Work
• To move an object we must do work
• Work is calculated as the force applied to
the object through a distance or:

 W  F ( d )
• Work has the units Newton meters (N m)
or Joules
• 1 Joule = 1 N m
Energy
• There are 2 types of Energy that we will
deal with, Kinetic energy and Potential
Energy
• Potential Energy: is the energy of position
or stored energy
Ep = F (Δd)
• Kinetic Energy: is the energy of motion
Ek = ½ mv2
Work and Energy Examples
• What amount of work • What is the Kinetic
is done by Jane as
she lifts a box of
mass 20.0 kg to a
height of 1.5 m?

W = F (x)
g
W = (20.0 kg)(9.81
m/s2)(1.5 m)
W = 294 J
energy of an object
moving at 5.00 m/s
that has a mass of
5.00 kg?
Ek = ½ mv2
Ek = ½(5.00 kg)(5.00
m/s)2
Ek = 62.5 J
What are Waves??
• They are the motion of a disturbance.
• They are a means of transferring energy
without the particle moving.
Classifications of Waves
Mechanical
Waves
Electromagnetic Matter Waves
Waves
1-Dimensional (waves
on a spring or rope)
3-Dimensional (light,
x-rays)
3-Dimensional (waves
associated with
electrons, protons etc)
Do not require a
medium to travel
through
Do not require a
medium to travel
through
2-Dimensional (waves
in Water)
3-Dimensional (sound
waves)
All require a medium
to travel through
Governed by Newton’s Governed by
Laws
Electromagnetic Wave
Theory
Governed by Quantum
Mechanics
Periodic Motion
• Motion that repeats itself over and over
– Ex: heart beats, ticking clock, moving on a
swing
• The time it takes for one complete cycle of
the motion is called the …….
Other Terms to Know
• Cycle – One complete back and forth
motion
• Frequency – the number of cycles per unit
time. It is measured in Hertz (Hz)
• Displacement – the distance an object
moves from the equilibrium position
• Amplitude – the maximum displacement
Simple Harmonic Motion (SHM)
• A type of periodic motion
• Objects that vibrate with SHM are called
Simple Harmonic Oscillators
– An example of this is a mass on a spring,
pendulums, and waves
Mass on a spring
• When there is a mass on a spring, there
are 2 forces that are acting on it.
– Gravity and the Tension of the spring
• Tension on the spring is governed by
Hooke’s Law
Hooke’s Law

F  kx
F is Force
k is the spring constant
X is the displacement
– When the spring is stretched FT > Fg then the mass
moves upwards
– When the spring is compressed Fg > FT then the mass
moves downwards
Hooke’s Law Example
• A mass of 15.0 kg is suspended from a
spring. If the spring has a spring constant
is 6.00 N/m, what is the restoring force of
the spring when the mass is 0.30 m from
equilibrium?

F


kx

-(6.00 N/m)(0.30 m)
F


F  -1.8 N
MASS ON A SPRING
e
M
A
Stretch &
Release
k = the spring constant in N m1
m
T  2
k
Mass on a Spring Example
• A 0.23 kg object vibrates at the end of a
horizontal spring (k = 32 N/m) along a
frictionless surface. What is the period of
the vibration?
T = 2√(m/k)
T = 2√(0.23 kg / 32 N/m)
T = 0.53 s
Hooke’s Law Cont.
• If there was no force to slow the motion
down, it would continue forever
• The force that causes the slowing of the
motion is called the Restoring Force
• The Restoring force is governed by the
spring constant, k
DAMPING
DISPLACEMENT
INITIAL AMPLITUDE
time
THE AMPLITUDE DECAYS EXPONENTIALLY WITH TIME
Hooke’s Law Cont.
• When there is a Restoring force, the
systems will become damped
• Where is this idea of a damped system
used in your daily life???
THE PENDULUM
The period, T, is the time for one complete cycle.
l
T  2
l
g
Pendulum Example
• Find the length of a pendulum that has a
period of 0.90 s.
T = 2√(l/g)
0.90 s = 2√(l / 9.81 m/s2)
l = (0.90 s / 2)2(9.81 m/s2)
l = 0.20 m
Energy in SHM
• Work is done on an object when we apply
a force over a distance

