Download Notes (2a Waves, Light and EM Spectrum)

PHYSICS
NATIONAL 4/5
Unit 2a
Waves, Light and
the EM Spectrum
Course Notes
High School of Dundee
Physics Department
Some things you should learn …
Wave Characteristics
Waves transfer energy from one place to another, often with no transfer of mass –
in other words the stuff carrying the wave (the water, or the air, etc) ends up in pretty
much the same place as it started even though the wave can travel miles!
1. There are two main types of wave:
 Longitudinal waves – the particle vibrations are parallel to the direction the wave is
travelling.
 Examples include sound waves or waves on a slinky
Wave velocity
vibrations


Transverse waves – the vibrations are at right angles (90°) to the direction of
travel.
Examples include water waves and electromagnetic waves (light, microwaves etc)
Wave velocity
vibrations
2. Wavelength and amplitude

The top of a wave is called the crest. The bottom is
called the trough.

The distance between 2 crests, or 2 troughs, or any
2 corresponding points is called the wavelength, λ,
measured in metres.

The distance from the equilibrium
(middle of the wave) to the peak, or
from the equilibrium to the trough is
called the amplitude, a, measured in
metres.
3. Frequency
 The number of waves that are produced by the source every second is called the
frequency, f, measured in Hertz, Hz.
 1 Hz = 1 wave per second

Frequency can be worked out using the equation:
𝑓=
𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑤𝑎𝑣𝑒𝑠
𝑡𝑖𝑚𝑒 𝑡𝑎𝑘𝑒𝑛
N = the number of waves produced
t = the time in seconds taken to produce the waves.
4. Period
 The time taken for a complete wave to be produced by the source is called the
period, T, measured in seconds, s.

The period and frequency of a wave are linked by the equation:
𝑇=
1
𝑓
5. Wave speed
 The distance travelled by the wave each second is called the speed, v of the wave
measured in metres per second or ms-1.

Speed can be worked out using the equation:
𝑣=
𝑑
𝑡
d = the distance travelled by the wave
t = the time taken to travel that distance
6. The wave equation
 The speed, wavelength and frequency of a wave are linked by the equation:
𝑣 =𝑓×𝜆
Diffraction
When a wave passes through a gap or around an obstacle the wave spreads out – this is
called diffraction.

When the gap is small there is more diffraction.
large gap – little diffraction

small gap – lots of diffraction
Long waves diffract more easily than short wavelengths
Long waves diffract
easily





Because TV waves have a much shorter wavelength
than radio waves, they diffract less.
This means radio reception (especially for long wave or
medium wave radio but less so for FM radio) in hilly
regions is much better than TV reception.
Satellite TV is transmitted on very high frequency
microwaves – which have a very short wavelength.
This means satellite TV signals hardly diffract at all,
yet reception is good in hilly areas.
This is because the signal is transmitted to a
geostationary satellite, 36000 km above the
equator. The signal is amplified and retransmitted
back to earth on a slightly different frequency.
Thus the hills cannot get in the way of the signal!
Short waves do
not diffract much
Example 1
A water wave is produced in a tank, as shown in the diagram.
50 cm

4m
Is this a transverse or longitudinal wave?



Label a peak and a trough on the diagram
Draw a wavelength on the diagram
Draw an amplitude on the diagram

