften (less freq
uen
tly) beh
ind
th
e bu
g.
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Bats hunt moths in
darkness by echo loca-tion and the D
oppler effect. Som
e moths
are protected by a thick covering of fuzzy scales that deaden the echoes.
! FIG
URE 25.17
The pitch of sound is higher w
hen the source m
oves toward
you, and lower w
hen the source m
oves aw
ay.
Sound T
he Doppler effect is evident w
hen you hear the changing pitch of a siren as a firetruck passes you. Look at Figure 25.17. W
hen the firetruck approaches, the pitch sounds higher than norm
al. This
occurs because the sound wave crests are encountering you m
ore fre-quently. W
hen the firetruck passes and moves aw
ay, you hear a drop in pitch because the w
ave crests are encountering you less frequently.Police m
ake use of the Doppler effect of radar w
aves in measur-
ing the speeds of cars on the highway. R
adar waves are electrom
ag-netic w
aves, lower in frequency than light and higher in frequency
than radio waves. Police bounce them
off moving cars as show
n in Figure 25.18. A
computer built into the radar system
calculates the speed of the car relative to the radar unit by com
paring the frequency of the radar w
ith the frequency of the reflected waves.
Light The D
oppler effect also occurs for light. When a light source
approaches, there is an increase in its measured frequency, and
when it recedes, there is a decrease in its frequency. A
n increase in frequency is called a blue shift, because the increase is tow
ard the high-frequency, or blue, end of the color spectrum
. A decrease in
frequency is called a red shift, referring to the low-frequency, or
red, end of the color spectrum. D
istant galaxies, for example, show
a red shift in the light they em
it. A m
easurement of this shift enables
astronomers to calculate their speeds of recession. A
rapidly spinning star show
s a red shift on the side turning away from
us and a blue shift on the side turning tow
ard us. This enables a calculation of the
star’s spin rate.
CON
CEPT
CHECK
......How
does the ap
parent freq
uency of waves chang
e as a w
ave source moves?
CH
APTER 25
VIBRATION
S AN
D W
AVES 503
! FIG
URE 25.18
The police calculate a car’s speed by m
easur-ing the D
oppler effect of radar w
aves.
thin
k!
When a source m
oves tow
ard you, do you m
easure an increase or decrease in w
ave speed? Answ
er: 25.9
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503
" Teach
ing
Tip R
elate the
con
cept o
f the m
ovin
g b
ug
to th
e w
aves from
the m
ovin
g so
urces
in Fig
ures 25.17 an
d 25.18.
Ask The w
aves are more
crowded in front of the
swim
ming bug and m
ore spread out behind. Is the w
ave speed greater in front of the bug (and less behind the bug)? N
o!
Frequ
ency, n
ot sp
eed, is g
reater in
fron
t of th
e bu
g an
d less
beh
ind
.
" Teach
ing
Tip Em
ph
asize the
distin
ction
betw
een w
ave speed
an
d w
ave frequ
ency.
" Teach
ing
Tip Sw
ing
a sou
nd
so
urce at th
e end
of a strin
g in
a h
orizo
ntal circle. R
elate this
to th
e siren o
f a fire eng
ine
and
the rad
ar of th
e hig
hw
ay p
atrol (Fig
ures 25.17 an
d 25.18).
(Men
tion
that so
un
d req
uires a
med
ium
; radar d
oesn
’t.)
" Teach
ing
Tip Po
int o
ut
that lig
ht, rad
ar, TV, an
d rad
io
waves are all electro
mag
netic
in n
ature. Th
e waves d
iffer o
nly in
frequ
ency (an
d h
ence
wavelen
gth
) and
energ
y per
ph
oto
n.
" Teach
ing
Tip R
elate the p
itch
of so
un
d to
the co
lor o
f ligh
t. B
oth
dep
end
on
frequ
ency.
A
s a wave so
urce
app
roach
es, an
ob
server enco
un
ters waves w
ith
a hig
her freq
uen
cy. As th
e wave
sou
rce mo
ves away, an
ob
server en
cou
nters w
aves with
a lo
wer freq
uen
cy.
Te
ac
hin
g R
es
ou
rc
es
• Concept-Developm
ent Practice Book 25-1
• Problem-Solving Exercises
in Physics 13-2• Laboratory M
anual 70
CON
CEPT
CHECK
......
CON
CEPT
CHECK
......
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504
25.10 Bow
Waves
When the speed of the source in a m
edium is as great as the speed
of the waves it produces, som
ething interesting happens. The w
aves pile up. C
onsider the bug in the previous example w
hen it swim
s as fast as the w
ave speed. Can you see that the bug w
ill keep up with the
wave crests it produces? Instead of the crests getting ahead of the bug,
they pile up or superimpose on one another directly in front of the
bug, as suggested in Figure 25.19. The bug m
oves right along with the
leading edge of the waves it is producing.