W  Fx
• For a spring, the work is moving the
object to its maximum displacement

W  1 2 Fx
Energy in SHM Cont.
• Potential Energy
stored in the spring is

 Ep = ½ F x

– And F  k x
– So Ep = ½ k x2
• But the mass moves
on the spring back
and forth changing
from Kinetic to
potential Energy
• Kinetic Energy is:
 Ek = ½ mv2
• Total Mechanical
Energy is:
 ET = Ep + Ek
 ET = ½ k x2 + ½ mv2
Are there different Types of
Waves??
You bet there are
Types of Waves
• Longitudinal
• Transverse
• Surface
Transverse waves
• The wave particles
•
•
vibrate perpendicular
to the transfer of
energy
An example of this is
a wave on a string
Waves in solids are
transverse waves
Transverse waves
• Crests
Highest part of a wave
• Troughs
The low points of the wave
Longitudinal Waves
• The wave particles
•
•
vibrate parallel to the
transfer of energy
An example of this is
a sound wave
Waves in gases and
liquids usually are
longitudinal waves
• Compressions
The close together part of the wave
• Rarefactions
The spread-out parts of a wave
What the waves look like
Surface Waves
• These are waves that move particles in
both longitudinally and transversely
– Ex: Water waves
Wave Characteristics
• All waves have 5 Characteristics
– Frequency
– Period
– Wavelength
– Velocity
– Amplitude
Wave Characteristics Cont.
• Frequency (f)
– the number of cycles or oscillations per
second.
– Measured as 1/s, or s-1, or Hertz (Hz)
– 1 Hz = 1 cycle per second
• Ex: A car travels 8 times around a track in
4 seconds. What is the frequency?
• f = #cycles/time = 8/4 = 2 Hz
Wave Characteristics Cont.
• Period (T)
– The time required for one cycle to be
completed
– Measured in seconds (s)
T = 1/f
• Ex: What is the period from the previous
question?
• T = 1/f = ½ = 0.5 s
Wave Characteristics Cont.
• Wavelength (l)
– The distance between
successive parts of a
wave.
– The parts can be
either the Crest or the
Trough of the wave
Wave Characteristics Cont.
• Velocity (v)
– The speed of a wave through a medium depends on
the Elasticity and the density of the medium
• V = √(elasticity/density)
• The speed of the wave can also be determined
using the wave characteristics
 v = l/ T or v = lf
– Which is known as the Universal Wave Equation
– Which is a form of uniform motion: v = Δd/Δt
Velocity Example
• Ex: What is the velocity of a wave with a
frequency of 10 Hz and a wavelength of
10 m?
• v = lf
• v = 10 Hz * 10 m
• v = 100 m/s
Wave Characteristics Cont.
• Amplitude (x)
– The maximum
displacement from
equilibrium (or rest
position) of a wave
Wave Characteristics
10 Characteristics of Waves
1.
2.
3.
4.
5.
Propagation
Reflection
Polarization
Refraction
Diffraction
6. Interference
7. Diffusion
8. Color
9. Dispersion
10.Scattering
Propagation
• How a wave moves from one position to
another
• All the motion is in a straight line
• Wave speed is determined by the medium
that it is traveling in
• Calculated using either
v = Δd/Δt
v = fλ
Reflection
• The bouncing of a
•
wave off a reflective
boundary
Law of Reflection
 Θi = Θreflection
• v, f, T, and λ DO NOT
CHANGE
Polarization
• When the displacement
•
•
•
of the particles is in the
same plane
Passing a wave through a
slit aligned in a direction
produces a polarized
wave
If 2 slits that are
perpendicular are used,
the wave is destroyed
Does not occur in
Longitudinal waves only
Transverse waves
Refraction
• Occurs when a wave
•
meets a boundary at
an angle
Where the wave and
the boundary meet,
the angle taken from
the normal is called
the Angle of
Incidence Θi
Refraction Cont.
• v and λ must change because you are going into
•
•
•
a new medium
The speed will decrease when the wave refracts
to the normal
The speed will increase when the wave refracts
away from the normal
To calculate the angles, speed, and wavelengths
λ1 = sin Θ1 = v1 = n2
λ2 sin Θ2 v2 n1
Refraction Cont.
• n refers to the Index of Refraction and is
an indication of the density in comparison
to the density of air
• i refers to the incident medium and r to
the refractive medium
• In this form, the equations are only to be
used with mechanical waves
Refraction Example
• Waves travel from deep water into shallow
o
water. If the angle of incidence is 30.0 ,
o
and the angle of refraction is 20.0 , what
is the index of refraction?
• sinΘ1 = n
sinΘ2
o
sin 30.0 = n
n = 1.46
o
sin 20.0
Diffraction
• Are waves able to bend around corners?
• Yes they can, this is called Diffraction
• How much they bend depends on the