Calculate the wavelength

Calculate the amplitude

All of the waves were produced in 30 seconds. Calculate the frequency
f=
N=
t=

Use the wave equation to calculate the wave speed.
f=
λ=
v=

The tank is 4 m long. Calculate the time taken for a wave to travel the length of
the tank
v=
d=
t=
Example 2
A wave machine produces 60 waves in 5 minutes. The distance from the peak of
one wave to the peak of the next is 40 cm.
Calculate the frequency and period of the waves.
State the wavelength of the waves.
Calculate the speed of the waves.
How far will the waves travel in 1 minute?
Example 3
Use your knowledge of physics to explain, in as much detail as you can, why if you
live at the bottom of a big hill you can get good radio reception but poor TV
reception. Why might a friend who lives further from the transmitter and further
from the hill get better TV reception?
Example 4
Radio signals travel at 3 × 108 𝑚/𝑠 . How long will it take a satellite TV signal to
travel from London to Dundee via a geostationary satellite above the equator?
Sound
Sound waves travel as longitudinal waves through a material.
1. Speed of sound
The speed of sound can be measured by measuring the distance travelled, d, by a
sound wave and the time taken, t, for it to travel this distance. The speed, v, is then
𝑑
calculated using the equation: 𝑣 = 𝑡

Echo method
o the distance, across the playing field is measured using a trundle wheel.
The distance, 𝑑 travelled by the sound is double this distance (the sound
goes there and back!)
o a sound is made by hitting a hammer on a piece of metal.
o the time, 𝑡 between hearing the sound its echo is measured using a stop
clock.
𝑑
o The speed, v, is then calculated using the equation 𝑣 = 𝑡

Light and sound method
This method works because the light travels much faster than the speed of sound.
o the distance, 𝑑 across the playing field is measured using a trundle wheel.
o a sound is made by hitting a cymbal from the far side of the playing field.
o the time taken, 𝑡 between seeing the cymbal being hit and hearing the crash
is measured using a stop clock.
𝑑
o The speed, v, is then calculated using the equation 𝑣 = 𝑡
Both of these methods will have considerable inaccuracy because the time measured is
very short as the speed of sound is so fast. As a result, human reaction times will
make the time measured inaccurate.

Automatic timer
o two microphones are connected to an automatic timer.
o the microphones are placed a distance, 𝑑 apart, measured with a ruler.
o a sound is made by hitting a piece of metal with a hammer.
o the timer will start when sound reaches the first microphone and stops when
the sound reaches the second, measuring the time, 𝑡 that the sound takes to
travel between the microphones.
𝑑
o The speed, v, is then calculated using the equation 𝑣 = 𝑡
Because this method uses an automatic timer, human reaction does not make the
results inaccurate.
Sounds travel at different speeds in different materials. They travel fastest in solids
and least well in gases. Sounds cannot travel in a vacuum as particles are required to
pass on the vibrations.
2. Echoes
Whenever you are working out the speed of sound, or using it to calculate a distance
or a time remember that if the sound has been reflected the distance travelled is there
and back so either the distance or time will need to be needs to be doubled or halved
– this will require some thought to figure out what’s going on!
3. Sound wave forms


As the amplitude of a sound wave increases its volume gets louder.
As the frequency of a sound wave increases its pitch increases. (For those of you
who are musical, if the frequency doubles the pitch goes up by one octave).
4. Loudness of sounds

The loudness of a sound
is measured using a
sound level meter in
units called decibels, dB.

Exposure to sounds over
80 dB for long periods of
time can cause hearing
damage. (low
frequencies – bass notes
– can cause damage
meaning you are unable
to hear high
frequencies).

Exposure to sounds over
140 dB can cause
hearing damage, even
with short exposure. It
might even be painful.

Ear defenders reduce sound levels to below 80 dB, at all
frequencies. A hard outer casing reflects sound energy. A
soft inner absorbs sound energy. Padding ensures that
sound can’t get in round the edges.
5. Ultrasounds
 Humans can hear a range
of frequencies of sound
between approximately
20 and 20 000 Hertz.
 A sound with a frequency
higher than humans can
hear is called an
ultrasound.
 The range of frequencies
we are able to hear
shrinks with age and
exposure to loud sounds.
 Different animals have
different ranges of
hearing.
6. Uses of ultrasounds
Ultrasound travels at different speeds in different materials. Whenever ultrasound
changes speed, some of the sound will be reflected. This makes ultrasound useful for
scanning objects inside other objects.
Ultrasound scanning is quicker and less harmful
than using radiation such as X-rays (which can
damage healthy cells) to see inside an object or
person!