The sam
e thing happens when an aircraft travels at the speed of
sound. In the early days of jet aircraft, it was believed that this pileup
of sound waves in front of the airplane im
posed a “sound barrier” and that to go faster than the speed of sound, the plane w
ould have to “break the sound barrier.” W
hat actually happens is that the overlapping w
ave crests disrupt the flow of air over the w
ings, so that it is harder to control the plane w
hen it is flying close to the speed of sound. B
ut the barrier is not real. Just as a boat can easily travel faster than the speed of w
ater waves, an airplane w
ith sufficient pow
er can easily travel faster than the speed of sound. Then w
e say that it is supersonic—
faster than sound. A supersonic airplane flies
into smooth, undisturbed air because no sound w
ave can propagate out in front of it. Sim
ilarly, a bug swim
ming faster than the speed
of water w
aves finds itself always entering into w
ater with a sm
ooth, unrippled surface.
When the bug sw
ims faster than w
ave speed, ideally it produces a w
ave pattern as shown in Figure 25.20. It outruns the w
ave crests it produces. T
he crests overlap at the edges, and the pattern made
by these overlapping crests is a V shape, called a bow
wave, w
hich appears to be dragging behind the bug.
A bow
wave occurs w
hen a w
ave source moves faster than the w
aves it produces. The fam
iliar bow
wave generated by a speedboat knifing through the w
ater is pro-duced by the overlapping of m
any circular wave crests.
FIGU
RE 25.19 !
A bug sw
imm
ing at the w
ave speed “keeps up” w
ith the wave crests it
produces.
FIGU
RE 25.20 "A
bug swim
ming faster
than the wave speed
produces a wave pattern
in which the w
ave crests overlap at the edges.
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50
4
25.10 Bow W
avesK
ey
Term
bo
w w
ave
" Teach
ing
Tip A
sk the class
to co
nsid
er the w
aves mad
e by
two
ston
es thro
wn
in th
e water.
Sketch th
e overlap
pin
g w
aves as sh
ow
n b
elow
.
Ask w
here th
e water is h
igh
est ab
ove th
e no
rmal w
ater level, an
d th
en in
dicate th
e two
p
laces wh
ere the w
aves overlap
w
ith X
’s. This is co
nstru
ctive in
terference. Exten
d th
e sw
imm
ing
bu
g co
ncep
t to sp
eeds
greater th
an w
ave speed
s and
sh
ow
the reg
ion
s of o
verlap th
at p
rod
uce th
e bo
w w
ave (sketchin
g
Figu
res 25.15, 25.16, and
25.19). Sh
ow
ho
w a series o
f overlap
s m
akes up
the V
-shap
ed en
velop
e sh
ow
n in
Figu
re 25.21.
" Teach
ing
Tip Exp
lain th
at th
e form
ation
of th
e bo
w
wave in
Figu
re 25.20 is ano
ther
examp
le of co
nstru
ctive in
terference, w
ith an
app
reciable
resultin
g am
plitu
de.
A
bo
w w
ave occu
rs w
hen
a wave so
urce
mo
ves faster than
the w
aves it p
rod
uces.
Te
ac
hin
g R
es
ou
rc
es
• Reading and Study W
orkbook • Transparency 53• Presentation
EXPR
ESS
• Interactive Textbook
CO
NCEP
TCH
ECK
......
CO
NCEP
TCH
ECK
......
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Don’t confuse super-
sonic with ultrasonic.
Supersonic has to do w
ith speed—faster
than sound. Ultrasonic
involves frequency—higher than w
e can hear.
FIGU
RE 25.21 !The w
ave patterns made
by a bug swim
ming at suc-
cessively greater speeds change. O
verlapping at the edges occurs only w
hen the source travels faster than w
ave speed.
Figure 25.21 shows som
e wave patterns m
ade by sources mov-
ing at various speeds. After the speed of the source exceeds the w
ave speed, increased speed produces a bow
wave w
ith a narrower V
shape.
CON
CEPT
CHECK
......What causes a b
ow w
ave?
25.11 Shock Waves
A speedboat knifing through the w
ater generates a two-dim
ensional bow
wave. A
supersonic aircraft similarly generates a shock w
ave. A
shock wave is a three-dim
ensional wave that consists of overlap-
ping spheres that form a cone.
A shock w
ave occurs when an
object moves faster than the speed of sound. Just as the bow
wave
of a speedboat spreads until it reaches the shore of a lake, the conical shock w
ave generated by a supersonic craft spreads until it reaches the ground, as show
n in Figure 25.22.T
he bow w
ave of a speedboat that passes by can splash and douse you if you are at the w
ater’s edge. In a sense, you can say that you are hit by a “w
ater boom.” In the sam
e way, a conical shell of com
pressed air sw
eeps behind a supersonic aircraft. The sharp crack heard w
hen the shock w
ave that sweeps behind a supersonic aircraft reaches the
listeners is called a sonic boom.