wavelength and the size of the opening
• ↑ the λ the ↑ the diffraction and vice versa
• ↓ the opening the ↑ the diffraction
Diffraction
Interference
• Occurs when 2 waves simultaneously act
on the same particles
• 2 types of Interference
– Constructive Interference
– Destructive Interference
• Also known as the Principle of
Superposition
Constructive Interference
• When 2 waves come
together and the
resulting wave is
GREATER than either
of the original waves
Destructive Interference
• When 2 waves come
together and the
resulting wave is
SMALLER than either
of the original waves
Diffusion
• The ability of the wave to spread
The Other Characteristics
8. Color
9. Dispersion
10.Scattering
• All of these characteristics will be
discussed during Light waves
2-Dimensional Waves
• Speed varies with
respect to the depth
– Small depth, small
speed and vice versa
• Amplitude varies with
respect to the depth
– Small depth, big
amplitude
Tsunami
Tsunami Warning
• On December 26, they were playing in the sea when
•
•
Tilly suddenly found the water was bubbling, like on top
of a beer. She immediately realized tsunami was coming
because the scene reminded her of a geography lesson
about Hawaii's 1946 tsunami.
Right away, Tilly told her parents, sister and other
tourists to escape quickly, but at first they were in half
belief. However, seeing Tilly's serious and firm
expression, people started to be convinced of the
seriousness of the thing and instantly left the beach.
At last over 100 tourists were ended up in safety with no
death
http://www.phy.ntnu.edu.tw/java/propagation/propagation.html
Ripple Tank
• Most of the characteristics of waves can
be seen through the use of a ripple tank
3-Dimensional Waves
• Ex: Sound waves
• These move as
•
•
longitudinal waves in air
and transverse waves in
solids
These waves carry
energy that will stimulate
the ear drum
Sound is produced by the
compression and
rarefaction of the medium
3-D Waves Cont.
• The average person can hear frequencies
from:
• infrasonic←20 Hz to 20000 Hz→ultrasonic
• All sound waves have v, f, T, and λ
• Frequency of sound waves is the # of
vibrations per second
– This is also called the PITCH
Doppler Effect
• Have you ever noticed that as a siren
moves towards you, the sound gets louder
and when it moves away the sound is
quieter?
• This is called the Doppler Effect
Doppler Effect
• The Doppler Effect states that the
frequency of the observed sound is related
to the velocity of the sound, the velocity
of the observer and the frequency of the
original sound
vv
f  f(
)
vv
O
O
I
S
Doppler Effect Cont.
• Vo is + if the observer is moving towards
the sound
• Vo is – if the observer is moving away from
the sound
• Vs is – if the source is moving toward the
receiver
• Vs is + if the source is moving away from
the receiver
Doppler Effect Example
• A car is travelling 29 m/s toward a
stationary sound (whistle) that has a
frequency of 625 Hz. If the speed of
sound is 337 m/s, what is the apparent
frequency of the sound as heard by the
driver of the car?
Doppler Effect Example Cont.
vv
f  f(
)
vv
O
O
I
S
• = 625 Hz (337 m/s + 29 m/s)
337 m/s - 0 m/s
fo = 679 Hz
3-D Wave Cont.
• Amplitude is the
maximum
displacement from
equilibrium
– In the case of sound,
the amplitude is the
volume of the sound
Sound Intensity
• The intensity of a sound, or its loudness,
is measured in Decibels, dB
• 0 dB is the threshold of hearing
• An increase in 10 dB’s means that the
intensity increases by a factor of 10
• An increase from 40dB to 60 dB means
that 60 dB is 100 times as intense as 40
dB
Speed of Sound in Air
• At sea level the speed of sound is 331 m/s
• Velocity of the sound wave depends on
the temperature
v = (331 + 0.6T) m/s
• Where T is in oC
o
What is the speed of sound at 20 C
o
and at -20 C ?
• v = (331 + 0.6T) m/s
•
= 331 m/s +0.6(20oC)
= 331 m/s + 12 m/s
v = 343 m/s
v = (331 + 0.6T) m/s
= 331 m/s + 0.6(-20oC)
= 331 m/s - 12 m/s
v = 319 m/s
Diffraction
• This is the bending of a wave around a
corner.
• You can hear a person’s voice as it passes
through a doorway or window even if you
are around a corner.
• This is because the opening acts as a
barrier causing the sound wave to bend
around it.
Diffraction Cont.
• Those waves with long wavelengths will
diffract more than those with a smaller
wavelength
• The size of the opening also plays a role in
this
• Lower frequencies will diffract more
because of their long wavelengths
