Chap 19 - Vibrations &
Waves
Good Vibrations
-
-
vibration
is
a
periodic wiggle in
time.
A periodic wiggle in
both space and
time is a wave. A
wave extends from
one
place
to
another.
Examples:
–light,
which
is
an
electromagnetic wave that
needs no medium.
–sound,
which
is
a
mechanical wave that
needs a medium.
•Vibration
–Wiggle in time
•Wave
Wiggle in space and
time
Vibrations
Pendulum
of
a
which a ball falls to the
ground).
•The time of one to-and-fro
swing is called the period.
•The longer the length of a
pendulum, the longer the
period (just as the higher
you drop a ball from, the
longer it takes to reach the
ground).
*A
1-meter-long
pendulum has a bob with
a mass of 1 kg. Suppose
that the bob is now
replaced with a different
bob of mass 2 kg, how
will the period of the
pendulum change?
Answer: It will remain the
same because the period
of a pendulum depends
only on the length of the
pendulum, not on the
mass. So changing the
mass will not change the
period of the pendulum.
–depends only on the
length of the pendulum.
A
1-meter-long
pendulum has a bob with
a mass of 1 kg. Suppose
that the bob is now tied
to a different string so
that the length of the
pendulum is now 2 m.
How will the period of
the pendulum change?
–does not depend upon
the mass (just as mass
does not affect the rate at
Answer: It will increase
because the period of a
pendulum increases with
•If we suspend a stone at
the end of a piece of
string, we have a simple
pendulum.
•The pendulum swings to
and fro at a rate that
the
length
pendulum.
of
the
Wave Description
•A wave is pictorially
represented by a sine
curve.
•A sine curve is obtained
when you trace out the
path
of
a
vibrating
pendulum over time.
–Put some sand in the
pendulum and let it swing.
–The sand drops through
a hole in the pendulum
onto a sheet of paper.
–As the pendulum swings
back and forth, pull the
sheet of paper on which
the sand falls.
–The sand makes a sine
curve on the paper.
- When a bob vibrates up
and down, a marking pen
traces out a sine curve on
the paper that moves
horizontally at constant
speed.
•Vibration and wave
characteristics
–Crests
•high points of the wave
–Troughs
•low points of the wave
•Vibration
and
characteristics
wave
–Amplitude
•distance
from
the
midpoint to the crest or to
the trough
–Wavelength
•distance from the top of
one crest to the top of the
next crest, or distance
between
successive
identical parts of the wave
•How
frequently
a
vibration occurs is called
the frequency.
–The unit for frequency is
Hertz (Hz), after Heinrich
Hertz
–A frequency of 1 Hz is a
vibration that occurs once
each second.
–Mechanical objects (e.g.,
pendulums)
have
frequencies of a few Hz.
–Sound has a frequency
of a few 100 or 1000 Hz.
–Radio
waves
have
frequencies of a few
million Hz (MHz).
–Cell phones operate at
few billon Hz (GHz).
•Frequency
–Specifies the number of
to and fro vibrations in a
given time
–Number
of
waves
passing any point per
second
Example:
-2 vibrations occurring in 1
second is a frequency of 2
vibrations per second.
•Drop a stone in a quiet
pond and the resulting
ripples carry no water
across the pond.
•Period
•Waves
travel
across
grass on a windy day.
–Time to complete one
vibration
Period = 1/frequency
•Molecules
in
air
propagate a disturbance
through air.
or, vice versa
Wave speed
Frequency = 1/period
–Describes how fast a
disturbance
moves
through a medium
•Example:
Pendulum
makes 2 vibrations in 1
second. Frequency is 2
Hz. Period of vibration is
1/2 second.
*A sound wave has a
frequency of 500 Hz.
What is the period of
vibration of the air
molecules due to the
sound wave?
