Topic 11: Wave phenomena
11.1 Standing (stationary) waves
11.1.1 Describe the nature of standing
(stationary) waves.
Students should consider energy transfer,
amplitude and phase.
Formation of standing waves
The reflected wave is 180º phase
shifted
How do the incident and reflected
waves superimpose?
Reflection from fixed or free end
Boundary conditions on a string
Click to play
Pulse
Boundary conditions for a wave
Click to play
Standing wave
Standing wave
Nodes and antinodes
λ
Hyperlink
Modes of vibration in strings
Hyperlink
λ
λ
Standing waves on a string
Click to play
Fixed / free
Free / free
Fixed / fixed
15 cm
2m
rubber cord (4 mm2)
vibration
generator
Set up this experiment and
produce the first 8 standing
waves. Record the wavelength
for each one. Record the
frequency for each resonant
standing wave. Plot a suitable
graph to determine the
relationship between frequency
and wavelength.
bench
Frequency Adjust
5
3
7
2
8
1
10Hz
100Hz
1kHz
10kHz
9
100kHz
Frequency range
1000
100
10
1
1000
10
100
Frequency
Wave
55 Hz
power
signal generator
Outputs
A
Modes of vibration in pipes
Closed pipe i.e.
node at one end and
antinode at the other
Hyperlink
Open pipe i.e.
Antinode at
both ends.
Nodes and antinodes
Nodes and Antinodes
A 0.3 m section of discarded garden hose will produce a trumpet sound when
blown as one blows a trumpet. Changing the length will change the pitch of the
"trumpet".
Measurement of velocity of sound
1. Measure difference in length between
2 successive resonances.
2. Use this distance to calculate the
wavelength.
3. Use this value and the frequency of
the tuning fork to calculate the speed
of sound.
http://www.physics.uc.edu/~sitko/CollegePhysicsIII/
Questions from Hamper page 134 Q’s 15,16.
Hyperlink
Complete the table
Stationary wave
Amplitude
Frequency
Wavelength
Phase
Energy
Traveling wave
Stationary wave
Traveling wave
Amplitude
All points have different amplitudes.
Maximum at the antinodes.
All points have the same amplitude.
Frequency
Same for all points on the wave.
Same for all points on the wave.
Wavelength
Double the distance between 2 nodes.
Distance between 2 successive points in
phase.
Phase
All points between 2 nodes are in phase.
All points along 1 wavelength have a
different phase.
Energy
Energy is not transmitted by the wave, but
contained within it.
Energy is transmitted by the wave.
Questions from Tsokos
• Page 256 Questions 1 – 6,8,10-14.
The Doppler effect
Johann Christian Doppler
1803-1853
The diagram below represents waves emitted by a
source of sound, S, which is stationary relative to
the air.
The velocity of the sound waves relative to the air is v.
Doppler wavefronts
Click to play
Doppler hyperlink
Which gives you the most
chocolates?
Explain the Doppler effect by
reference to wavefront diagrams for
moving-detector and moving-source
situations.
The next diagram represents waves emitted by a source
which is moving (with velocity vs) relative to the air.
λ
λ
Speed same, frequency and wavelength change
Motion of the source produces a change in the wavelength,
longer wavelength behind, shorter wavelength in front of source.
Doppler effect for sound
Hyperlink
Doppler effect for sound with
moving observer
Moving observer
Wavelength fixed, speed and frequency change
Doppler shift for SOUND source
Be careful to apply the + or – the correct way.
Doppler sound problems
Answers
Questions
Tsokos page 248 Q’s 1-7
Hamper page 136 Q’s 17-19.
Solve problems on the Doppler effect
for electromagnetic waves using the
approximation
Students should appreciate that the
approximation
may be used only when v << c.
Caught by the fuzz.
Take the case of the car and the radar speed trap. The
emitted frequency of the police radar gun is f, the car acts like
a moving observer receiving it at f'. It reflects it back at f',
acting now as a moving source and the police receive it back
shifted once again as f''.
The total change in frequency (f'' - f) is therefore doubled.
Question
It can be shown that the relative Doppler shift for electromagnetic radiations like light, radio waves etc is given
(approximately) by
where c is the speed of light and v is the relative speed of
source and observer. The speed of a car is being measured by
a police-person using a "radar speed-measuring gun". The
frequency of the transmitted signal is 5GHz. When "mixed" the
transmitted and received signals beat with a frequency of
750Hz. If the speed limit for the road is 110kmh-1, should the
driver be fined or not?
Adding colour
Analysing blood flow
Questions
Hamper page 138 Q’s 20-22.
11.3 Diffraction
Sketch the variation with angle of
diffraction of the relative intensity of
light diffracted at a single slit.
Hyperlink
Diffraction
Because of Huygen’s Principle, light passing through barriers do not
continue as straight plane waves as in (a), but as spherical waves as
in (b). This spreading out is called diffraction.
Even a single slit can
produce interference!
This occurs because light
waves from one part of the
slit can interfere with light
waves from another part of
the slit.
Hyperlink
Diffraction at a single aperture
Single slit
distant screen
intensity
across
screen
Effect of slit width
Single Aperture Diffraction
Pattern
Single Aperture Diffraction
Pattern: Narrower Aperture
Effect of wavelength
θ =λ/b
θ =2λ/b
Derive the formula
If the path difference
between rays from C and A
to a point on a distant
screen is λ, then the path
difference between rays
from A and B is λ/2.