We don’t hear a sonic boom
from a slow
er-than-sound, or sub-sonic, aircraft, because the sound w
ave crests reach our ears one at a tim
e and are perceived as a continuous tone. Only w
hen the craft m
oves faster than sound do the crests overlap and encounter the lis-tener in a single burst. T
he sudden increase in pressure has much the
same effect as the sudden expansion of air produced by an explosion.
Both processes direct a burst of high-pressure air to the listener. T
he ear cannot distinguish betw
een the high pressure from an explosion
and the high pressure from m
any overlapping wave crests.
CH
APTER 25
VIBRATION
S AN
D W
AVES 505
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505
25.11 Shock Waves
Ke
y Te
rms
sho
ck wave, so
nic b
oo
m
Co
mm
on
Misco
ncep
tion
A sonic boom
is a mom
entary burst of high pressure produced w
hen som
ething exceeds the speed of sound.
FAC
T A so
nic b
oo
m is actu
ally a co
ntin
uo
us fro
nt o
f hig
h p
ressure
gen
erated b
y faster-than
-sou
nd
so
urces.
" Teach
ing
Tip Q
uestio
ns
raised b
y stud
ents ab
ou
t sho
ck w
aves and
the so
nic b
oo
m can
b
e effectively answ
ered b
y su
bstitu
ting
the exam
ple o
f an
aircraft in th
e air for th
e examp
le o
f a speed
bo
at knifin
g th
rou
gh
th
e water. If yo
u’re en
joyin
g
a picn
ic lun
ch at th
e edg
e of a
river wh
en a sp
eedb
oat co
mes
by an
d d
rench
es you
, you
wo
n’t
attribu
te this to
the id
ea that
the sp
eedb
oat ju
st exceeded
the
speed
of th
e water w
aves. Yo
u
kno
w th
e bo
at is gen
erating
a co
ntin
uo
us b
ow
wave so
lon
g
as it travels faster than
waves in
w
ater. Likewise fo
r aircraft.
Ask W
hy can’t a subsonic aircraft, no m
atter how loud it
may be, produce a shock w
ave or sonic boom
? There w
ill be n
o
overlap
pin
g o
f sph
erical waves
to fo
rm a co
ne u
nless th
e aircraft m
oves faster th
an th
e waves
it gen
erates.
The analogy between bow waves in water and shock waves in air is useful when discussing the shock waves produced by supersonic aircraft.
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506
A com
mon m
isconception is that sonic booms are produced at
the mom
ent that an aircraft flies through the “sound barrier”—that
is, just as the aircraft surpasses the speed of sound. This is equivalent
to saying that a boat produces a bow w
ave only when it first over-
takes its own w
aves. This is not so. T
he fact is that a shock wave and
its resulting sonic boom are sw
ept continuously behind an aircraft traveling faster than sound, just as a bow
wave is sw
ept continuously behind a speedboat. In Figure 25.23, listener B
is in the process of hearing a sonic boom
. Listener A has already heard it, and listener C
w
ill hear it shortly. The aircraft that generated this shock w
ave may
have broken through the sound barrier hours ago!It is not necessary that the m
oving source emit sound for it to
produce a shock wave. O
nce an object is moving faster than the speed
of sound, it will m
ake sound. A supersonic bullet passing overhead
produces a crack, which is a sm
all sonic boom. If the bullet w
ere larger and disturbed m
ore air in its path, the crack would be m
ore boom
like. When a lion tam
er cracks a circus whip, the cracking
sound is actually a sonic boom produced by the tip of the w
hip when
it travels faster than the speed of sound. Snap a towel and the end can
exceed the speed of sound and produce a mini sonic boom
. The bul-
let, whip, and tow
el are not in themselves sound sources, but w
hen traveling at supersonic speeds they produce their ow
n sound as waves
of air are generated to the sides of the moving objects.
On the m
atter of sound in general: You know that you’ll dam
-age your eyes if you stare at the sun. W
hat many people don’t know
is that you’ll sim
ilarly damage your ears if you overexpose them
to loud sounds. D
o as your author does when in a room
with very loud
music—
leave. If for any reason you don’t want to leave—
really enjoy-able m
usic or good camaraderie w
ith friends—stay, but use ear plugs
of some kind! You’re not being a w
imp w
hen you give the same care
to your ears that you give to your eyes.
CON
CEPT
CHECK
......What causes a shock w
ave?
Watch for the advent
of newly designed air-
craft that fly 1.8 times
the speed of sound and produce sonic boom
s only one-hundredth the strength of the super-sonic Concorde, w
hich w
as grounded following
a fatal accident in 2000.
