19 & 20
VIBRATIONS & WAVES
Sound in a Vacuum
• Sound is the
propagation of
vibrations through a
material medium—a
solid, liquid, or gas.
• If there is no medium to
vibrate, then no sound is
possible.
• Sound cannot travel in a
vacuum.
Vibrations and Waves
“Wiggles in Time”
• Oar in Water
• Wings of a Bee
• Electrons in an Light
Bulb
“Wiggles in Space”
 Water Waves
 Sound Waves
 Light Waves
Vibrations and Waves
• Waves transmit energy and information.
• Sound and Light are both waves.
If you drop two balls of
different mass they
accelerate at g.
• Let them slide without friction down
the same incline, and they slide
together at the same fraction of g.
• Tie them to strings of the same length
so they are pendulums, and they swing
to and fro in unison.
• In all cases, the motions are
independent of mass
Pendulums & Galileo
• The period does not depend on the amount of
mass.
• The period does depend on the length of the
pendulum.
T  2 l g
Period
Time required for a full
oscillation (one round
trip) is called the period
of oscillation.
Pendulum that is about
one meter long has a
period of two seconds
per oscillation.
Note: Measure the period of
a pendulum in lab.
19-Mar-16
Physics 1 (Garcia) SJSU
Frequency
Frequency is the inverse of the period,
(Frequency) =
1
(Period)
For example, for a period of 2 seconds per
oscillation, the frequency is ½ oscillation per
second or ½ Hertz.
1 Hertz = 1 oscillation per second
19-Mar-16
Physics 1 (Garcia) SJSU
Amplitude
The distance from
the rest position
is the amplitude
of oscillation.
Amplitude
A sine curve is a pictorial
representation of a wave.
Like a water wave, a sine
wave has crests, troughs
and amplitude
• Amplitude
• the distance from the midpoint to the
crest (or trough) of the wave.
• So the amplitude equals the maximum
displacement from equilibrium.
Waves
Concept of vibrations extends into the
phenomenon of wave motion.
String
Sound
Water waves
Radio
19-Mar-16
Physics 1 (Garcia) SJSU
Light waves
The to-and-fro vibratory motion (often called oscillatory motion) of a
swinging pendulum in a small arc is called simple harmonic motion.
WAVE DESCRIPTION
Wave Motion
• medium - the stuff that carries the wave
Waves
Medium
water waves
water
waves on a rope
rope
stadium waves
people
sound
air
light
space (vacuum)
water wave
a stone dropped into a quiet
pond has waves travel outward
in expanding circles
• barring obstacles the surface of the water will
have been disturbed, but the water itself will
have gone nowhere.
• A leaf on the surface will bob up and down as the
waves pass, but will end up where it started.
Wave Motion
• When energy is transferred by a wave from a
vibrating source to a distant receiver, there is
no transfer of matter between the two points
• The energy transferred from a vibrating source
to a receiver is carried by a disturbance in a
medium, not by matter moving from one
place to another within the medium
Wave Speed...
• the speed with which waves pass by a
particular point
• e.g. the speed of a surfer
• It depends only on the type of medium.
• Wave Speed = Frequency  Wavelength
Waves on a Rope
Table in Notes – Appearance, Node, Antinodes, Wavelength, Frequency
The frequency of the vibrating source
and the frequency of the wave it
produces are the same.
Electrons in the transmitting antenna
vibrate 940,000 times each second and
produce 940-kHz radio waves.
• A station at 101.7 MHz
FM -a frequency of
101,700,000 hertz.
• The source of all
waves is something
that vibrates.
Wave Motion
Wave Speed...
• the speed with which waves pass by a
particular point
• e.g. the speed of a surfer
• It depends only on the type of medium.
• Wave Speed = Frequency  Wavelength
Waves on a Rope
Table in Notes – Appearance, Node, Antinodes, Wavelength, Frequency
Wave Speed Problem
The water waves below are traveling with a speed of 2 m/s
and splashing periodically against the Wilbert's perch. Each
adjacent crest is 4 meters apart and splashes Wilbert’s feet
upon reaching his perch. How much time passes between
each successive drenching?
Transverse Waves
For transverse waves the wave’s amplitude is
perpendicular to the wave’s motion.
Amplitude
Wave Motion
Amplitude
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Wavelength
Wavelength is distance between crests or
between troughs of waves.
Longitudinal
Transverse
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Physics 1 (Garcia) SJSU
Transverse Waves
• side to side vibration in a direction
perpendicular to the wave's motion
• Examples:
– water waves
– waves on a rope
– string musical instruments
Transverse Waves
Longitudinal Waves
• back and forth vibration in a
direction parallel to the wave's
motion
• Examples:
– slinky waves
– sounds waves (vortex box)
Longitudinal Waves
Doing “The Wave”
Synchronized standing and sitting
by a stadium’s crowd is an
example of a transverse wave.
