Wave
Transfers Energy Without
Transferring Matter
Wave
• A wave can be described as a
disturbance that travels through a
medium from one location to
another location.
There are three types of waves:
• Mechanical waves require a material
medium to travel (air, water, ropes).
• Electromagnetic waves do not require a
medium to travel (light, radio).
• Matter waves are produced by electrons
and particles.
Mechanical Waves
• Transverse waves cause the medium to
move perpendicular to the direction of
the wave.
• Longitudinal waves cause the medium to
move parallel to the direction of the
wave.
• Surface waves are both transverse
waves and longitudinal waves mixed in
one medium. (Such as water waves)
• Torsional waves produce a twisting
motion through the medium – such as the
ones which caused the collapse of the
Tacoma Narrows Bridge.
Tacoma Narrows Bridge
Torsional Oscillation
Mechanical Universe Video
Transverse & Longitudinal
Waves
• In a transverse wave, the particles of the
medium oscillate perpendicular to the
direction of wave travel.
• In a longitudinal wave, the particles of the
medium oscillate along the direction of
wave travel.
3 Types of Mechanical
Waves
Wave Tutorial Links
• http://library.thinkquest.org/10796/ch8/
ch8.htm
• http://www.physicsclassroom.com/Class/w
aves/wavestoc.html
Longitudinal Tuning Fork Wave
• Vibrating tines
produce an
alternating pattern
of high pressure and
low pressure regions.
• This pattern travels
away from the fork.
• Compression – high
pressure
• Rarefaction – low
pressure
Period: T
• The PERIOD of a
wave is the time
for a particle of
the medium to
complete one
oscillation.
• The SI unit for
period is the
second.
Frequency: f
• The FREQUENCY of a
wave is the number of
cycles per unit time.
• The unit is Hertz (Hz)
which is a cycle per
second.
• FREQUENCY is also
the reciprocal of the
period.
1
f 
T
1
T
f
Amplitude: A
• The AMPLITUDE of a wave is the maximum
distance of a particle from the equilibrium
position.
• The SI unit for amplitude is meter
Wavelength: l (lambda)
• The
WAVELENGTH of
a wave is the length
of one complete
cycle.
• It is the distance
between two
consecutive “in
phase” points.
• In phase points are
those that are
moving in step with
each other.
Wave Applets
•
•
•
•
•
•
Wavelength, Amplitude, Phase
Frequency, Wavelength, Speed
Longitudinal Wave
Transverse Wave
Superposition Principle 1
Superposition Principle 2
Wave Equation
• The speed of a wave
is equal to the
product of the wave’s
frequency and
wavelength.
• v: wave speed
• f: frequency
• l : wavelength
v fl
Speed of Wave on String
v
F

m

L
Sound Waves
• The origin of any sound is a vibrating
object
– Usually the frequency of the sound is the
same as that of the vibrating object
• Frequency Range:
Sound: 20 Hz – 20,000 Hz
Ultrasound: >20,000 Hz
Infrasound: < 20 Hz
Forced Vibration & Resonance
• forced vibration – example -- strike tuning
fork and hold the stem against the table
• sounding board -- used to amplify sound in
music boxes and all string
• resonance -- when the frequency of
forced vibrations matches the object's
natural frequency, a dramatic increase in
amplitude occurs
Speed of Sound
Material
Speed (m/s)
Aluminum
6420
Granite
6000
Steel
5960
Pyrex glass
5640
Copper
5010
Plastic
2680
Fresh water (20 ºC)
1482
Fresh water (0 ºC)
1402
Hydrogen (0 ºC)
1284
Helium (0 ºC)
965
Air (20 ºC)
343
Air (0 ºC)
331
Speed of Sound in Air
• depends on wind conditions, temperature,
and humidity
• does NOT depend on loudness or
frequency of the sound
• all sounds travel at the same speed in the
same medium in dry air at 0°C ~ 331 m/s
(1200 km/h) (740 mi/h)
• Sound travels faster through warm air
than cold air.
• In air, vsound = 331.4 m/s + (0.6 m/s/Co)*TC
Distance to Lightning
• Light travels at
3 x 108 m/s in air
• Sound travels at
about 330 m/s in
air at 0oC
• It takes about 5 seconds for the sound (the
thunder) to travel 1 mile.
• Count the seconds between the flash and the
sound, divide by 5, and you have the
approximate distance in miles to the
lightning.
Pitch & Loudness
• Pitch – frequency
Double frequency – go up an octave
• Loudness – amplitude
Energy  Amplitude2
Energy
Power
Intensity 