FIGU
RE 25.22 !A
shock wave is sw
ept continuously behind a supersonic aircraft.
FIGU
RE 25.23 "
The shock wave has not yet
encountered listener C, but
is now encountering listener
B, and has already passed
listener A.
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50
6
! Teach
ing
Tip C
on
struct a
sho
ck wave o
n th
e bo
ard as
follo
ws: First p
lace you
r chalk
anyw
here o
n th
e bo
ard to
sign
ify tim
e zero. D
raw a 1-m
-lon
g
ho
rizon
tal line to
the rig
ht to
rep
resent h
ow
far an aircraft h
as m
oved
in a certain
time. Su
pp
ose
it mo
ves at twice th
e speed
of
sou
nd
(Mach
2).
Du
ring
the tim
e it mo
ves 1 m, th
e so
un
d it in
itially mad
e has m
oved
h
alf this d
istance, w
hich
you
m
ark on
the m
idp
oin
t of yo
ur
line. Exp
lain th
at the in
itial sou
nd
h
as expan
ded
sph
erically, wh
ich
you
represen
t two
-dim
ensio
nally
by d
rawin
g a circle. Exp
lain th
at th
is circle represen
ts on
ly on
e of
the n
early infin
ite nu
mb
er of
circles that m
ake up
the sh
ock
wave, w
hich
you
draw
by m
aking
tan
gen
ts from
the en
d p
oin
t to
the circle. Th
e sho
ck wave sh
ou
ld
be a 60
8 wed
ge (30
8 abo
ve you
r h
orizo
ntal lin
e, and
308 b
elow
). M
ove th
e center 10 cm
at a time
in th
e directio
n o
f travel and
d
raw circles (red
uce th
e radiu
s each
time) w
ithin
the tw
o
tang
ents. Exp
lain h
ow
the sp
eed
of th
e craft is simp
ly the ratio
of
the h
orizo
ntal lin
e (1 m) to
the
radial d
istance (0.5 m
) of th
e big
circle (an
d likew
ise the resp
ective h
orizo
ntal lin
es to rad
ii of
smaller circles).
A
sho
ck wave o
ccurs
wh
en an
ob
ject m
oves faster th
an th
e speed
o
f sou
nd
.
Te
ac
hin
g R
es
ou
rc
es
• Concept-Developm
ent Practice Book 25-2, 25-3
• Next-Tim
e Question 25-2
CO
NCEP
TCH
ECK
......
CO
NCEP
TCH
ECK
......
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REVIEW
For:Visit:W
eb Code: –
Self-Assessment
PHSchool.com
csa 2500
Conce
pt Su
mm
ary
••
•••
•
•
The period of a pendulum
depends only on the length of the pendulum
and the acceleration of gravity.
•
The source of all w
aves is a vibration.
•
The energy in w
aves is carried by a dis-turbance in a m
edium.
•
Calculate the w
ave speed by multiplying
the wavelength and the frequency.
•
Waves in the stretched strings of m
usical instrum
ents and electromagnetic w
aves are transverse. Sound w
aves are longitu-dinal.
•
Interference patterns occur when w
aves from
different sources arrive at the same
point—at the sam
e time.
•
A standing w
ave forms if a m
ultiple of half a w
avelength fits into the length of the m
edium.
•
As a w
ave source approaches, an observer encounters w
aves with a higher fre-
quency. As a w
ave source moves aw
ay, an observer encounters w
aves with a low
er frequency.
•
A bow
wave occurs w
hen a wave source
moves faster than the w
aves it produces.
•
A shock w
ave occurs when an object
moves faster than the speed of sound.
5crest (p. 492)
trough (p. 492)
amplitude (p. 492)
wavelength (p. 492)
frequency (p. 492)
hertz (p. 492)
transverse wave
(p. 497)
longitudinal wave
(p. 497)
interference pattern
(p. 498)
constructive interference(p. 498)
destructive interference (p. 498)
out of phase (p. 499)
in phase (p. 499)
standing wave
(p. 500)
node (p. 500)
antinodes (p. 500)
Doppler effect(p. 502)
blue shift (p. 503)
red shift (p. 503)
bow w
ave (p. 504)
shock wave (p. 505)
sonic boom (p. 505)
CH
APTER 25
VIBRATION
S AN
D W
AVES 507
25.2.1 A
100-Hz w
ave vibrates 100 times/s.
25.2.110 s.
The period is �
�1 vib
0.1 Hz
1 vib0.1 vib/s
�
25.4.1 T
he frequency of the wave is 2 H
z; its w
avelength is 1.5 m; and its w
ave speed is %
�ƒ
�(1.5 m
)�
(2 Hz)
�3 m
/s.
25.4.2 T
he wavelength m
ust be 1 m. T
hen wave
speed�
(1 m)
�(340 H
z)�
340 m/s.