Video analysis indicates that it takes only a few dozen
fans leaping to their feet with their arms up to trigger
a wave. Once started, it usually rolls in a clockwise
direction at a rate of about 40 feet per second, or
about 20 seats per second. At any given time, the
wave pulse is about 15 seats wide.
19-Mar-16
Physics 1 (Garcia) SJSU
• Waves generated by an
earthquake. P waves are
longitudinal and travel through
both molten and solid
materials.
• S waves are transverse and
travel only through solid
materials.
• Reflections and refractions of
the waves provide information
about the Earth’s interior.
Longitudinal Waves
For longitudinal waves, amplitude and wave
motion are parallel.
Wave Motion
Amplitude
Amplitude
1 (Garcia)
SJSU
A19-Mar-16
crowd can do a longitudinal wave Physics
by moving
side-to-side
instead of up-and-down
Transverse vs Longitudinal
Demonstration
Wave Speed
The speed at which waves travel is called the
wave speed.
Speed of sound = 330 m/s = 725 mi/hr
Speed of light = 300,000,000 m/s
Water waves at the beach move a few miles per hour
19-Mar-16
Physics 1 (Garcia) SJSU
Tsunami Waves
Tsunamis are ordinary water waves, just like waves in your
bathtub, but because they are typically generated by deep sea
earthquakes they carry huge amounts of energy and
momentum, traveling at almost 500 mph while in the deep
ocean.
The tsunami of 26 December 26th 2004
was produced by an earthquake whose
epicenter was located off the coast of
Indonesia in the Indian Ocean. The death
toll is estimated at over a quarter of a
million persons.
Animation by Vasily V. Titov
19-Mar-16
Physics 1 (Garcia) SJSU
Wave Relations
Wave speed, wavelength & frequency related.
(Wave speed) = (Wavelength) x (Frequency)
(Wave speed)
(Wave length) =
(Frequency)
(Wave speed)
(Frequency) =
(Wavelength)
19-Mar-16
Physics 1 (Garcia) SJSU
Ruben’s Flame Demo
If a water wave oscillated up and down three
times each second and the distance
between wave crest is 2 m, what is its
frequency?
Answer: 3 Hz
What is its period?
Answer: 1/3 second
What is its wavelength?
Answer: 2 m
What is its wave speed?
Answer: 6 m/s
*
Example Test Question:
If you double the frequency of a vibrating
object, what happens to the period?
a) the period doubles
b) the period stays the same
c) the period is cut in half
d) not enough information is given
to answer this question.
Example Question
*
Changing which of the following affects
the period of a pendulum?
– a) mass
– b) amplitude
– c) length
– d) angle
What is the frequency in vibrations per
second of a 60-Hz wave?
Answer: 60 cycles per second
What is its period?
Answer: 1/60 second
Demo: Hearing Sound
Range of human hearing is roughly 20 Hertz to
20,000 Hertz.
Wave speed for sound is 330 m/s
Wavelength of 20 Hertz is 16 m (about 50 ft)
Wavelength of 20,000 Hz is 1.6 cm (½ inch)
19-Mar-16
Physics 1 (Garcia) SJSU
Hearing in Animals
Frequency range varies widely, depending on natural adaptation
using sound to communicate, locate food, avoid predators, etc.
Transverse Wave
Crest
Wavelength
Amplitude
Trough
Baseline
INTERFERENCE
• Constructive or destructive interference
results when waves add.
• Standing Waves - wave pattern produced
from interfering waves
– Examples
• Vibrating Strings in Lab
• Organ Pipe in Lab
• Bell Wave Machine in Class
Interference
• Interference Pattern – within a pattern, wave effects
may be increased, decreased, or neutralized
• Constructive Interference (reinforcement) – the crest
of one wave overlaps the crest of another, their
individual effects add together producing an
increased amplitude
• Destructive Interference (cancellation) – the crest of
one wave overlaps the trough of another, their
individual effects are reduced
• When waves produce areas of zero amplitude, they
are “out of phase”
• When the crest of one wave overlaps the crest of
another, they are “in phase”
constructive interference.
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,
their individual effects are
reduced. The high part of one
wave simply fills in the low part
of another.