–Related to frequency and
wavelength of a wave
Wave speed = frequency
x wavelength
•Example:
–A wave with wavelength
1 meter and frequency of
1 Hz has a speed of 1 m/s.
Answer: 0.002 seconds
because
Period = 1/frequency
Period = 1/500 Hz = 0.002
*If the frequency of a
particular wave is 20 Hz,
its period is
Answer: 1/20 s
Note when ƒ = 20 Hz, T =
1/ƒ = 1/(20 Hz) = 1/20
second.
Wave Motion
–Waves transport energy
and not matter.
Example:
*A wave with wavelength
10 meters and time
between crests of 0.5
second is traveling in
water. What is the wave
speed?
Answer: 20 m/s. Because
Frequency = 1/period
Frequency = 1/0.5 = 2 Hz
Also: Wave speed =
frequency x wavelength
So: Wave speed = 2 Hz x
10 m = 20 m/s
Transverse
Longitudinal Waves
&
•Two common types of
waves that differ because
of the direction in which
the
medium
vibrates
compared
with
the
direction of travel:
– longitudinal wave
– transverse wave
identical parts
waveform.
of
the
*The vibrations along a
transverse wave move in
a direction
Answer: perpendicular to
the wave because The
vibrations in a longitudinal
wave, in contrast, are
along (or parallel to) the
direction of wave travel.
Longitudinal wave
Transverse Waves
–Medium
vibrates
perpendicularly
to
direction of energy transfer
–Side-to-side movement
Example:
•Vibrations in
strings
of
instruments
stretched
musical
•Radio waves
•Light waves
•S-waves that travel in the
ground (providing geologic
information)
*The distance between
adjacent peaks in the
direction of travel for a
transverse wave is its
Answer:
wavelength
because the wavelength of
a transverse wave is also
the
distance
between
adjacent
troughs,
or
between any adjacent
–Medium vibrates parallel
to direction of energy
transfer
–Backward and forward
movement consists of
•compressions
compressed)
(wave
•rarefactions
(stretched
region
between
compressions)
Example: sound waves in
solid,
liquid,
gas or
P-waves that travel in the
ground (providing geologic
information)
*The wavelength of a
longitudinal wave is the
distance between
Answer:
successive
compressions
and
successive rarefactions
Wave interference
Wave interference occurs
when two or more waves
interact with each other
because they occur in the
same place at the same
time.
•Superposition principle:
The displacement due the
interference of waves is
determined by adding the
disturbances produced by
each wave.
Constructive
interference is when the
crest of one wave overlaps
the crest of another, their
individual
effects
add
together to produce a
wave
of
increased
amplitude.
Destructive interference:
When the crest of one
wave overlaps the trough
of another, the high part of
one wave simply fills in the
low part of another. So,
their individual effects are
reduced (or even canceled
out).
Examples
of
interference:
wave
–We see the interference
pattern made when two
vibrating objects touch the
surface of water.
–The regions where a
crest of one wave overlaps
the trough of another to
produce regions of zero
amplitude.
•Antinodes
are
the
regions
of
maximum
displacement
and
maximum energy.
–Decrease
in
light
frequency
when
light
source moves away from
you
•Antinodes and nodes
occur equally apart from
each other.
–Star's spin speed can be
determined
by
shift
measurement
•Tie a tube to a firm
support. Shake the tube
from side to side with your
hand.
•Doppler effect of light
–At points along these
regions, the waves arrive
out of step, i.e., out of
phase with each other.
•If you shake the tube with
the right frequency, you
will set up a standing
wave.
Standing Wave
•If you shake the tube with
twice the frequency, a
standing wave of half the
wavelength, having two
loops results.
•If we tie a rope to a wall
and shake the free end up
and down, we produce a
train of waves in the rope.
•The wall is too rigid to
shake, so the waves are
reflected back along the
rope.
•By shaking the rope just
right, we can cause the
incident
and
reflected
waves to form a standing
wave.
•Nodes are the regions of
minimal
or
zero
displacement, with minimal
or zero energy.
