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Waves Notes FT/HT
Waves can be produced in ropes, springs and on the
surface of water.
When waves travel along ropes or springs or across the
surface of water they set up regular patterns of
disturbance. They are a way of transferring energy from
one point to another without transferring matter.
 The maximum disturbance caused by a wave is
called its amplitude
 The distance between a particular point on one
disturbance and the same point on the next is called
the wavelength
 The number of waves each second produced by a
source (or passing a particular point) is called the
frequency, and is measured in hertz (Hz).
We can find the speed of a wave from the formula;
wave speed
=
frequency
x wavelength
v  f 
v = velocity in m/s or ms-1
f = frequency in Hz (s-1)
 = wavelength in m.
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Example
This waveform has a wavelength of 3m. By inspection it
takes 2 seconds for a complete cycle (1 up & 1 down)
3m
To work out the frequency then wave speed we must
find out how many cycles there are in one second;
1
f 
time for a cycle
v  f 
1
f 
2s
f  0.5s 1
v  1 .5 m / s
f  0.5 Hz
v  0.5 Hz  3m
v  1.5ms
1
The formula can be rearranged to work out any of the
three variables.
v  f 
v

f
v
 f

Mr Powell HT & FT Notes Year 11 Physics 2003/4
Simple Wave Questions
1. Work out the frequency of a wave which travels at a
speed of 666ms-1 and has a wavelength of 3m?
2. What is the speed of a wave which has a frequency of
125Hz, and wavelength of 0.03m?
3. What is the speed of a wave which has a frequency of
2000Hz, and wavelength of 73m?
4. What is the wavelength of a wave travelling at 10,000
ms-1 if its frequency is 25MHz?
5. What is the speed of a wave with wavelength of
0.000001m and frequency 1 MHz?
Answers
1. 666 ms-1/ 3 m = 222 s-1 = 222 Hz
2. 125 Hz x 0.03m = 3.75 m/s = 3.75 ms-1
3. 2000 Hz x 73m = 146,000 m/s = 146 kms-1
4. 10,000 ms-1 / 25 MHz = 10,000 ms-1 / 25,000,000 Hz
= 0.0004 m = 0.4 mm
5. 0.000001m = 1 x 10-6 m and 1 MHz = 1,000,000s-1
Therefore the product of the two = 1;
0.000001m x 1,000,000s-1 = 1 ms-1
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Reflection
Waves travelling along a rope
or spring, or across the surface
of water, can be reflected.
When this wave reaches a
concrete harbour, some of the
energy of the wave is absorbed
and some is reflected.
If we look at
this image we
can see how
light
waves
reflect off the
surface of the
water.
Normal
Incident ray
Reflected ray
i
r
i = r
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Questions
1. When a water wave reaches the shore what happens
to the energy carried in the wave?
2. What is the law of reflection?
3. Draw a diagram to show this?
4. What happens when a light wave or ray is incident on
a 100% mirror?
5. What would happen if a light wave or ray was incident
on a 50% mirror?
Answers
1. Some energy is reflected back into the sea and some
is absorbed by the land.
2. The angle of reflection is the same as the angle of
incidence from the normal.
3. See notes above.
4. All of the light is reflected back away at the same
angle from the normal as it arrives.
5. Half of the light would go through and half of the light
would behave as in question 4.
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Refraction
Waves travelling from air through
the surface of water can also be
refracted. This is the technical
word for the wave changing
speed and course.
This happens when the “medium”
or type of material changes. Mainly
the refraction is to do with the
change in density and structure of
the medium.
Glass
Air
Air
In the case of this glass block we
can see that when the medium
becomes denser (the glass) the
light rays bend or refract towards
the normal. Then when the medium
becomes less dense (the air) the
rays bend away or refract away
from the normal.
We also find that the red
light does not refract as
much as the blue light.
This is because the blue
light has a shorter
wavelength. So when
light rays slow down or
speed up they change direction
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Refraction & the Wave formula
This phenomemon can also be explained via mathematics and
the wave formula;
v  f 
The frequency of a wave is fixed
from the source. This means that if
the wave slows down, for the
relationship to stay true the
wavelength must also decrease.
An example could be;
v = f
= 3Hz x 3m
= 3 s-1x 3m
= 9 ms-1
However, if v is reduced to 6 ms-1 so must the speed
v = f
6ms-1 = 3Hz x 
6ms-1 = 3 s-1 x 
6ms-1/ 3 s-1 = 2m
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Refraction & the Wave formula
The two rules are simple;
1. When waves slow down they are
refracted towards the normal.
(deep to shallow water or light to
heavy medium)
2. When wave speed up they are
refracted away from the normal
(shallow to deep or heavy to light
medium)
The reasons for the rules are;
 Heavy mediums i.e. glass
slow down waves
 Shallow water i.e. the
beach cause friction to the wave
and slow them down
Mr Powell HT & FT Notes Year 11 Physics 2003/4
However, this picture is overly
simplistic and we find that the
effects of refection and reflection
are usually combined.
This prism shows how part of the
light is reflected and part is
refracted.
A simpler diagram is the one
below which shows a light ray
entering a glass prism. The beam
is split.
This diagram shows the combined
ray diagrams which show both the
effect of refraction and the effect of
reflection.
The same effect is seen when water waves arrive at a shelf in
the sea. When the water changes depth this makes a wave
(except that travelling at 900 to the shelf) refract or change
direction.
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Questions
1. When a water wave reaches the shore what can
happen to the direction of the wave?
2. Why do waves refract?
3. For a glass block draw an accurate diagram of the
wave in which an incident red light ray will behave?