Example Wave
2 ½ meters
20 cm
Wavelength = 1 m
Amplitude = 10 cm
Number of Nodes = 6
Noise-Canceling Headphones
Noise-canceling headphones use a microphone that
listens for noise and a speaker that produces the
same noise but out of phase (cancellation by
destructive interference)
External Noise
Canceling Sound
Standing Waves
When two sets of waves of equal amplitude and
wavelength pass through each other in
opposite directions, it is possible to create an
interference pattern that looks like a wave that
is
“standing still.”
It is a changing interference pattern.
Today you will create such patterns on a
vibrating string.
Parameters of a Standing Wave
l
There is no vibration at a node.
There is maximum vibration at an antinode.
l is twice the distance between successive nodes
or successive antinotes.
Standing Waves and Phase
19-Mar-16
Standing waves are another
example of constructive and
destructive interference.
Physics 1 (Garcia) SJSU
Two sets of overlapping water waves produce an
interference pattern. The left image is an idealized drawing
of the expanding waves from the two sources. The right
image is a photograph of an actual interference pattern.
Interference is
characteristic of all wave
motion, whether the
waves are water waves,
sound waves, or light
waves
Waves are out of phase with each other when the regions where a crest of one wave overlaps
the trough of another to produce regions of zero amplitude and wave points along these
regions arrive out of step.
Interference Animation
Doppler Effect
Sound coming from a moving object has a different wavelength
and frequency than if it were stationary.
If moving towards you, wavelength shorter and frequency higher.
If moving away, wavelength longer and frequency lower.
19-Mar-16
Physics 1 (Garcia) SJSU
DOPPLER EFFECT
• the change in wavelength due to motion of
the source
• "Wheeeeeeeeeeee…….Oooooooooooooo”
• Examples:
– moving cars and trains
– moving buzzer in a nerf ball (in class)
– rotating whistle
 Java
Doppler Effect
Draw Doppler Picture
The Doppler Effect
• Doppler Effect – the apparent change in frequency due
to the motion of the source (or receiver)
• Spherical sound or light wave crests ahead of a moving
source are closer together than those behind the source
and encounter a receiver more frequently
• Blue Shift – an increase in frequency towards the highfrequency, or blue, end of the light spectrum (light
source is moving towards receiver)
• Red Shift - a decrease in frequency towards the lowfrequency, or red, end of the light spectrum (light source
is moving away from the receiver)
• Distant galaxies show a red shift in the light they emit,
indicating that the universe is expanding (or moving
further apart)
The Doppler Effect
• When a light source
approaches, there is
an increase in its
measured frequency
called a blue shift;
and, when it recedes,
there is a decrease in
its frequency called a
red shift spectrum
Blue Shift and Red
Shift
Bow Waves
In the early days of jet
aircraft, it was believed
that a pile-up of sound
waves in front of the
airplane imposed a “sound
barrier” and that, in order
to go faster than the speed
of sound, the plane would
have to “break the sound
barrier.”
•
What actually happens is that the
overlapping wave crests disrupt the flow of
air over the wings, making it more difficult
to control the craft. But the barrier is not
real.
Bow and Shock Waves
• Bow Wave – when the speed of the source in
a medium is as great, or greater, than the
speed of the wave it produces it will catch up
to the wave crests and pass them producing a
v-shape
• Shock Wave – like a bow wave, but in three
dimensions, produces a cone-shape
• Sonic Boom – produced when the conical
shell of compressed air that sweeps behind a
supersonic jet reaches listeners on the ground
below
Bow Wave
after the speed of the
source exceeds wave
speed, increased speed of
the source produces a
narrower V shape
• Patterns produced by a bug
swimming at successively greater
speeds. Overlapping at the edges
occurs only when the bug swims
faster than wave speed.
Sonic Booms
We don’t hear a sonic
boom from slowerthan-sound, or
subsonic, aircraft
because the sound
waves reaching our
ears are perceived as
one continuous tone.
•
Only when the craft moves faster than
sound do the waves overlap to reach the
listener in a single burst.
• The sudden increase in pressure is much the
same in effect as the sudden expansion of
air produced by an explosion.
• Both processes direct a burst of highpressure air to the listener.
• The ear is hard pressed to distinguish
between the high pressure from an
explosion and the high pressure from many
overlapping waves.
The mach cone and shock wavefronts are
very noticeable
The speed of sound in the medium (vs = v, or Mach 1). The speed of sound in air at sea level is
about 340 m/s or about 750 mph.
The wavefronts in front of the source are now all bunched up at the same point. As a result, an
observer in front of the source will detect nothing until the source arrives. The pressure front
will be quite intense (a shock wave), due to all the wavefronts adding together, and will not be
percieved as a pitch but as a "thump" of sound as the pressure wall passes by.