•If you shake the tube with
three times the frequency,
a
standing
wave of
one-third the wavelength,
having three loops results.
–Blue shift
•increase
in
light
frequency toward the blue
end of the spectrum
–Red shift
•decrease
in
light
frequency toward the red
end of the spectrum
Example:
Rapidly
spinning star shows a red
shift on the side facing
away from us and a blue
shift on the side facing us.
*The Doppler
occurs on
effects
Answer: sound and light
because the Doppler effect
occurs for both sound and
light.
Astronomers
measure the spin rates of
stars by the Doppler effect
Ex:
Bow Waves
-Waves in a guitar string
•Wave barrier
-Sound waves in a trumpet
–Waves
superimpose
directly on top of one
another producing a "wall".
•The Doppler effect also
applies to light.
–Increase
in
light
frequency
when
light
source approaches you
–Example: bug swimming
as fast as the wave it
makes
•Supersonic
•Sonic boom
–Aircraft flying faster than
the speed of sound.
–Sharp cracking sound
generated by a supersonic
aircraft
•Bow wave
–V-shape
form
of
overlapping waves when
object travels faster than
wave speed.
–Intensity
due
to
overpressure and under
pressure of atmospheric
pressure between
–An increase in speed will
produce a narrower
the two cones of the shock
waves
V-shape
waves.
–Produced before it broke
the sound
of
overlapping
barrier
Example:
•Shock wave
–Pattern of overlapping
spheres that form a cone
from
objects traveling
faster than the speed of
sound.
-Consists of two cones.
•a high-pressure cone
generated at the bow of
the supersonic aircraft
•a low-pressure cone that
follows toward (or at) the
tail of the aircraft
–It is not required that a
moving
source be noisy.
•supersonic bullet
•crack of circus whip
Which of these
affected by mass?
Answer: None of the
above
The pendulum with the
greatest frequency is
one with the
Answer:
wavelength
shortest
The source
waves is
of
Both
a transverse
wave
and
a
longitudinal
wave
have
A. wavelength
What is a wiggle in
time called? What do
you call a wiggle in
space and time?
B. frequency
What is meant by the
period of a pendulum?
Answer:
the
time
interval of a to-and-fro
swing
How does a sine curve
describe a wave?
Answer: A sine curve is
a
pictorial
representation
of
a
wave
all
Answer: something that
vibrates
QUIZLET QUESTIONS:
Answer: a vibration, a
wave
is
C. speed
D. amplitude
Answer : E. all of the
above
The amplitude of a
wave is 1 meter. The
crest-to-trough
distance of the wave is
Answer: 2m
A fishing-boat captain
returns to port saying,
"It's rough out there
with waves that are 4
meters high." He is
probably talking of
waves of amplitude
Answer: 2m
The frequency of a
simple pendulum does
NOT depend on
Answer: its mass
A
60-vibration-per-secon
d wave travels 30
meters in 1 second. Its
frequency is
Answer: 60 Hz and it
travels 30 m/s
A weight suspended
from a spring bobs up
and down over a
distance of 1 meter in
two
seconds.
Its
frequency is
Answer: 0.5 Hz
The compressions and
rarefactions
in
a
longitudinal
wave
travel in
Answer:
direction
the
same
Which of these is a
longitudinal wave?
Answer: sound
The vibrations of a
transverse wave move
Answer: at right angles
to the direction of wave
travel
Does the medium in
which a wave travels
move with the wave?
Answer: No
The wavelength of a
transverse wave is the
distance
between
successive crests (or
troughs). What is the
wavelength
of
a
longitudinal wave?
with
waves?
Answer: the wavelength
is the distance between
successive
maximum
compressions
(or
rarefactions)
Answer: an approaching
source has increased
light frequency - a blue
shift. A receding source
has
a
decreasing
frequency - a red shift
What is meant by the
superposition
principle?