There will therefore be destructive interference between light
from A and light from B. From the diagram, it is clear that
Now consider the aperture to be made up of pairs of point
sources, A and B, A’ and B’, etc, as shown in the next diagram.
Light from all these pairs of points will also interfere
destructively
Now consider the aperture to be made up of pairs of point
sources, A and B, A’ and B’, etc, as shown in the next diagram.
Light from all these pairs of points will also interfere
destructively
As the angles are small, we can write
IB Question
Red light from a laser is passed through a single narrow slit, as shown in Figure 1. A
pattern of bright and dark regions can be observed on the screen which is placed
several metres beyond the slit.
(a) The pattern on the screen may be represented as a graph of intensity against
distance along the screen. The graph has been started in outline in Figure 2. The
central bright region is already shown. Complete this graph to represent the rest of the
pattern by drawing on Figure 2.
(b) State the effect on the pattern if each of the following changes is made separately.
(i) The width of the narrow slit is reduced
(ii) With the original slit width, the intense red source is replaced with an intense
source of green light.
intensity
screen
narrow slit
laser
distance along screen
centre of pattern
Figure 2
Figure 1
Questions
Hamper page 141 Q’s 23,24
Tsokos page 265 Q’s 1-3a.
11.4 Resolution
2 objects can just be resolved
when the maximum of 1 peak
aligns with the minimum of the
second peak
Resolution by separation of
sources
Click to play
Resolution depending on aperture
Click to play
Resolution depending on
wavelength
Click to play
Circular apperture
Diffraction/interference patterns
Hyperlink
When the maxima in an interference pattern (or
from two light sources) are too close together, it
cannot be determined that there are actually two
sources…thus it would be “unresolved”
2 objects to be resolved
L
D
b
θ=L/D
Problem
The camera of a spy satellite orbiting at 200. km
above the ground has a diameter of 35.0 cm.
What is the smallest distance this camera can
resolve on the surface of the Earth? (Assume an
average wavelength of 500. nm for visible light)
The headlights of a car are 2.00 m apart. The pupil of
the human eye has a diameter of about 2.0 mm.
Suppose that light of wavelength 500. nm is being
used. What is the maximum distance at which the
two headlights are seen as distinct?
The pupil of the human eye has a diameter of about
2.0 mm and the distance between the pupil and the
back of the eye (the retina) where the image is formed
is about 20. mm. Suppose the eye uses light of
wavelength 500 nm. Use this information to estimate
the distance between the receptors in the eye.
Questions
Hamper page 143 Q’s 25,26,27.
Tsokos page 270 Q’s 1-4.
Describe the significance of resolution in the
development of devices such as CDs and DVDs, the
electron microscope and radio telescopes.
What limits the resolution of a
microscope, DVD, or telescope?
11.5 Polarisation
Consider a single wave of light:
If you looked at it “end on” it might look like this:
And lots of them
might look like this:
Plane polarised e.m. wave
Plane polarised wave
Click to play
Describe what is meant by
polarized light.
Polarisation
Hyperlink
State and apply Brewster’s law.
Φ
For a particular angle Φ, the beam
is completely plane-polarised,
Brewster found that
where n is the refractive
index of the material
Polarising Filter
Picture has hyperlink
Hamper page 145 Q’s 28,29.
Polarisation of microwaves
Explain the terms polariser and
analyser.
Hyperlink
2I0
A beam of unpolarized light can be thought of
as containing a uniform mixture of linear
polarizations at all possible angles. Since the
average value of cos2θ is 1/2, the
transmission coefficient becomes
2I0 = I0
Hamper page 146 Q 30
Calculate the intensity of a transmitted
beam of polarized light using Malus’
law.
2I0
Optical activity
Some materials can rotate the plane of polarisation of light as
it passes through them.
The liquid crystals used
in calculator displays,
digital watches and lap
top computer screens are
also optically active. The
amount of rotation in
these crystals can also
be altered by applying an
electric field between the
two faces of the screen
and this is how the
display is turned from
bright to dark.Fig1.
The polarimeter
Describe the use
of polarization in
the determination
of the
concentration of
certain solutions.
The specific rotation of a given
liquid may be found using a
polarimeter as shown in Figure 2.
The two polaroids are adjusted to
give a minimum light intensity, and
the scale reading noted. A
measured length of solution of
known concentration is then placed
in the inner tube and the polaroids
readjusted to regain a minimum
and the scale is read again. The
rotation of the plane of polarization
of the light by the solution may then
be found from the difference in the
two scale readings.
POLARIMETER
analyser
liquid
polariser
h
Measuring the concentration of solutions
Certain solutions rotate the plane of polarisation of light
passing through them. The angle through which the plane
of polarisation is rotated depends on the concentration of
the solution.
Hamper page 148 Q31.
Outline qualitatively how polarisation may be
used in stress analysis.
The first photograph below shows
a small part of a plastic set square
viewed under normal conditions
The next photograph shows the
same object when placed
between crossed polaroids
Liquid crystal displays
The screen of an LCD TV is made of millions of liquid crystals. Each
crystal is like the shutter of a camera either blocking the light or allowing it
to pass through. You can control the amount of light that passes through
by applying a voltage to a crystal or pixel. It does this by rotating the plane
of polarisation of the light. A much-simplified diagram of this action is
shown in Figure 1.
Questions
Hamper page 149 practice questions 4-8.
Tsokos page 278 Q’s 1-4,7,11,17,18,19.