The figure at right shows a bullet travelling at Mach 1.01. You can see the shock wave front just
ahead of the bullet. Jet pilots flying at Mach 1 report that there is a noticeable "wall" or
"barrier" which must be penetrated before achieving supersonic speeds. This "wall" is due to
the intense pressure front, and flying within this pressure front produces a very turbulent and
bouncy ride. Chuck Yeager was the first person to break the sound barrier when he flew faster
than the speed of sound in the X-1 rocket-powered aircraft on October 14, 1947.
Shock Wave
http://observe.phy.sfasu.edu/courses/phy101/lectures101/
Subsonic - slower than the speed of sound
Supersonic - faster than the speed of sound
Mach Number
=
speed of object
speed of sound
Bow and Shock Waves
Shock wave of a bullet
piercing a sheet of
Plexiglass.
Light deflecting as the bullet passes
through the compressed air makes the
shock visible.
• Look carefully and see the
second shock wave
originating at the tail of the
bullet.
a shock wave
usually consists of two
cones: a high-pressure
cone generated at the
bow of the supersonic
aircraft and a lowpressure cone that
follows at the tail of
the craft.
• Between these two cones, the air
pressure rises sharply to above
atmospheric pressure, then falls
below atmospheric pressure before
sharply returning to normal beyond
the inner tail cone
• This overpressure suddenly
followed by underpressure
intensifies the sonic boom.
The shock wave
A graph of the air pressure at ground
level between the cones takes the
shape of the letter N.
A common misconception is that sonic
booms
• The fact is that a shock wave
and its resulting sonic boom
are swept continuously
behind and below an aircraft
traveling faster than sound,
just as a bow wave is swept
continuously behind a
speedboat.
Sonic Boom
• listener B is in the process of
hearing a sonic boom.
• Listener C has already heard it,
• listener A will hear it shortly.
• The aircraft that generated this
shock wave may have broken
through the sound barrier many
minutes ago!
What determines the speed of a
wave?
(a) the frequency
(b) the wavelength
(c) the amplitude
(d) the period
(e) the medium of transmission
What dictates the frequency of a
sound wave?
(a) wavelength
(b) medium
(c) source of the sound
(d) speed
(e) amplitude
Example Question
*
The distance from trough to trough on a
periodic wave is called its...
– a) frequency.
– b) period.
– c) wavelength.
– d) amplitude.
Example Question
*
A train whistle at rest has a frequency of 3000
Hertz. If you are standing still and observe
the frequency to be 3010 Hertz, then you can
conclude that...
– a) the train is moving away from you.
– b) the train is moving toward you
– c) the sound from the whistle has echoed
– d) not enough information is given
Chapter 20
Sound
Web Page
Sound...
• ...a longitudinal wave in air caused by a
vibrating object.
• Demos:
– Vortex Box
– Card and rotating blades
– Oscillator and Speaker
Origin of Sound
• infrasonic
– frequencies < 20 Hz
• ultrasonic
– frequencies > 20,000 Hz
• human hearing range
– frequencies between 20 Hz and 20,000 Hz
Nature of Sound in Air
• Sound requires a medium.
– solid, liquid or gas
– Demo: Bell in a evacuated Bell Jar
• Sound waves have compression and
rarefaction regions.
Origin of Sound
• infrasonic
– frequencies < 20 Hz
• ultrasonic
– frequencies > 20,000 Hz
• human hearing range
– frequencies between 20 Hz and 20,000 Hz
Speed of Sound in Air
• 340 meters/second
• 760 miles/hour
• Mach 1
• Video Segments
– A lumberjack, lightning, and an explosion at a
distance. *
SPEED OF SOUND
How it varies: increases with humidity
increases with temperature
increases with density
Lightning and Thunder
What is the approximate distance of a
thunderstorm when you note a 3 second delay
between the flash of the lightning and the
sound of the thunder?
Answer: 3 seconds  340 meters/second
= 1020 meters
Acoustics...
• ...the study of sound properties.
• When a sound wave strikes a surface it can be.…
–
–
–
–

(a) reflected.
(b) transmitted.
(c) absorbed.
(d) all of these.
Reflection of Sound
• e.g. an echo
• Reverberation - re-echoed sound, multiple
reflections of sound waves from walls
• Compare reflections from a hard wall with
that from a carpet wall.
Demo: Whip
Refraction of Sound
• Refraction - the bending of a wave
• Sound travels faster in warm air than in
cool air.
• Sound waves bend toward cooler air.
Desert and Lake Example
Forced Vibrations...
• …the setting up of vibrations in an object
by a vibrating force.