time * area area
P
I
A
– Units – W/m2
Human Ear
Decibel Scale
• incredibly sensitive
• can hear everything
from fingertip brushing
lightly over fabric to a
loud jet engine
• sound of jet engine is
about 1012 times more
powerful than smallest
audible sound
• a big difference!
• decibel scale -- smallest
audible sound is 0 dB
• A sound 10 times more
powerful is 10 dB
• A sound 100 times more
powerful than near total
silence is 20 dB
Sound Intensities
(W/m2)
Loudest sound produced in laboratory 109
Saturn V rocket at 50 m
108
Rupture of the eardrum
104
Jet engine at 50 m
10
Threshold of pain
1
Rock concert
10–1
Jackhammer at 1 m
10–3
Heavy street traffic
10–5
Conversation at 1 m
10–6
Classroom
10–7
Whisper at 1 m
10–10
Normal breathing
10–11
Threshold of hearing
10–12
Intensity Level
• Logarithmic Scale
 I 
  10log  
 I0 
• Dimensionless
• I0 = 10-12 W/m2
Decibel Levels
•
•
•
•
•
•
•
Near total silence - 0 dB
A whisper - 15 dB
Normal conversation - 60 dB
A lawnmower - 90 dB
A car horn - 110 dB
A rock concert or a jet engine - 120 dB
A gunshot or firecracker - 140 dB
Doppler Effect
• Doppler Effect Lesson
Doppler Effect
• Moving Source
 1 
f
f
1 u 
v

(
f   1 u
• General Expression
 1  uo
v
f
 us
1
v

Moving Observer

f



v
f
Superposition Principle
• Wave interference occurs when two or more
waves act simultaneously on a medium.
• Whenever two or more waves pass through
each other, the resulting disturbance at a
given point in the medium may usually be
found by adding the individual displacements
that each wave would have caused. (Principle
of Superposition)
Constructive Interference
• Constructive
interference occurs
when the waves are
trying to displace the
medium in the same
direction.
Destructive Interference
• When these two waves are completely
overlapping, there will be complete
destructive interference.
• Destructive interference occurs when the
waves are trying to displace the medium in
opposite directions.
Pulse/Wave Reflection
Fixed End Reflection
Free End Reflection
Interference between incident and
reflected pulse in a fixed end reflection
• Fixed/Free End Reflection of Sine Wave
Standing Waves
• For certain
frequencies, the
interference of the
incident and
reflected waves
results in a
standing wave
pattern.
Fundamental Frequency
and Harmonics
l fundamental  2 L
f fundamental
v

2L
Standing Waves in a Tube
• Closed on one end:
• Open on both ends:
l fundamental  4 L
l fundamental  2 L
v

4L
v

2L
f fundamental
f fundamental
Waves Moving in and Out of Phase
• When the 2 waves
are in phase, the
resulting
disturbance has a
maximum
amplitude.
• When the 2 waves
are out of phase,
the resulting
disturbance has a
minimum amplitude.
Beats
• Waves of slightly
different
frequencies form a
pattern of
alternating
maximum and
minimum amplitude.
• The packets of
maximum amplitude
are called beats.
Noise Canceling
• tiny microphones, one on each
earpiece, detect ambient noise
before it gets to your ears.
• noise-cancellation circuitry
inverts the captured signal,
turning the noise's sound wave
upside down.
• noise-cancellation system adds
the sonic opposite of the
external noise to whatever
you're listening to
• eliminating most of the pollution
and leaving you with just your
music.
Standing Waves
• http://phet.colorado.edu
Fundamental & Harmonics