4. For a triangular glass prism attempt to draw the same
diagram, also add in the reflected ray?
Answers
1. The wave will refract and slow down if travelling at an
angle to the normal.
2. If the density of the medium in which they are
travelling changes the wave will either speed up or
slow down. This causes the change in direction.
3. As per this diagram;
Mr Powell HT & FT Notes Year 11 Physics 2003/4
4. As per this diagram;
Normal
Normal
i
r
r
i
The Critical Angle
The critical angle is quite simply the angle at which a refracted
ray becomes a reflected ray off the internal surface of a prism.
As the angle of reflection moves towards 42.2 the refracted ray
moves towards the surface of the prism. At 42.2 the refracted
and reflected rays meet;
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Prisms
This picture shows how we can use a glass prism and the effect
of refraction to separate light rays of different wavelengths. As
the beam of white light passes through several prisms it
diverges or splits more and more.
The blue light (shorter wavelength) is refracted more than the
red light (longer wavelength).
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Transverse & Longitudinal
There are two types of disturbances which fall under the main
categories of waves.
Transverse - where the motion of the particles or energy
contained in the wave moves at 900 to the direction of the wave.
We think of this type of wave as a side to side or up and down
motion. Examples of this type of wave are any EM waves from
the EM Spectrum. The can travel through vacuums. The wave
has Peaks and Troughs
P
P
P
T
T
T
Longitudinal – where the motion of the particles or energy
contained in the waves moves in the direction of the wave. We
think of this type of wave as a push pull type of wave as the
particles are pushed and pulled forwards and backwards. An
example of this type of wave is sound. This type of wave needs
a medium and cannot travel through a vacuum. The wave has
Compressions and Rarefactions just like a transverse wave.
The diagram helps compare the two;
R
C
R
C
R
P
P
T
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Transverse & Longitudinal Questions
1. Why can’t longitudinal waves such as sound travel through a
vacuum?
2. What do we call a peak on a longitudinal wave?
3. Draw an example of a longitudinal waveform.
4. Draw an example of a transverse waveform.
5. Where is the energy directed in a transverse wave?
Answers
1. Longitudinal waves like sound depend on the push and pull
of matter. In space there is no matter to push and pull hence
the waveform cannot progress.
2. A Compression.
3. See notes.
4. See notes.
5. At 900 to the direction of wave motion.
Mr Powell HT & FT Notes Year 11 Physics 2003/4
6. EM Spectrum FT & HT
This picture shows the EM Spectrum. In the middle is visible
light. Between 400nm and 700nm (nano metres or 1x10-9m =
0.000000001m). The eye is sensitive to this light and by
monitoring the reflection of light from the objects around us we
are able to distinguish the distance of the objects and the type
of materials from which they are made. Our eyes are very
complex organs which have specialised cells on the back of the
eye to absorb the light. This is what we call the retina.
If the wavelength gets shorter or longer you get a different type
of wave which has different properties. However, all EM waves
travel at the same speed in a vacuum. 3 x 108 m/s or
300,000,000 m/s or you may see it as 186,000 miles per
second (in old units)
This is because the frequency of an EM wave increases as the
wavelength decreases. If we increase the wavelength by x2 the
frequency will half, and the effect is cancelled out.
v  f 
v  const
v  f 
1
v  f  2
2
v  f
Mr Powell HT & FT Notes Year 11 Physics 2003/4
This is the EM Spectrum. The shorter the wavelength the more
dangerous the waves are. We only see the visible light ROY-GBIV in the centre.
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Seismic Waves FT and HT
Our knowledge of the structure of the Earth comes mainly from
studying how the shockwaves from earthquakes (seismic
waves) travel through it. These waves are detected using
seismographs. By examining how the different waves travel
through the core of the Earth we can tell which parts are liquid
and which parts are solid. This is because the transverse or Swaves will only travel through a solid and not a liquid. By this
technique we have found that the Earth has a structure like this;
Crust
Core
Inner core
Mantle
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Seismic Waves HT Only
Earthquakes produce surface waves that can cause earthquake
damage and two types of waves that can travel through the
Earth.
 faster travelling P waves, which are longitudinal and travel
through liquids as well as solids
 slower travelling S waves which are transverse and travel
only through solids.
The speed of both types of waves increases with depth through
the mantle. The waves travel in curved paths as their speed
changes gradually through a material. When the state of the
transmitting medium changes abruptly e.g. when moving from
solid to liquid, the wave direction also changes abruptly.
It is by observing the paths of these waves that scientists have
been able to work out details of the Earth’s layered structure.
Candidates should be able to interpret diagrams of the paths of
seismic waves inside the Earth in terms of:
 the liquid nature of the
Earth’s outer core;
 refraction at the
boundaries between
layers;
 refraction due to
changes in speed within
a particular layer.
Crust
Inner
core
Core
Mantle
p
s
S-wave
shadow
region
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Seismometers
It is easy to find the Focus of an Earthquake. If three
seismometers are recording an earthquake, they can each work
out how far they are from the epicentre. Combining the three
measurements finds where the epicentre is.
70km
C
A
40km
Focus
B
100km
Mr Powell HT & FT Notes Year 11 Physics 2003/4
Structure of the Earth
 From the outside in, there is:
 The Crust: The hard surface we live on.
 The Mantle: This is a very thick liquid which goes down half
way to the inner core.
 The core: Very hot liquid
 The inner core: Very hot, but under so much pressure this
part of the Earth is a solid.
Crust
Inner core
Core
Mantle
Mr Powell HT & FT Notes Year 11 Physics 2003/4