Answer: when two or
more waves occupy the
same
space,
wave
displacements add at
every point
What is a node? What
is an antinode?
Answer: in a standing
wave, a node always
has zero displacement
and an antinode always
has
maximum
displacement
In the Doppler effect,
does
frequency
change? Does wave
speed change?
Answer: only frequency
changes
Can the Doppler effect
be
observed
with
longitudinal waves or
transverse
Answer: both
What is meant by a
blue shift and a red
shift for light?
Wave
interference
occurs for
A. light waves
B. water waves
C. sound waves
Answer: D. all of the
above
E. none of the above
A standing wave is
likely produced when
Answer: a wave reflects
upon itself
A
Doppler
effect
occurs when a source
of sound waves
A. towards you
B. away from you
Answer:
these
C. either of
D. neither of these
A red shift for light
indicates that the light
source is moving
Answer: away from you
If you quickly run
toward the orchestra
at a concert, the
frequency
of
the
sound you hear will be
Answer: increased
A shock wave is
produced
when
a
wave source moves
Answer: faster than the
wave it produces
An aircraft that flies
faster than the speed
of sound is said to be
Answer: supersonic
As
a
supersonic
aircraft increases in
speed, the angle of its
V-shaped shock wave
becomes
Answer: narrower
A jet traveling at 1500
km/h
passes
overhead. The sonic
boom produced is
heard by
Answer: a listener on
the ground
Chap 20 - Sound
Nature of Sound
-Sound is a form of energy
that exists whether or not it
is heard
Origin
•Most sounds are waves
produced by the vibrations
of matter.
–For example:
•In a piano, a violin, and a
guitar, the sound is
produced by the vibrating
strings;
•in a saxophone, by a
vibrating reed;
•in a flute, by a fluttering
column of air at the
mouthpiece;
•in your voice due to the
vibration of your vocal
chords.
•The original vibration
stimulates the vibration of
something larger or more
massive, such as
–the sounding board of a
stringed instrument,
–the air column within a
reed or wind instrument, or
–the air in the throat and
mouth of a singer.
•This vibrating material
then sends a disturbance
through the surrounding
medium, usually air, in the
form of longitudinal sound
waves.
•Under
ordinary
conditions, the frequencies
of the vibrating source and
sound
same.
waves
are
the
•The subjective impression
about the frequency of
sound is called pitch.
•The ear of a young
person can normally hear
pitches corresponding to
the range of frequencies
between about 20 and
20,000 Hertz.
•As we grow older, the
limits of this human
hearing
range
shrink,
especially
at
the
high-frequency end.
•Sound
waves
with
frequencies below 20 hertz
are infrasonic (frequency
too
low
for
human
hearing).
•Sound
waves
with
frequencies above 20,000
hertz are called ultrasonic
(frequency too high for
human hearing).
•We
cannot
hear
infrasonic and ultrasonic
sound.
Sound In Air
•Sound waves
–are vibrations made of
compressions
and
rarefactions.
–are longitudinal waves.
–require a medium.
–travel through solids,
liquids, and gases.
•Wavelength of sound
–Distance
between
successive compressions
or rarefactions
•How sound is heard from
a radio loudspeaker
–Radio loudspeaker is a
paper cone that vibrates.
–Air molecules next to the
loudspeaker
set
into
vibration.
–Produces compressions
and rarefactions traveling
in air.
–Sound waves reach your
ears,
setting
your
eardrums into vibration.
–Sound is heard.
Media
Sound
That
Transmit
•Any elastic substance —
solid, liquid, gas, or
plasma — can transmit
sound.
•In elastic liquids and
solids, the atoms are
relatively close together,
respond quickly to one
another's motions, and
transmit energy with little
loss.
•Sound travels about 4
times faster in water than
in air and about 15 times
faster in steel than in air.