25.8 Yes. T
his is called destructive interference. In a standing w
ave, for example, parts of
the wave have no am
plitude—the nodes.
25.9 N
either! It is the frequency of a wave that
undergoes a change, not the wave speed.
thin
k!
Answ
ers
Key Te
rms
••
•••
•
vibration (p. 490)
wave (p. 490)
period (p. 491)
simple harm
onic m
otion (p. 491)
sine curve (p. 491)
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507
R
EVIEW
Te
ac
hin
g R
es
ou
rc
es
• TeacherEXPR
ESS
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508
Check
Conce
pts
••
••
••
Section 25.0 1. D
oes a vibration or a wave spread out
through space?
Section 25.1 2. W
hat is the period of a pendulum that takes
one second to make a com
plete back-and-forth vibration?
3. Suppose that a pendulum has a period of
1.5 seconds. How
long does it take to make
a complete back-and-forth vibration?
4. Is a pendulum w
ith a 1.5-second period longer or shorter in length than a pendulum
w
ith a 1-second period?
Section 25.2 5. H
ow is a sine curve related to a w
ave?
6. Distinguish am
ong these different parts of a w
ave: amplitude, crest, trough, and w
ave-length.
7. Distinguish betw
een the period and the frequency of a vibration or a w
ave. How
do they relate to one another?
Section 25.3 8. D
oes the medium
in which a w
ave travels m
ove along with the w
ave itself? Defend
your answer.
Section 25.4 9. H
ow does the speed of a w
ave relate to its w
avelength and frequency?
10. As the frequency of sound is increased, does
the wavelength increase or decrease? G
ive an exam
ple.
Sections 25.5 and 25.6 11. D
istinguish between a transverse w
ave and a longitudinal w
ave.
Section 25.7 12. D
istinguish between constructive interfer-
ence and destructive interference.
13. Is interference a property of only some
types of waves or of all types of w
aves?
Section 25.8 14. W
hat causes a standing wave?
Section 25.9 15. W
hen a wave source m
oves toward a receiv-
er, does the receiver encounter an increase in w
ave frequency, wave speed, or both?
16. Does the D
oppler effect occur for only some
types of waves or all types of w
aves?
ASSESS
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8
A
SSESS
Check
Conce
pts
1. A
wave spreads out through
space.
2. 1 s
3. 1.5 s
4. longer
5. A
sine curve is a pictorial representation of a w
ave.
6. A
mplitude—
maxim
um
displacement; crest—
point of greatest positive displacem
ent; trough—point of greatest negative displacem
ent; wavelength—
distance from one crest to
the next
7. Period—
time to com
plete one cycle; frequency—
how m
any cycles occur in a given tim
e
8. N
o. The disturbance, not the m
aterial itself, moves.
9. Speed 5
wavelength 3
frequency
10. Decreases; sm
aller musical
instruments produce higher
frequency sounds.
11. Transverse—m
edium m
oves perpendicular to w
ave direction; longitudinal—m
edium m
oves back and
forth parallel to wave
direction.
12. Constructive—causes an
additive effect; destructive—canceling effect
13. All. It is a prim
e test for wave
properties.
14. Interference of original wave
with reflected w
ave
15. Increase in frequency only 16. A
ll
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APTER 25
VIBRATION
S AN
D W
AVES 509
Section 25.10 17. C
ompared w
ith the speed of water w
aves how
fast must a bug sw
im to keep up w
ith the w
aves it produces? How
fast must a boat
move to produce a bow
wave?
18. Distinguish a bow
wave from
a shock wave.
Section 25.11 19. a. W
hat is a sonic boom?
b. H
ow fast m
ust an aircraft fly in order to produce a sonic boom
?
20. If you encounter a sonic boom, is that
evidence that an aircraft just exceeded the speed of sound to becom
e supersonic?
Thin
k a
nd R
ank •
•••
••
Rank each of the follow
ing sets of scenarios in order of the quantity or property involved. List them
from left to right. If scenarios have equal
rankings, then separate them w
ith an equal sign. (e.g., A
= B
)
21. A fire engine’s siren em
its a certain frequency. R
ank from greatest to least the
apparent frequency heard by the stationary listener in each scenario.
(A) T
he fire engine is traveling toward a
listener at 30 m/s.
(B) T
he fire engine is traveling away from
a listener at 5 m
/s. (C
) The fire engine is traveling tow
ard a listener at 5 m
/s. (D
) The fire engine is traveling aw
ay from a
listener at 30 m/s.
22. Shown below
are four different pairs of transverse w
ave pulses that move tow
ard each other. A
t some point in tim
e the pulses m
eet and interact (interfere) with each
other. Rank the four cases from
greatest to least on the basis of the height of the peak that results w
hen the centers of the pairs coincide.
23. All the w
aves below have the sam
e speed in the sam
e medium
. Use a ruler and rank
these waves from
greatest to least according to am
plitude, wavelength, frequency, and
period.