• Examples of Forced Vibration:
– A tuning fork touching a wood surface
– Sounding boards for stringed instruments
– Matching tuning fork boxes
Natural Frequency...
• …the frequency at which an elastic object
naturally tends to vibrate.
• At this frequency, a minimum energy is
required to produce a forced vibration.
Natural Frequency...
• The natural frequency of a body depends
on its ...
– elasticity
– size
– shape
Natural Frequency Examples
•
•
•
•
•
•
•
•
•
Mass on a Spring
Ringing Small and Large Bells
Xylophone
Singing Rod
Rubbing a Wine Glass
Dropping Aluminum Rods
Boom Whackers
Organ Pipe
Ruben’s Tube (http://www.youtube.com/watch?v=HpovwbPGEoo)
Resonance...
• …is the result of forced vibrations in a body
when the applied frequency…
• ...matches the natural frequency of the body.
• The resulting vibration has a high amplitude
and can destroy the body that is vibrating.
Resonance Demos
•
•
•
•
Chinese Spouting Bowl
Tibetan Bowl
PVP Pipes
Iron Tube
Examples of Resonance
•
•
•
•
•
•
mass on a spring at resonance
swinging your legs in a swing
breaking a wine glass using sound
a singing rod caused by forced vibration
fog horn
a tuning fork exciting a guitar string
– http://observe.phy.sfasu.edu/courses/phy101/lectures101/Movies/
• In 1940, the Tacoma Narrows Bridge was
destroyed by wind-generated resonance.
•
Imagine you’re sitting on a swing and want
to go higher. You pump your legs at a certain
rate to increase your swinging.
•
This is an example of you creating resonance
by matching the frequency of the swing.
Tacoma
Narrows
Bridge
Resonance allows energy to be
transferred to a vibrating object
efficiently if the energy is delivered at
the natural frequency of vibration.
Sound Interference
• Overlapping compressions of a sound wave will result
in…
– …constructive interference.
– …and a louder sound.
• Overlapping a compression and a rarefaction results
in...
– …destructive interference.
– …and a softer sound.
Constructive Interference
Destructive Interference
Constructive Interference occurs when waves are in
phase, that is when crests are superimposed and
troughs are superimposed.
Destructive interference occurs when waves are out of
phase, that is when crests are superimposed with
troughs.
10. SHOCK WAVES
• Just as circular waves move out from a swimming bug,
spherical waves move out from a flying object. If the object
flies faster than the waves, the result is a cone-shaped
shock wave.
• Demo - Cone of Waves
• There are two booms, one from the front of the flying object
and one from the back.
9. BOW WAVES
• Waves in front of moving object pile up.
• Slide - Wave Barrier
• Slide - “Bow” Wave
• The familiar bow wave generated by a speedboat knifing
through the water is a non-periodic wave produced by the
overlapping of many periodic circular waves. It has a constant
shape.
10. SHOCK WAVES
• Just as circular waves move out from a swimming bug,
spherical waves move out from a flying object. If the object
flies faster than the waves, the result is a cone-shaped
shock wave.
• Demo - Cone of Waves
• There are two booms, one from the front of the flying object
and one from the back.

Demo - Crack whip
• Video - FB-111 Sonic Boom
• MPEG - FS14 Sonic Boom
• Word Doc - Sonic Boom
• The boom is not produced just when the flying
object “breaks” through the sound barrier.
Subsonic
• Supersonic
Mach Number
- slower than the speed of sound
- faster than the speed of sound
speed of object
=
speed of sound
• Beats - the periodic variation in loudness of
two sounds played together
• The beat frequency is equal to the difference
in the frequency of the two sounds.
• What is the beat frequency when a 262 Hz and
a 266 Hz tuning fork are sounded together?
Radio Broadcasts
• Modulation - an impression of the sound wave on a
higher frequency radio wave
• AM
– Amplitude Modulation
• 535 kHz to 1605 kHz
• FM
– Frequency Modulation
• 88 MHz to 108 MHz
Constructive Interference occurs when waves are
in phase, that is when crests are superimposed
and troughs are superimposed.
Destructive interference occurs when waves are
out of phase, that is when crests are
superimposed with troughs.
Once an object is moving faster than the speed of
sound, it will make sound
• A supersonic bullet passing overhead produces a crack, which
is a small sonic boom.
• If the bullet were larger and disturbed more air in its path, the
crack would be more boomlike.
• When a lion tamer cracks a circus whip, the cracking sound is
actually a sonic boom produced by the tip of the whip when it
travels faster than the speed of sound.
• Both the bullet and the whip are not in themselves sound
sources, but, when traveling at supersonic speeds, they
produce their own sound as they generate shock waves.