Speed of Sound In Air
•Speed of sound
–Depends
conditions,
humidity
on
wind
temperature,
•Speed in dry air at 0ºC is
about 330 m/s.
•In water vapor slightly
faster.
•In warm air faster than
cold air.
–Each degree rise in
temperature above 0ºC,
speed of sound in air
increases by 0.6 m/s
–Speed in water about 4
times speed in air.
–Speed in steel about 15
times its speed in air.
*You watch a person
chopping wood and note
that after the last chop
you hear it 1 second
later. How far away is the
chopper?
Answer: 330 m
*You hear thunder 2
seconds after you see a
lightning flash. How far
away is the lightning?
*Reverberations are best
heard when you sing in a
room with
Answer:
hard-surfaced
walls because rigid walls
better
reflect
sound
energy.
Fabric
is
absorbent,
and
open
windows let sound energy
escape from the room.
A
Situation
about
Reflection of Sound
•Consider
a
person
attending a concert that is
being broadcast over the
radio. The person sits
about 45 m from the stage
and listens to the radio
broadcast with a transistor
radio over one ear and a
nonbroadcast sound signal
with the other ear. Further
suppose that the radio
signal must travel all the
way around the world
before reaching the ear.
*Which signal will be
heard first?
Answer: radio signal &
nonbroadcast
sound
signal because a radio
signal travels at the speed
of light, 3 x 108 m/s.
–Process in which sound
encountering a surface is
returned
Time to travel 45 m at 340
m/s ≈ 0.13 s. Time to
travel 4 x 107 m (Earth's
circumference) at 3 x 108
m/s ≈ 0.13 s. Therefore, if
you sit farther back at the
concert, the radio signal
would reach you first!
–Often called an echo
Reflection of Sound
–Multiple
reflections—called
reverberations
•Acoustics
Answer: 660 m/s
Reflection of Sound
•Reflection
–Study of sound
–Example: A concert hall
aims
for
a
balance
between reverberation and
absorption. Some have
reflectors to direct sound
(which
also
reflect
light—so what you see is
what you hear).
Refraction of Sound
–Bending
of
waves—caused
by
changes in speed affected
by
•wind variations.
•temperature variations.
*When air near the
ground on a warm day is
warmed more than the
air above, sound tends
to bend
Answer: upward
*In the evening, when air
directly above a pond is
cooler than air above,
sound across a pond
tends to bend
Answer: downward
Reflection
and
Refraction of Sound
•Multiple reflection and
refractions of ultrasonic
waves
–Device
sends
high-frequency
sounds
into the body and reflects
the waves more strongly
from the exterior of the
organs,
producing
an
image of the organs.
–Used instead of X-rays
by physicians to see the
interior of the body.
-•Dolphins emit ultrasonic
waves to enable them to
locate objects
environment.
in
their
Forced Vibration
–Superposition of waves
that may either reinforce
or cancel each other
–Setting up of vibrations in
an object by a vibrating
force
–Example: factory floor
vibration
caused
by
running
of
heavy
machinery
Natural Frequency
–Own unique frequency
(or set of frequencies)
*Interference
is
property of both
–Dependent on
Answer: sound and light
•elasticity
Because iInterestingly, the
presence of interference
tells a physicist whether
something is wavelike. All
types of waves can
interfere.
shape of object
Resonance
•A phenomenon in which
the frequency of forced
vibrations on an object
matches
the
object's
natural frequency
–Examples:
•Swinging in rhythm with
the natural frequency of a
swing
•Tuning a radio station to
the "carrier frequency" of
the radio station
•Troops
marching
in
rhythm with the natural
frequency of a bridge (a
no-no!)
