Download Waves

Waves: light and sound
What are waves?
 Waves
 Many



are a transmission of energy
waves travel through matter such as
Waves through water
Sound through air, water, walls, etc.
Earthquake waves through the earth
 Some
waves travel do not require matter
such as electro-magnetic waves
EQ and sound waves
Light is an e-m wave
 Many
thanks to Faraday and Maxwell!!
 Behavior
of light can
 be described using
 the previous vocab
 Also
has unique behaviors and properties
Einstein kept pictures of Maxwell and Newton
in his room
Characteristics that describe all
waves

Can be described using vocabulary of simple
harmonic motion






Crest and trough
Amplitude
Wavelength
Frequency in Hertz (cycles/sec)
Speed
Either a transverse OR a longitudinal
(compression) wave
Types of Waves – Traveling
Waves

Flip one end of a long
rope that is under
tension and fixed at
one end
 The pulse travels to
the right with a
definite speed
 A disturbance of this
type is called a
traveling wave
Types of Waves – Transverse

In a transverse wave, each element that is
disturbed moves in a direction perpendicular to
the wave motion
 Examples: e-m, light, water, waves on string
Types of Waves – Longitudinal

In a longitudinal wave, the elements of the
medium undergo displacements parallel to the
motion of the wave
 A longitudinal wave is also called a compression
wave
 Sound is a compression/longitudinal wave
Waveform – A Picture of a
Wave




The brown curve is a
“snapshot” of the wave
at some instant in time
The blue curve is later
in time
The high points are
crests of the wave
The low points are
troughs of the wave
Longitudinal Wave Represented as
a Sine Curve



A longitudinal wave can also be represented as a sine
curve
Compressions correspond to crests and stretches
correspond to troughs
Also called density waves or pressure waves
Description of a Wave



A steady stream of pulses
on a very long string
produces a continuous
wave
The blade oscillates in
simple harmonic motion
Each small segment of
the string, such as P,
oscillates with simple
harmonic motion
Amplitude and Wavelength


Amplitude is the
maximum displacement
of string above the
equilibrium position
Wavelength, λ, is the
distance between two
successive points that
behave identically
Speed of a Wave

v=ƒλ

derived from the basic speed equation of distance/time

a general equation that can be applied to many types of
waves

Speed of light = assumed constant




variable ‘c’, for ‘celeritas’, Latin for swiftness
approx 3 x 108 m/s in a vacuum
slows down slightly while passing through glass, etc.
Speed of sound, water, etc. depends on many variables
First a review of properties and
behavior of waves
 What






do waves do?
transmit energy
can be reflected
can be refracted or bent when they hit a
boundary or edge
can interfere with each other
Under the right circumstances they can form
harmonious patterns on a string
They can pass through some materials better
than others
To study properties of light,
simplify light into rays
 Although
light travels in all directions and
hits all surfaces from all directions, it is
useful to

Think of light travelling as parallel rays
Synopsis of light lab stations











1. internet
2. 1 flat mirror & laser
3. 2 flat mirrors & laser
4. concave mirror & laser
5. convex mirror & laser
6. carpet and wheels
7. mug with water
8. water, oil etc in clear containers, laser
9. internet
10. interference, concentric circles
11. CDs and DVDs & lasers
Light labs
Move through quickly!!
Groups of 3 at the most
Important to draw accurate diagrams for incoming
and outgoing rays!
After we review the results as a class, I will post
expected answers ONLINE.
Station 1: All about Waves

http://faraday.physics.utoronto.ca/IYearLab/Intros/StandingWaves/Flash/sta2fix.html

Answers in separate document
Station 2: Reflect on this
 Flat
mirror and laser
 Results:
angle of incoming ray is equal to
outgoing ray, if measured from a line
perpendicular to the mirror
Station 2: Law of Reflection

The normal is a line
perpendicular to the
surface
 The incident (incoming)
ray makes an angle of
θ1 with the normal
 The reflected (outgoing)
ray makes an angle of
θ1’ with the normal
 The angle of reflection
is equal to the angle of
incidence
 θ1= θ1
Law of Reflection, cont
This is true for all types and shapes of
reflecting surfaces
 Why do you see a reflection on some
surfaces and not on others???
Station 3: Target Practice

Rays follow law of reflection

http://paer.rutgers.edu/pt3/experiment.php?topici
d=12&exptid=176

Conclusion: incoming and outgoing rays are
parallel to each other no matter what the
orientation of the incoming

