Download Waves Revision

Waves
Classification of Waves
• Waves can be classified as either
mechanical or electromagnetic.
• Mechanical wave examples: water waves,
waves on a spring, sound waves and
ultrasonic waves.
• Mechanical waves must have a medium to
travel through and cannot travel in a
vacuum.
• A mechanical wave passing through a
medium is vibrations being passed on from
molecule to molecule.
Classification of Waves
• Electromagnetic wave examples: radio
waves, microwaves, infra-red waves,
‘visible’ light waves, ultraviolet waves, Xrays and gamma-rays.
• Electromagnetic waves can travel through
a vacuum and do not need a medium to
travel through.
• Electromagnetic waves travel fastest in a
vacuum at a speed of 3 x 108 metres per
second (speed of light).
Waves on a Spring
• If you hold a number of coils together – called a
compression – let them go and the compression
moves along the spring.
• After the compression passes a point on the
spring, the coils in that part become stretched
more than normal.
• This is called a rarefaction.
Waves Are a Means of
Transferring Energy
• When waves move along water or a rope, there is
no overall motion as the wave passes.
• As the wave pulse passes a point, the medium
around the point is disturbed, but when the pulse
has passed, the medium at that point is no longer
moving.
• A Travelling Mechanical Wave is a disturbance
carrying energy through a medium without any
overall motion of that medium.
Electromagnetic Waves
• When an electromagnetic wave passes
through a region of space, there is a
rapidly changing electric and magnetic
field in that region.
• By this means, energy gets transferred
from one place to another by the wave
(Heat energy).
• A travelling wave, either mechanical or
electromagnetic, is a disturbance that
travels out from the source producing it,
transferring energy from the source to
other places through which it passes.
Some definitions…
Crest
1) Amplitude – this is
height of the wave.
Trough
2) Wavelength () – this is the
distance between two
corresponding points on the
wave and is measured in metres:
3) Frequency – this is how many waves pass by a
point every second and is measured in Hertz (Hz)
Longitudinal Wave
Some definitions…
Transverse waves are
when the displacement
is at right angles to the
direction of the wave…
e.g.Light
Longitudinal waves
are when the
displacement is
parallel to the
direction of the wave…
e.g.Sound
Transverse waves are when
the oscillation is at 90o to the
direction of propagation
Longitudinal waves
are when the
oscillation is parallel
to the direction of
propagation
“Seeing” a wave
1) Quiet sound, low frequency
(i.e. high wavelength):
2) Quiet sound, high frequency
(i.e. low wavelength):
3) Loud sound, low frequency:
4) Loud sound, high frequency:
The Wave Equation
The wave equation relates the speed of the wave to its
frequency and wavelength:
Wave speed (v) = frequency (f) x wavelength ()
in m/s
in Hz
in m
V
f

f
Remember Frequency – this is how many waves
pass by a point every second and is measured in
Hertz (Hz)
Using this formula we can
convert any wavelength to a
frequency.
Some example wave equation questions
1) A water wave has a frequency of 2Hz and a wavelength of 0.3m.
How fast is it moving?
0.6m/s
2) A water wave travels through a pond with a speed of 1m/s and a
frequency of 5Hz. What is the wavelength of the waves?
0.2m
3) The speed of sound is 330m/s (in air). When Dave hears this sound
his ear vibrates 660 times a second. What was the wavelength of
the sound?
0.5m
4) Purple light has a wavelength of around 6x10-7m and a frequency of
5x1014Hz. What is the speed of purple light?
3x108m/s
Reflection
• Reflection is when a wave meets an
obstacle in its path, it bounces off that
obstacle.
• This can be seen with a
water wave, the reflection
of light waves in a mirror
and sound waves through
an echo.
Reflection
Waves Changing Speed
• Waves change speed when they go from
one medium to another.
• Their frequency remains the same.
• The wavelength increases if the wave
speeds up and the wavelength decreases
if the wave slows down.
Refraction through a glass block:
Wave slows down and bends
towards the normal due to
entering a more dense medium
Wave slows down but is
not bent, due to entering
along the normal
Wave speeds up and bends
away from the normal due to
entering a less dense medium
Refraction
Refraction is when waves ____ __ or slow down due to
travelling in a different _________. A medium is
something that waves will travel through.