Refraction
• The speed of sound
is dependant on the
temperature that the
air is at
• Sound will travel
faster in warm air
than in cold air
Refraction Cont.
• During the day, your voice will tend to rise
because of refraction. The air above is
colder than the air below
• During the night, your voice will tend
toward the ground because the air below
is colder
• At night or over water your voice will
travel further
Interference
• When 2 sound waves that of different
frequencies, when they meet you will
hear a beat
• The waves will be move from in-phase to
out of phase
• The will come when the frequency are in
phase
• This is call the Beat Frequency
Beat Frequency
• The beat frequency is the result of the
interference of 2 waves
• It is calculated as follows:
– # of beats = f1 – f2
Natural Frequency
• The frequency at which an object will
vibrate
• Ex: swinging on a swing, windows rattling
when a truck goes by
• The tendency for an object to vibrate at
it’s natural frequency is called
RESONANCE
Resonance
• There are 2 types of Resonance
– Mechanical
– Acoustical
Mechanical Resonance
• Mechanical Resonance is created when
one object is forced to vibrate at its
natural frequency by a physical force
being placed on the object
• Examples of this would include marching
on a bridge or the Tacoma Bridge Disaster
Acoustical Resonance
• Resonance can occur when a standing
wave is generated
• The wavelength for resonance to occur is
called the resonant frequency
• Examples of this include the guitar, violin,
cello, or any other string instrument
Acoustical Resonance Cont.
• A resonant frequency can also be set up in a
•
•
•
wind instrument
The sound travels through the pipe of the
instrument and is reflected back
If the wavelength of the sound waves are
matched, the waves will create a standing wave
pattern
The sound emitted will have the same frequency
as that of the waves in the pipe
Resonance in Air Columns
• When a tuning fork is held over an open
end of a hollow tube of a certain length
then Resonance may be heard
• This is caused by the interference
produced by the standing waves
Standing Waves
• Occurs when 2 waves
•
of equal wavelength
and amplitude travel
in opposite directions
on the same medium
They have alternating
nodes and antinodes
Standing Waves Cont.
• The distance between
nodes is ½ λ
– This is also true for
the distance between
antinodes
• Node: area where
•
there is zero
amplitude
Antinode: Area where
amplitude is a
maximum
Terminology
• Natural Frequency: the
•
•
•
•
frequency that a medium
vibrates
Resonant Frequency: the
frequency that causes an
air column to vibrate
Fundamental Frequency:
the lowest natural
frequency. Also called the
First Harmonic
2nd Harmonic: Frequency
of 2 x the fundamental
3rd Harmonic: Frequency
of 3 x the fundamental
Closed At One End
• Resonance can only occur
•
•
if there is an ANTINODE
at the open end and a
NODE at the closed end
This is necessary for a
standing wave to be
produced for resonance
The length of the air
column must be
equivalent to ¼ of the
wavelength produced by
the tuning fork
Closed At One End Cont.
• Resonance can also occur when the length
of the tube is ¾ λ
• The 1st resonance occurs when the air
column length is ¼ λ
• The 2nd resonance occurs when the air
column length is ¾ λ
• Each successive resonance will occur
when the lengths are 5/4, 7/4…….
Open At Both Ends
• Resonance can only occur
•
•
if there is an ANTINODE
at both ends
This is necessary for a
standing wave to be
produced for resonance
The length of the air
column must be
equivalent to ½ λ
Open At Both Ends Cont.
• The 1st resonance occurs when the air
column length is ½ λ of the tuning fork
• The 2nd resonance occurs when the air
column length is 2/2 λ of the tuning fork
• Each successive resonance occurs when
the air column length is 3/2, 4/2, ……
The power of Resonance
Earthquakes
• Earthquakes occur when the ground
moves
• This moving earth produces 2 types of
waves: Primary or P waves and Secondary
or S waves
Primary Waves
• The Primary waves are
•
•
the first to come from the
earthquake
These waves are able to
pass through the crust of
the Earth as well as the
core of the Earth
The waves will refract as
they pass through the
core
Secondary Waves
• Secondary waves are
•
•
the second waves to
be felt during an
earthquake
These waves can only
move through the
crust of the Earth
These waves will
reflect off the core
Generate an Earthquake