Caveat: incoming ray must reflect off both
mirrors
Big Idea
 Without
 What
 The
light there can be no sight!
does that mean?
only way we can
 See objects is
 Because they…

We see objects that reflect light back into
our eyes!!!
 No
light at all, can’t see the object
 No
direct path of reflected light, can’t see it
A
blockage in the path, can’t see it
Prisms can be used like mirrors
Spherical Mirrors

A spherical mirror has the shape of a segment of
a sphere
 A concave spherical mirror has the silvered
surface of the mirror on the inner, or concave,
side of the curve
 A convex spherical mirror has the silvered
surface of the mirror on the outer, or convex,
side of the curve
Specific data about non-flat mirrors

The mirror has a radius
of curvature of R

Its center of curvature is
the point C

Point V is the center of
the spherical segment

A line drawn from C to
V is called the principal
axis of the mirror
Station 4: Why..look funny? Pt1
 Working
 Answers
with CONCAVE mirrors
also available in separate word
document on my website
Ray Diagram for Concave
Mirror, p > R

The object is outside the center of curvature
of the mirror
 The image is inverted
 The image is smaller than the object
Ray Diagram for a Concave
Mirror, p < f

The object is between the mirror and the focal
point
 The image is upright
 The image is larger than the object
Focal Length Shown by Parallel
Rays
Station 5: Why…so funny? Pt2
 Working
 Answers
with CONVEX mirrors
also available in separate word
document on my website
Ray Diagram for a Convex
Mirror
 The
object is in front of a convex mirror
 The image is upright
 The image is smaller than the object
Image Formed by a Convex
Mirror
Convex Mirrors

sometimes called a diverging mirror

The rays from any point on the object diverge
after reflection as though they were coming from
some point behind the mirror

The image is virtual because it lies behind the
mirror at the point where the reflected rays
appear to originate
Stations 6, 7,8: Got the bends 1,2,3
 Wheels,
 Mug,
carpeted or smooth surface
coin and water
 Laser
and different liquids
 REFRACTION
IS THE MESSAGE!
IS THE OBJECT YOU SEE REALLY
WHERE YOU THINK IT IS??
If you are trying to spear a fish, where should you aim??
Closer to you or farther away?
Aim closer!!
 You
are fooled into
thinking the light is
coming in a
straight line to your eye.
 The
fish is closer than you think
Following the Reflected and
Refracted Rays





Ray  is the incident
ray
Ray  is the reflected
ray
Ray  is refracted into
the lucite
Ray  is internally
reflected in the lucite
Ray  is refracted as it
enters the air from the
lucite
Refraction of Light

When a ray of light traveling through a
transparent medium encounters a boundary
leading into another transparent medium, part of
the ray is reflected and part of the ray enters the
second medium
 The ray that enters the second medium is bent
at the boundary

This bending of the ray is called refraction
Refraction of Light, cont


The incident ray, the
reflected ray, the
refracted ray, and the
normal all lie on the same
plane
The angle of refraction,
θ2, depends on the
properties of the medium
Refraction in a Prism

The amount the ray is
bent away from its
original direction is
called the angle of
deviation, δ
 Since all the colors
have different angles of
deviation, they will
spread out into a
spectrum


Violet deviates the most
Red deviates the least
Explaining the mysteries of nature
with physics!!



If a raindrop high in the sky is observed, the red ray is
seen
A drop lower in the sky would direct violet light to the
observer
The other colors of the spectra lie in between the red
and the violet
Explaining nature’s rainbows pt2

At the back surface the light
is reflected
 It is refracted again as it
returns to the front surface
and moves into the air
 The rays leave the drop at
various angles


The angle between the white
light and the violet ray is 40°
The angle between the white
light and the red ray is 42°
Total Internal Reflection:
like aiming a pebble at just the right angle so
it skips off the water

Total internal reflection
can occur when light
attempts to move from
a medium with a high
index of refraction to
one with a lower index
of refraction

Ray 5 shows internal
reflection
Station 9: It all adds up

Superposition and
interference

Colorado website
light/sound/water waves

http://faraday.physics.utoronto.ca/IYearLab/Intro
s/StandingWaves/Flash/reflect.html
Interference of Waves

Two traveling waves can meet and pass through
each other without being destroyed or even
altered
 Waves obey the Superposition Principle


If two or more traveling waves are moving through a
medium, the resulting wave is found by adding
together the displacements of the individual waves
point by point
Actually only true for waves with small amplitudes
Constructive Interference

Two waves, a and b,
have the same
frequency and
amplitude


Are in phase
The combined wave,
c, has the same
frequency and a
greater amplitude
Destructive Interference