In this case the light rays are slowed down by the water
and are _____, causing the ruler to look odd. The two
mediums in this example are ______ and _______.
Words – speed up, water, air, bent, medium
The wavelength also changes.
Internet Diagram
Wave diagrams
1) Reflection
2) Refraction
3) Refraction
4) Diffraction
Diffraction
Diffraction is when waves spread out from the edge of a gap.
More diffraction if the size of the gap is similar to the wavelength
More diffraction if wavelength is increased (or frequency decreased)
Sound bends better around corners
Interference of Waves
• Interference is when two waves from two
sources meet and a new wave is produced.
• When waves arrive crest with crest and
trough with trough, they are said to be in
phase.
Interference of Waves
Finding the Critical Angle…
1) Ray gets refracted
3) Ray still gets refracted (just!)
THE CRITICAL
ANGLE
2) Ray still gets refracted
4) Ray gets
internally reflected
Uses of Total Internal Reflection
Optical fibres:
An optical fibre is a long, thin, transparent rod made of glass
or plastic. Light is internally reflected from one end to the
other, making it possible to send large chunks of
information
Optical fibres can be used for communications by sending e-m signals
through the cable. The main advantage of this is a reduced signal loss.
Also no magnetic interference.
It is important to coat the strand in a material of low n.
The light can not leak into the next strand.
Other uses of total internal reflection
1) Endoscopes (a medical device used to see inside the body):
2) Binoculars and periscopes (using “reflecting prisms”)
How does ultrasound work?
Ultrasound is the region of sound above 20,000Hz – it can’t
be heard by humans. It can be used in pre-natal scanning:
How does it work?
Ultrasonic waves are partly _________ at the boundary as they pass from
one _______ to another. The time taken for these reflections can be
used to measure the _______ of the reflecting surface and this
information is used to build up a __________ of the object.
Words – depth, reflected, picture, medium
Other uses of ultrasound
1) Echo sounding
The ultrasound is reflected from the
sea floor.
2) Breaking down kidney stones
Ultrasonic waves break kidney
stones into much smaller pieces
3) Cleaning (including teeth)
Ultrasound causes dirt to vibrate
dirt off without damaging the object
The electromagnetic spectrum
Each type of radiation shown in the electromagnetic spectrum has a
different wavelength and a different frequency:
High frequency,
short wavelength
Gamma
rays
X-rays
Low frequency,long
wavelength
Ultra violet
Visible
light
Infra red
Microwaves
Radio/TV
γ
Each of these types travels at the same speed through a vacuum and can
be polarised. Different wavelengths are absorbed by different surfaces
(e.g. infra red is absorbed very well by black surfaces). This absorption
may heat the material up (like infra red and microwaves) or cause an
alternating current (like in a TV Ariel).
The higher the frequency of the wave, the greater its energy.
This makes X-rays dangerous and radio waves safe
Detection
• Waves invisible to
the eye have to be
detected using
special apparatus
• IR (Infra-Red) is
a heat wave so a
blackened
thermometer bulb
Night Vision Camera
• Of course we could just skip forward
100years
UV Light
• Ever walked into a nightclub
• White cloth washed in optical
brighteners glows in UV light
Gamma
• Bubble chambers where the wave
leaves a trail of bubbles
How Microwaves and Infra-red work
Microwaves are absorbed by
water molecules up to a depth of
a few centimetres. The heat
then reaches the centre of the
food by conduction.
Infra-red waves are absorbed by
the surface of the material and
the energy is then passed to the
centre of the food by
conduction.
The higher the frequency of the
wave, the greater its energy
X-rays and gamma () rays
X-rays are absorbed by ____ parts of the body, like ____.
Unfortunately, over-exposure to x-rays will damage cells.
Gamma rays can be used to treat _______. A
gamma ray source is placed outside the body
and rotated around the outside of the tumour.
Doing this can ___ the cancerous cells without
the need for ______ but it may damage other
cells and cause sickness.
Tracers can also be used – these are small amounts of
___________ material that can be put into a body to see
how well an organ or ______ is working.