C
HA
PTER 25 VIBRATIO
NS A
ND
WA
VES 509
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17. As fast as the w
aves move;
faster than the waves m
ove
18. Bow—
a 2-D “V
” on the water
surface; shock—a 3-D
cone in
the air
19. a. Incident shock wave
b. Faster than sound 20. N
o; it could have been any tim
e ago. It depends on
speed, not time.
Thin
k a
nd R
ank
21. A, C, B, D
22. A, B, D
, C
23. Am
plitude: D, B, A
, C
Wavelength: D
, A, B, C
Frequency: C, B, A
, D
Period: D, A
, B, C
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(continued)
510
24. The four sets of w
aves below are a top view
of circular w
ave patterns made by a bug
jiggling on the surface of water. R
ank them
from greatest to least based on the speed of
the bug.
25. The shock w
aves depicted below are pro-
duced by supersonic aircraft. Rank them
from
greatest to least based on the speed of the aircraft.
Plu
g a
nd Ch
ug •
••
••
•
26. A nurse counts 76 heartbeats in one m
inute. W
hat are the period and frequency of the heart’s oscillations?
27. New
York’s 300-m high C
iticorp® Tower
oscillates in the wind w
ith a period of 6.80 s. C
alculate its frequency of vibration.
28. Calculate the speed of w
aves in a puddle that are 0.15 m
apart and made by tapping
the water surface tw
ice each second.
29. Calculate the speed of w
aves in water that
are 0.4 m apart and have a frequency of 2 H
z.
30. The low
est frequency we can hear is about
20 Hz. C
alculate the wavelength associated
with this frequency for sound that travels at
340 m/s. H
ow long is this in feet?
Thin
k a
nd Ex
pla
in ••
••
••
31. Does the period of a pendulum
depend of the m
ass of the bob? On the length of the
string?
32. If a pendulum is shortened, does the fre-
quency increase or decrease? What about its
period?
33. Carm
elita swings to and fro in a sitting posi-
tion on a playground swing. W
illiam says
that if she stands while sw
inging, a longer tim
e will occur betw
een back-and-forth sw
ings. Carlos says no, that the to-and-fro
time of the sw
ing will be unaffected. W
ho, if either, do you agree w
ith?
34. You dip your finger repeatedly into a puddle of w
ater and make w
aves. What happens to
the wavelength if you dip your finger m
ore frequently?
35. If you double the frequency of a vibrat-ing object, w
hat happens to its period?
36. How
does the frequency of vibration of a sm
all object floating in water com
pare to the num
ber of waves passing it each second?
37. If you triple the frequency of a vibrating object, w
hat will happen to its period?
5
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51
0
24. D, C, B, A
25. A, C, B
Plu
g a
nd Ch
ug
26. T 5 (1/76) m
in; f 5 76/m
in
27. f 5 1/(6.80 s) 5
0.15 Hz
28. v 5 lf 5
(0.15 m)(2/s) 5
0.3 m/s
29. v 5 lf 5
(0.4 m)(2/s) 5
0.8 m/s
30. l 5
v/f 5 (340 m
/s)/(20/s) 5
17 m or 56 ft
Thin
k a
nd Ex
pla
in 31. Pendulum
period depends on
its length, but not its mass.
32. Shorter pendulum, higher
frequency, shorter period
33. Disagree w
ith both. CG of
“bob” is closer to pivot, so
shorter pendulum has shorter
period.
34. Higher frequency of dip
m
akes shorter wavelength.
35. f = 1/T, and T = 1/f. Double
one, then other is half. So 2f gives 1/2 T.
36. Both are the same.
37. f and T are reciprocals of each other, so tripling the frequency results in one third
the period.
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APTER 25
VIBRATION
S AN
D W
AVES 511
38. Red light has a longer w
avelength than vio-let light. W
hich has the greater frequency?
39. How
far, in terms of w
avelength, does a w
ave travel in one period?
40. If a wave vibrates up and dow
n twice each
second and travels a distance of 20 m each
second, what is its frequency? Its w
ave speed? (W
hy is this question best answered
by careful reading of the question rather than searching for a form
ula?)
41. The w
ave patterns seen in Figure 25.6 are com
posed of circles. What does this tell you
about the speed of the waves in different
directions?
42. Sound from Source A
has a frequency twice
as great as the frequency of sound from
Source B. C
ompare the w
avelengths of sound from
the two sources.
43. What kind of m
otion should you impart to
a stretched coiled spring to produce a trans-verse w
ave? A longitudinal w
ave?
44. Would it be correct to say that the D
oppler effect is the apparent change in the speed of a w
ave due to the motion of the source?
(Why is this question a test of reading
comprehension as w
ell as a test of physics know
ledge?)