Two waves, a and b,
have the same
amplitude and frequency
 They are 180° out of
phase
 When they combine, the
waveforms cancel
Interference
 Constructive
interference
 Destructive
interference
Nodes or
areas of zero
amplitude

CD vs DVD
 See
ppt on ‘applications’
 See Word document on ‘light stations’
Producing a Sound Wave

Sound waves are longitudinal waves traveling
through a medium
 A tuning fork can be used as an example of
producing a sound wave
Using a Tuning Fork to Produce
a Sound Wave




A tuning fork will produce a pure
musical note
As the tines vibrate, they disturb
the air near them
As the tine swings to the right, it
forces the air molecules near it
closer together
This produces a high density
area in the air

This is an area of compression
Using a Tuning Fork, cont.

As the tine moves toward
the left, the air molecules
to the right of the tine
spread out
 This produces an area of
low density

This area is called a
rarefaction
Using a Tuning Fork, final


As the tuning fork continues to vibrate, a succession of
compressions and rarefactions spread out from the fork
A sinusoidal curve can be used to represent the
longitudinal wave

Crests correspond to compressions and troughs to rarefactions
Speed of Sound

Speed is higher in solids than in gases

The molecules in a solid interact more strongly

Can you use this info to hear better?

Old mechanic’s trick of putting one end of a
wrench against forehead and other against part
of engine to ‘listen’ for source of engine noise

Try different spots on engine

Noise will be loudest at one spot
Categories of Sound Waves

Audible waves



Infrasonic waves



Lay within the normal range of hearing of the human
ear
Normally between 20 Hz to 20,000 Hz
Frequencies are below the audible range
Earthquakes are an example
Ultrasonic waves


Frequencies are above the audible range
Dog whistles are an example
Applications of Ultrasound

Can be used to produce images of small objects
 Widely used as a diagnostic and treatment tool
in medicine





Ultrasonic flow meter to measure blood flow
May use piezoelectric devices that transform electrical energy into
mechanical energy
• Reversible: mechanical to electrical
Ultrasounds to observe babies in the womb
Cavitron Ultrasonic Surgical Aspirator (CUSA) used to surgically remove
brain tumors
Ultrasonic ranging unit for cameras
Intensity of Sound, I

Threshold of hearing



Threshold of pain



Faintest sound most humans can hear
About 1 x 10-12 W/m2
Loudest sound most humans can tolerate
About 1 W/m2
The ear is a very sensitive detector of sound
waves

It can detect pressure fluctuations as small as about 3
parts in 1010
What are decibels?
β
is the intensity level or the decibel level
of the sound compared to the human
threshold of hearing
I
  10 log
Io
 Io is the threshold of hearing
Various Intensity Levels
 Threshold
of hearing is 0 dB
 Threshold of pain is 120 dB
 Jet airplanes are about 150 dB
 Table 14.2 lists intensity levels of various
sounds

Multiplying a given intensity by 10 adds 10 dB
to the intensity level
Frequency Response Curves

Bottom curve is the
threshold of hearing



Threshold of hearing is
strongly dependent on
frequency
Easiest frequency to hear is
about 3300 Hz
When the sound is loud (top
curve, threshold of pain) all
frequencies can be heard
equally well
What can you normally hear?
What defines hearing loss?
What, if anything, can ‘old people’ hear?
 Can’t
hear high frequencies, 14,000 Hz max
 Not bad if you look at the previous graph
 Take a hearing test
 http://www.phys.unsw.edu.au/jw/hearing.ht
ml
 Is
this normal aging process useful info?
 It’s the basis for ‘The Mosquito’!
The Mosquito…
innovation driven by need
 http://en.wikipedia.org/wiki/The_Mosquito
 http://www.nytimes.com/2005/11/29/inter
national/europe/29repellent.html
 http://www.npr.org/templates/story/story.p
hp?storyId=129581152
Sound and NASCAR
 Why
do the cars sound funny when they
go by?
 http://www.youtube.com/watch?v=a3RfUL
w7aAY&feature=related
Doppler Effect
 Commonly
 But
common to all waves
 Usually


experienced with sound waves,
experienced with
listener being stationary and
source in motion
Source in Motion

As the source moves toward
the observer (A), the
wavelength appears shorter
and the frequency increases


car moving toward him sounds
high pitched
As the source moves away
from the observer (B), the
wavelength appears longer
and the frequency appears to
be lower

Car moving away from her
sounds lower pitched
When object is moving so fast it is ‘catching’ up
with the sound waves it’s producing….