Words – radioactive, gland, cancer, hard, bones, kill, surgery
Sun is not
Yellow
As the light is filtered through
more atmosphere more
frequencies absorbed
Sky appears blue as scattered blue light from sun appears
to be coming from lots of different directions
Wave 1
Wave 2
Resultant wave
Coherent Waves
• Same Frequency
• In Phase
Or Constant phase
difference
Phase difference in
measured in
degrees of a circle
Coherent Waves
• Same Frequency
• In Phase
Or Constant phase
difference
Phase difference in
measured in
degrees of a circle
Interference is where 2 coherent waves meet.
The resultant is the algebraic sum of the 2
waves at any point.
+
=
Constructive
Interference
If 180 degrees out of phase.
+
=
Destructive
Interference
To Remember this we simplify it a little
White Light Interference
Proving the wave nature of Light
To get two
n=1
n=0
n=1
Constructive Interference
coherent
sources (same
frequency and
phase) we use one
source and two
slits.
The interference
patterns prove
light is a wave.
Internet Example
Equation
d

• d = 1/(N x1000)
(Grating Const
lines/mm)
n=1
So one wavelength
difference 
Constructive
Interference
Equation
• sin  = /d
• d sin  = 

d


• When more than one
wavelength difference
• d sin  = n
For the n=2 dot
2
• sin  = 2/d
• d sin  = 2
d


• When n wavelength
differences
• d sin  = n
• What we actually see on the screen is a
series of bright lines called fringes
where there is constructive interference.
This an interference pattern
n=3
n=1 n=1
n=2
n=0 n=2
n=3
3
wavelengths
difference
in path
MEASUREMENT OF THE WAVELENGTH
OF MONOCHROMATIC LIGHT
n=2
Metre
stick
n=1
Laser
θ
x
n=0
Diffraction
grating
D
Tan θ = x/D
n=1
n=2
1. Set up the apparatus as shown. Observe the
interference pattern on the metre stick – a series of
bright spots.
2. Calculate the mean distance x between the centre
(n=1) bright spot and the first (n =1) bright spot on
both sides of centre.
3. Measure the distance D from the grating to the
metre stick.
4. Calculate θ.
5. Calculate the distance d between the slits, using
d=1/N the grating number.
Calculate the wavelength λ using nλ = dsinθ.
6. Repeat this procedure for different values of n
and get the average value for λ
As nλ = dsinθ if d gets larger
then θ gets smaller
H/W
• 2005 HL Q7
Polarization of Light
Normally all e-m waves (Transverse) oscillate
in all perpendicular planes at once.
Polarization leaves only one plane of oscillation
Sound is a longitudinal wave and so can not be
Polarised
Polarizing Filters
Polarisation is the taking a transverse wave
that oscillates in all perpendicular planes
and filtering it so it oscillates in only one
perpendicular plane.
Hydrocarbons that absorb light that is
in it’s plane of orientation.
Standing Waves
When two coherent waves of the same amplitude traveling in
opposite directions meet the waves combine to form a
stationary wave
We draw this as the two extremes
n
A

http://www.absorblearning.com/media/attachme
nt.action?quick=8u&att=628
Real Standing Waves
Strings
/2
Closed
Tubes
/4
Open
Tubes
/2
MEASUREMENT OF THE SPEED
OF SOUND IN AIR
Tuning fork
A
l1
N
Graduated
cylinder
Tube
Water
MEASUREMENT OF THE SPEED
OF SOUND IN AIR
Tuning fork
l1
d
λ = 4(l1 + 0.3d)
Graduated
cylinder
Tube
Water
Method
1.
Strike the highest frequency (512 Hz)
tuning fork and hold it in a horizontal
position just above the mouth of the
tube.
2. Slide the tube slowly up/down until the
note heard from the tube is at its
loudest; resonance is now occurring.
3. Measure the length of the air column
(from the water level to the top of the
tube) l1 with a metre stick.
• An end correction factor has to be added to the
length e = 0.3d, where d is the average internal
diameter of the tube (measured using a vernier
callipers).
• Hence λ = 4(l1 + 0.3d)
•
•
c = f
c = 4f(l1 + 0.3d).
• Calculate a value of c for each tuning fork and
find an average value for the speed of sound.
Harmonics
Whole number multiples of the fundamental
frequency that happen at the same time as
the fundamental.
Violin Harmonics
Viola Harmonics
You can hear
the
difference as
the two
instruments
have
different
combinations
of harmonics
Stretched String
A low note on a Double Bass
contains all the harmonics
above it.