45. In the Doppler effect, does frequency
change? Does w
avelength change? Does
wave speed change?
46. Can the D
oppler effect be observed with
longitudinal waves, w
ith transverse waves,
or with both?
47. A railroad locom
otive is at rest with its
whistle shrieking, and then it starts m
oving tow
ard you.
a. Does the frequency that you hear increase,
decrease, or stay the same?
b. D
oes the wavelength that reaches your ear
increase, decrease, or stay the same?
c. H
ow about the speed of sound in the air
between you and the locom
otive?
48. When a driver blow
s his horn while ap-
proaching a stationary listener, the listener hears an increase in the frequency of the horn. W
ould the listener hear an increase in the frequency of the horn if she w
ere also in a car traveling at the sam
e speed in the same
direction as the first driver? Explain.
49. Astronom
ers find that light coming from
point A
at the edge of the sun has a slightly higher frequency than light from
point B at
the opposite side. What do these m
easure-m
ents tell us about the sun’s motion?
CH
APTER 25
VIBRATION
S AN
D W
AVES 511
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38. The speeds are the same, so
the w
ave with the shorter
wavelength has the greater
frequency—violet.
39. A w
ave takes a time equal to
one period to travel a distance of one w
avelength. D
istance 5 speed 3
time 5
(w
avelength 3 frequency) 3
period 5
(wavelength 3
1/period) 3
period 5
wavelength
40. 2 Hz; 20 m
/s
41. The waves travel at the sam
e speed in all directions.
42. Source A has half w
avelength
of Source B sound.
43. Transverse wave shakes back-
and-forth perpendicular to
coiled spring. Longitudinal w
ave shakes back-and-forth
along length.
44. No, it is the change in the
observed frequency of a w
ave due to motion of the
observer with respect to the
source. There is no change in w
ave speed when the
source moves.
45. Frequency and wavelength
change; not w
ave speed.
46. Both 47. a. Frequency increases.
b. W
avelength decreases.
c. N
o change in speed.
48. No. There is no relative
motion betw
een source and
listener.
49. The sun is spinning, since point A
must be m
oving
toward the observer and
point B m
ust be moving aw
ay.
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(continued)
512
50. Does a boat m
oving through the water
always produce a bow
wave? D
efend your answ
er.
51. Whenever you w
atch a high-flying aircraft overhead, it seem
s that its sound comes
from behind the craft rather than from
w
here you see it. Why is this?
52. How
does the angle of the V shape of a
bow w
ave depend on the speed of the w
ave source?
53. Why is it that a subsonic aircraft, no
matter how
loud it may be, cannot
produce a sonic boom?
54. True or false: A sonic boom
occurs only w
hen an aircraft is breaking through the sound barrier. D
efend your answer.
55. Consider an earthquake caused by a single
disturbance, which sends out both trans-
verse and longitudinal waves that travel w
ith distinctly different speeds in the ground. H
ow can earth scientists in different loca-
tions determine the earthquake origin?
Thin
k a
nd So
lve •
••
••
•
56. The period of a sim
ple pendulum is given
by Lg
�T
�2)
, where g
is the acceleration of gravity and L is the length of the pendulum
. In a lab, you w
ant to double the period of a certain pendulum
. Your friend says you’ll have to m
ake the pendulum tw
ice as long. D
o you agree with your friend?
57. Maria show
s her friends a simple
31-cm-long pendulum
. Her teacher, look-
ing on, asks if she can predict the period of the pendulum
before she demonstrates it.
What’s your prediction?
58. The Foucault pendulum
in the rotunda of the G
riffith Observatory in Los A
ngeles has a 110-kg brass ball at the end of a 12.2-m
- long cable. W
hat is the period of this pen-dulum
?
59. You are looking through your grandparents’ w
indow and notice a hum
mingbird feeder
hanging by a rope. You can’t see the top of the rope, but you notice that in a gentle breeze the feeder m
oves back and forth with
a period of 4.0 seconds. You make a calcula-
tion and announce to your grandparents that the rope is 4 m
long. Your grandparents go outside and m
easure the rope. Should they be im
pressed with you?
60. For your science fair project you decide to m
ake a simple pendulum
for a grandfather clock, such that the period of the pendulum
is 2.00 seconds. Show
that the length of your pendulum
should be just slightly less than the length of a m
eterstick. (Use g =
9.8 m/s
2
here.)
5
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51
2
50. If the speed of the boat exceeds w
ave speed, yes. If slow
er, no.
51. It takes negligible time for
light to get to you from
the airplane, but it takes a noticeable tim
e for sound to
reach you. When sound
from
a fast-moving source
reaches you, the source is farther along.
52. The narrower the angle, the
faster the source
53. At subsonic speeds, there
is no overlapping of waves
to produce high-pressure regions; w
here there is no
shock wave, there is no
sonic boom
.