Shock waves carry
energy concentrated on
the surface of the cone,
with correspondingly
great pressure variations
A jet produces a shock
wave seen as a fog
Interference of Sound Waves

Sound waves interfere



Constructive interference
Destructive interference
Example of concert halls, auditioriums

Sound is produced on stage
• Reflected by walls, etc
• Can be absorbed by curtains, seats, etc.
• Can be transmitted through walls, etc.

Acoustic design is extremely important to performers and to
the audience
Sound and Musical Instruments
 String
 Brass
 Woodwinds
 Percussion
Standing Waves on a String

Nodes must occur at the ends of the string
because these points are fixed
Standing Waves on a String,
final

The lowest frequency of
vibration (b) is called
the fundamental frequency
n
ƒ n  n ƒ1 
2L

F

Affected by:



F, tension of string,
L, length of vibrating portion of string,
Mass/unit length of the string
Standing Waves on a String –
Frequencies

ƒ1, ƒ2, ƒ3 form a harmonic series



ƒ1 is the fundamental and also the first harmonic
ƒ2 is the second harmonic
Waves in the string that are not in the harmonic
series are quickly damped out
When the string is disturbed,
it “selects” the standing wave
frequencies
Compare the equation variable to the
different parts of the instrument
 How



can these be varied
Tension
Length of string vibrating
Mass/unit length of string?
 Violin,
 What
viola, cello, bass, harp, piano…
is the function of the body of the
instrument?
Let’s compare
 Tuning
fork C at 256 ?
 Instrument’s
C…
Forced Vibrations
A
system with a driving force will force a
vibration at its frequency
 When the frequency of the driving force
equals the natural frequency of the
system, the system is said to be in
resonance
An Example of Resonance



Pendulum A is set in
motion
The others begin to
vibrate due to the
vibrations in the flexible
beam
Pendulum C oscillates
at the greatest
amplitude since its
length, and therefore
frequency, matches that
of A
Other Examples of Resonance
 Child
being pushed on a swing
 Shattering glasses
 Tacoma Narrows Bridge collapse due to
oscillations by the wind
 Upper deck of the Nimitz Freeway
collapse due to the Loma Prieta
earthquake
Brass
 Air
goes in one end and out the other
 Valves
are used to alter the total length of
the pipe
Woodwind
 Air
goes in one end and out at many
places

Generally ‘open ended’
 Keys
are used to alter the length of the
vibrating column
Standing Waves in Air Columns
 If
one end of the air column is closed, a
node must exist at this end since the
movement of the air is restricted
 If the end is open, the elements of the air
have complete freedom of movement and
an antinode exists
Tube Open at Both Ends
Resonance in Air Column Open
at Both Ends
 In
a pipe open at both ends, the natural
frequency of vibration forms a series
whose harmonics are equal to integral
multiples of the fundamental frequency
v
ƒn  n
 n ƒ 1 n  1, 2, 3,
2L
V
velocity of air
 L length of air column
Tube Closed at One End
Resonance in an Air Column
Closed at One End
 The
closed end must be a node
 The open end is an antinode
v
fn  n
 n ƒ1
4L
 There
n  1, 3, 5,
are no even multiples of the
fundamental harmonic
V
velocity of air
 L length of air column
Beats



Beats are alternations in loudness, due to interference
Waves have slightly different frequencies and the time
between constructive and destructive interference
alternates
The beat frequency equals the difference in frequency
between the two sources:
ƒb  ƒ2  ƒ1
Quality of Sound –
Tuning Fork

Tuning fork produces
only the fundamental
frequency
Quality of Sound –
Flute

The same note
played on a flute
sounds differently
 The second harmonic
is very strong
 The fourth harmonic
is close in strength to
the first
Quality of Sound –
Clarinet

The fifth harmonic is
very strong
 The first and fourth
harmonics are very
similar, with the third
being close to them
Timbre
 In
music, the characteristic sound of any
instrument is referred to as the quality of
sound, or the timbre, of the sound
 The quality depends on the mixture of
harmonics in the sound
Pitch

Pitch is related mainly, although not
completely, to the frequency of the sound
 Pitch is not a physical property of the sound
 Frequency is the stimulus and pitch is the
response

It is a psychological reaction that allows humans
to place the sound on a scale
The Ear

The outer ear consists of
the ear canal that
terminates at the eardrum
 Just behind the eardrum
is the middle ear
 The bones in the middle
ear transmit sounds to
the inner ear