This is what gives the
instrument its pleasant
timbre or quality.
Formula for stretched string
1 T
frequency 
2l 
1
f
l
L=length
T=tension
=mass/unit length
f T
INVESTIGATION OF THE
VARIATION OF FUNDAMENTAL
FREQUENCY OF A STRETCHED
STRING WITH LENGTH
Tuning
Fork
Paper rider
l
Sonometer
Bridge
Place the bridges as far apart as possible.
Strike the turning fork putting the end on the
bridge and reduce the length until the maximum
vibration is reached (the light paper rider should
jump off the wire).
Measure the length with a metre rule.
Note the value of this frequency on the tuning
fork.
Repeat this procedure for different tuning forks
and measure the corresponding lengths.
Plot a graph of frequency f
against inverse of length 1
f
l
1
l
INVESTIGATION OF THE VARIATION
OF THE FUNDAMENTAL FREQUENCY OF
A STRETCHED STRING WITH TENSION
Paper
rider
l
Pulley
Sonometer
Bridge
Weight
•Select a wire length l (e.g. 30 cm), by suitable
placement of the bridges. Keep this length
fixed throughout the experiment.
•Strike the tuning fork and hold it on the
bridge.
•Increase the tension by adding weight slowly
from lowest possible until resonance occurs.
(Jumping paper)
•Note tension from weight used (In Newtons)
and frequency from the tuning fork.
Plot a graph of frequency f
against square root of the tension
f
T
Musical Notes
Music waves have a regular
shape where noise is irregular
Three Qualities – called the characteristics
1. Pitch - This is frequency of the wave.
2. Loudness - this is the amplitude of the
wave.
3. Timbre or Quality - The wave shape that is
mainly due its overtones.
Demo
• Oscilloscope and microphone
Resonance
• Transfer of energy between two
objects with the same, or very
similar, natural frequency.
Barton’s Pendulum
String
Resonance
• If we set the driver in motion
Resonance
• The energy is transferred only to the
pendulum of the same length.
Barton’s Pendulum
Resonance
• And back again for a remarkably long
time.
A Stationary Source
• The waves
radiate out
from the
source
• The
wavelength
detected at
A is the same
as at B
A moving Source
• The waves
still radiate
out from the
source
• The
wavelength
detected at
A is the
longer than
that at B
Movement
of source
Doppler Effect
The apparent change in frequency due to
the motion of the observer or the source
• Hence the change in pitch as a car passes
• Used by the Gardai in to detect speeding cars
Red Shift of Stars
(Doppler in Light)
The Sun
Moved to longer
wavelengths proving the
star is moving away from us
Oh Bugger!
Example.
A train emits a whistle at 700Hz what is the
apparent frequency if it is traveling towards
you at 30m/s? (c=340m/s)
Using f’ = f.c/(c-v)
f’ = 700.340/(340-30)
= 767 Hz
Where f= Source Frequency and f’=Apparent Frequency
C=Speed of Wave and v=Speed of Object
H/W
• 2003 HL Q7
Tuning Forks - Both prongs
vibrate and create sound
Summary - Sound as a Wave
Interference proves sound is a wave.
If we twist a
tuning fork near
our ear it goes
loud and soft.
The two prongs
of the fork are
interfering with
each other.
L
O
U
D
S
O
F
T
L
O
U
D
S
O
F
T
L
O
U
D
S
O
F
T
L
O
U
D
S
O
F
T
Sound Intensity Level
• This is to measure the very large range of
energy levels the ear can respond to,
measured in decibels (dB). This is an
exponential scale so if the energy doubles
the level goes up by e dB.
• Home CD player 75 dB tops but a good rock
band maybe 110dB.
• Health and safety tell us that if you stay in
an environment above 85dB for more than 8
hrs you do permanent and un-repairable
damage to your ears. So Muse is right out.
Sound Intensity level
• Also called acoustic intensity level is a logarithmic
measure of the sound intensity in comparison to the
reference level of 0 dB (decibels).
• The measure of a ratio of two sound intensities is
• where J1 and J0 are the intensities.
• The sound intensity level is given the letter "LJ"
and is measured in "dB". Decibels (dB) are
dimensionless.