54. False; a sonic boom occurs
continuously for supersonic source.
55. From difference in arrival
times, each scientist calculates
distance, and draws a circle
of possible sources. Origin
of quake is w
here 3 such
circles drawn by different
scientists overlap.
Thin
k a
nd So
lve
56. No, don’t agree. T ~√
L so
L ~ T2. To double T, L m
ust be 4 tim
es as long.
57. T 5 2
p √
L/g 5
2p√
(0.31 m)/(10 m
/s 2) 5 1.1 s
58. T 5 2
p √
L/g 5
2p√
(12.2 m)/(10 m
/s 2) 5 6.9 s
(or 7.0 s using g 5 9.8 m
/s 2)
59. Yes. From
T 5 2
p √
L/g, L 5
gT2/4
p2 5
[(10 m
/s 2) 3 (4.0 s) 2]/4
p2 5
4.0 m
60. From T 5
2p
√L/g,
L 5 gT
2/4p
2 5 [(9.8 m
/s 2) 3
(2.00 s) 2]/4p
2 5 0.99 m
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APTER 25
VIBRATION
S AN
D W
AVES 513
61. Melanie is new
to the nursing program.
With a patient she counts 84 heartbeats in
one minute. She calculates that the period
and frequency of the heartbeats are 0.71 s and 1.4 H
z respectively. Is she correct?
62. A design engineer figures that a proposed
new skyscraper w
ill swing to and fro in
strong winds at a frequency of 0.15 H
z. A
new assistant asks how
much tim
e a person in the skyscraper w
ill experience during each com
plete swing. W
hat’s your answer?
63. In lab you strike a tuning fork that has a frequency of 340 H
z. For a speed of sound of 340 m
/s, how does the w
avelength of the resulting sound w
ave compare w
ith the length of a m
eter stick?
64. If a wave vibrates back and forth three tim
es each second, and its w
avelength is 2 meters,
what is its frequency? Its period? Its speed?
65. While w
atching ocean waves at the dock
of the bay, Otis notices that 10 w
aves pass beneath him
in 30 seconds. He also notices
that the crests of successive waves exactly
coincide with the posts that are 5 m
eters apart. W
hat are the period, frequency, wave-
length, and speed of the ocean waves?
66. The crests on a long surface w
ater wave are
20 m apart, and in 1 m
inute 10 crests pass by. W
hat is the speed of this wave?
67. Radio w
aves are electromagnetic w
aves that travel at the speed of light, 300,000 kilo-m
eters per second. What is the w
avelength of FM
radio waves received at 100 m
ega-hertz on your radio dial?
68. The w
avelength of red light is about 700 nanom
eters, or 7 ! 10
–7 m. T
he fre-quency of the red light reflected from
a m
etal surface and the frequency of the vibrating electron that produces it are the sam
e. What is this frequency?
69. The half-angle of the shock-w
ave cone generated by a supersonic aircraft is 45°. W
hat is the speed of the plane relative to the speed of sound?
Activ
ity•
••
••
•
70. Tie a rubber tube, a spring, or a rope to a
fixed support and produce standing waves,
as Figure 25.14 suggests. How
many nodes
can you produce? How
can you change the num
ber of nodes?
CH
APTER 25
VIBRATION
S AN
D W
AVES 513
More Problem
-Solving PracticeA
ppendix F
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513
61. She is correct. f = (84 beats)/(60 s) 5
1.4 Hz.; T 5
1/f 5
1/(1.4 s 21) 5
0.71 s
62. T 5 1/f 5
1/(0.15 s 21) 5
6.7 s
63. The same; from
v 5 lf,
l 5 v/f 5
(340 m/s)/(340 H
z) 5
1.0 m.
64. f 5 3 H
z; T 5 1/3 s; v 5
lf 5
(2 m)(3/s) 5
6 m/s
65. T 5 (30 s)/10 5
3 s; f 5
1/3 Hz; l 5
5 m; v 5
lf 5
(5 m)(1/3 H
z) 5 1.67 m
/s
66. v 5 lf 5
(20 m)(10/m
in) 5
200 m/m
in, or 3.3 m/s
67. l 5 v/f 5
(300,000 km/s) 4
(100,000,000/s) 5
0.003 km,
or 3 m
68. f 5 v/l 5
(3 3 10
8 m/s) 4
(7 3
102
7 m) 5
4.3 3 10
14 Hz,
an extraordinarily high
frequency by ordinary standards
69. The plane’s speed is 1.41 tim
es the speed of sound. In
right triangle, the distance A
B is √2 or 1.41 tim
es the distance A
C.
Activ
ity 70. Check students’ w
ork. The frequency of the incident w
ave determines the num
ber of nodes produced.
Te
ac
hin
g R
es
ou
rc
es
• Computer Test Bank
• Chapter and Unit Tests
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