•Dramatic
example
of
wind-generated resonance
•Two
patterns
interference
•Application
interference
of
sound
–Destructive
sound
interference
in
noisy
devices
such
as
jackhammers that are
equipped
with
microphones to produce
mirror-image
wave
patterns fed to operator's
earphone, canceling the
jackhammer's sound
a
of
–Constructive interference
•increased
amplitude
when the crest of one
wave overlaps the crest of
another wave
–Destructive interference
•reduced amplitude when
the crest of one wave
overlaps the trough of
another wave
•Application
of
sound
interference (continued)
–Sound interference in
stereo speakers out of
phase
sending
a
monoaural signal (one
speaker
sending
compressions of sound
and
other
sending
rarefactions)
–As speakers are brought
closer to each other,
sound is diminished.
Beats
•Periodic variations in the
loudness of sound due to
interference
Interference
•Occur with any kind of
wave
–Property of all waves and
wave motion
•Provide a comparison of
frequencies
B. ultrasonic sound
C. both of these
•Applications
–Piano tuning by listening
to the disappearance of
beats from a tuning fork
and a piano key
–Tuning instruments in an
orchestra by listening for
beats
between
instruments and piano
tone
QUIZLET QUESTIONS:
How
does
sound
relate to energy?
Answer: sound waves
transport energy from
one place to another
What is the average
range of a young
person's hearing?
Answer: 20 to 20,000 Hz
Distinguish
infrasonic
ultrasonic
waves
between
and
sound
Answer: infrasonic is too
low in frequency (below
20 Hz) for humans to
hear, whereas ultrasonic
is too high (above
20,000 Hz)
A
high-frequency
sound
source
produces a high
Answer: D. neither of
these
Answer: air temperature
Sound travels fastest
in
Sound travels in air if
the air temperature is
Answer: Steel
Answer: warm
Sound waves cannot
travel in
The wavelengths of
sound
that
carry
farther in air are
relatively
Answer: vacuum
The speed of sound
depends on
Answer: the medium in
which it travels
In air and in water the
same sound travels
with different
Answer: speeds
In choosing between
sound
waves
and
radio waves, which
has
the
greater
speed?
Answer: radio wave
Compression
and
rarefactions
are
characteristics of
Answer:
waves
longitudinal
Answer: long
To
estimate
the
distance in kilometers
of a flash of lightning,
count the number of
seconds
between
seeing the flash and
hearing
the
accompanying
thunder, then divide by
Answer: 3
When sound travels
faster near the ground
than above, bending
of sound tends to be
Answer: upward
Refraction of sound
can occur in
Which
does
NOT
belong to the same
family?
A. air
Answer: radio waves
Answer:
these
Answer: pitch
The kind of waves that
travel fastest through
a long metal rod have
Human hearing is best
in
Answer: all have the
same speed
A. infrasonic sound
The speed of a sound
wave in air depends
on
B. water
C.
both
of
D. neither of these
The explanation for
refraction
must
involve a change in
Answer: speed
In
perceiving
its
environment,
a
dolphin makes use of
A. ultrasound
Wave
interference
occurs in
A. transverse waves
B. longitudinal waves
B. echoes
C. the Doppler effect
Answer: D. all of the
above
E. none of the above
Answer: C. both of these
D. neither of these
When sound waves
superimpose they can
interfere
The natural frequency
of an object depends
on its
A. destructively
A. elasticity
Answer:
these
B. shape
B. constructively
C. either of
D. neither of these
C. size
Answer: D. all of the
above
The phenomenon of
beats is a result of
sound
E. none of the above
Answer: interference
The bell with the
highest
natural
frequency is relatively
The beat frequency
produced
when
a
240-hertz tuning fork
and a 246-hertz tuning
fork
are
sounded
together is
Answer: small
The
least
energy
required to produce
forced vibration in an
object occurs
Answer: at
frequency
its
natural
Reports are that singer
Caruso was able to
shatter
a
crystal
chandelier with his
voice, which illustrates
Answer: resonance
Answer: 6 Hz
Why will a struck
tuning
fork sound
louder when it is held
against a table?
Answer: the table is
forced to vibrate, and its
large surface vibrates
more air than the tuning
fork