• If J0 is the standard reference sound
intensity, where
• (W = watt), then instead of "dB" we
use "dB SIL". (SIL = sound intensity
level).
• We also have dBA, which is adjusted
to allow for the range of the human
ear.
Acoustics
• Use reflections and direct sound to
amplify sound in a concert hall.
To achieve a loud sound:
* If necessary, reflectors and diffusers
may be used to provide beneficial supporting
sound reflections
* The interior surfaces of the hall should be
hard to ensure that sound energy is not
absorbed and lost.
Threshold of Hearing
• The absolute threshold of hearing
(ATH) is the minimum sound level of a
pure tone that an average ear with
normal hearing can hear in a noiseless
environment at 1kHz.
Limit of Audibility
• The top and bottom
values of the range are
known as the limits of
audibility.
•
For the human ear, the
lower limit is approximately
20 Hz and the upper limit is
20,000 Hz. In other words,
our ears are supposed to be
able to hear sound with
frequencies that are
greater than 20 Hz and less
than 20,000 Hz.
• Different people have
different ranges of
audibility.
• People who are old
cannot hear as well as
those who are young.
The ability of the ear
drum to respond to
sound decreases with
age and the range of
audibility becomes very
much reduced as the
lower limit rises and the
upper limit falls.
High Tension
Voltage
X-Rays
• Electrons jump from the
surface of a hot metal –
• Thermionic Emission
Accelerated by high voltage they smash into tungsten
The electrons excite orbiting electrons to high energy
orbits-see next few slides for details
These fall back emitting high frequency waves.
Most of the electron energy is lost as heat.-about 90%
X-rays very penetrating, fog film, not effected by fields.
Photons
• Bohr first suggested a model for the
atom based on many orbits at
different energy levels
E2
E1
Photons
• If the electron in E1 is excited it can
only jump to E2.
E2
E1
Photons
• Then the electron falls back. The gap
is fixed so the energy it gives out is
always the same
E2
E1
Photons
• So Max Planck said all energy must come in
these packets called photons.
• He came up with a formula for the
frequency
E2 –E1 = h.f
E2
E1
Where f=frequency
h= Planck’s constant
QuickTime™ and a
TIFF (Uncompressed) decompressor
are needed to see this picture.
Albert Einstein
• Uncle Albert was already a published
scientist but the relativity stuff had
not set the world alight.
• He set his career in real motion when
he solved a problem and started the
science of Quantum Mechanics that
the old world Jew in him could never
come to terms with.
The Problem
• If you shine light on the surface of
metals electrons jump off
e
e
e
e
e
Polished Sodium Metal
• Electrons emitted
• This is The PHOTOELECTRIC EFFECT
We can prove this with the
experiment below
A charged Zinc plate
is attached to an
Electroscope
When a U.V. lamp is
shone on the plate
the leaf collapses as
all the electrons
leave the surface of
the zinc
The Photoelectric Effect
The more intensity you gave it the
more electrical current was produced
However something strange happened
when you looked at frequency
Electron
Energy
Newtonian Physics
could not explain this
Frequency of
light
Einstein’s Law
So we define the Photoelectric effect as:-
Electrons being ejected from the surface of a metal by
incident light of a suitable frequency.
Uncle Albert used Plank’s theory that as energy came in
packets
A small packet would not give the electron enough energy to
leave
Low frequency light had too small a parcel of energy to get the
electron free.
Energy of each
photon = h.f
Photo-Electric Effect
Electron
Energy
f0=Threshold
Frequency
Frequency of
light
Energy of incident photon =
h.f = h. f0+ KE of electron
Work Function,
Energy to release Electron
Energy
left over
turned
into
velocity
Reflection
Wave bouncing off
a solid object
Refraction
Waves changing
speed and direction
due to change in
density of medium
Echo
Frequency
stays the
same
Better with
long
wavelength
Sound round
corners
Spreading from
slit
Interference
Two coherent
waves meeting
combine wave at
any point is the
algebraic sum of
the two waves
Proves
things are
waves
Constructive
and
destructive
Polarisation
Reduces transverse
waves to one plane
of oscillation
Difference
between
transverse and
longitudinal
Snow
sunglasses
Diffraction
spreading of a wave
around an obstacle
or on the emergent
side of a slit.
Hear people
across a lake