Ultrasound pulses are produced by the transducer
held in contact with the skin.
Jelly is used between the transducer and the skin
to expel air, preventing reflections from the
boundary between the air and the skin.
Sound is reflected by the baby or at any boundary
between different types of tissue in the body.
The time taken between a pulse of sound and its
reflection is measured by a computer and used to
calculate the depth of the boundary.
This happens many times and the computer is
able to build an image of the baby.
Ultrasound can be used to break down kidney stones – a high powered ultrasound is
focused on the kidney and is used to make the stones vibrate themselves apart! The
fragments can then be passed out of the body in the normal way!
Ultrasound can also be used in industry – for example to detect cracks in metal or to
measure the thickness of a piece of plastic.
7. Amplified Sound
Radios, mobile phones and other audio appliances all require a device called an amplifier
which is used to increase the amplitude of the electrical (audio) signal so that when the
signal is sent to a loudspeaker the sound will be loud enough to here and the sound level
produced can be altered.
 The output signal from a CD-player is only about 10 mV (0.01 V) which would
be too small to drive a loudspeaker directly.
The output from an amplifier has the same frequency as the input. An amplifier only
alters the amplitude of the signal.
In audio appliances the amplifier is generally the volume control.
To amplify sounds such as the voice of a singer you need:
 A microphone – to change the sound into an electrical signal,
 An amplifier – to make the electrical signal stronger,
 A loudspeaker – to change the amplified electrical signal back into sound.
The output from an electrical guitar is also amplified before being sent to a loudspeaker.
Voltage Gain
The voltage gain of an amplifier tells you how many times bigger the output voltage is
compared to the input voltage, for example, if an amplifier has an input voltage of 0.5 V
and an output voltage of 5 V, then the output voltage is ten times greater than the input
voltage, that is, the voltage gain is 10.
voltage gain 
output voltage
input voltage
VG 
Vo
Vi
Note that since we are dividing volt by volt, voltage gain has no unit, it is a ratio.
Noise Cancellation
8. Interference
If two waves meet, the resultant wave is the sum of the individual waves. That is, waves
simply add together to produce a wave that is the addition of all the waves at that point.
This is called interference.
If we have two sound waves A and B as shown above:
 The crests of wave A meet the crests of wave B and the troughs of wave A meet
the troughs of wave B
 The resulting wave has a large amplitude and will be louder than wave A or wave
B.
However, if the crests of wave A meet the troughs of wave B and vice versa, the waves
will cancel each other out and there will be silence!
This principle can be used to reduce unwanted noise.
How noise cancellation works
 Incoming noise from the surrounding environment is picked up by a microphone
and sent to a noise cancellation circuit.
 The noise cancellation circuit inverts the incoming wave signal and sends it back to
a speaker inside the headphones.
 The inverted signal should then cancel the incoming noise signal.
Sound Engineering
Sound waves can also be added together to make musical recordings. Before the 1950s,
recording a song always depended on musicians and singers performing over and over
again together until they got the "perfect" take. Now songs are produced using a
multitrack recorder, which allows different "tracks" or channels of sound to be recorded
then played back together (the vocals on one track, guitar on another, and so on). Each
track can be re-recorded or deleted without affecting the other tracks.
The diagram above shows how three simple waveforms can combine to form a more
complex waveform.
Example 1
The speed at which sound travels can be found in a laboratory by using an electronic
timer. Two microphones are set up a measured distance apart and connected to the
timer as shown.
Write a method to explain how to use this apparatus to measure the speed of
sound.
Example 2
A family is watching a firework display that is happening 5 km away from them.
Explain why there is a delay between them seeing the flash of the fireworks and
hearing the bang.
The speed of sound in air is 340 m/s. Calculate how long the time delay between
seeing the flash and hearing the bang will be.
v=
d=
t=
Example 3
Draw a sound wave. Then draw a second with exactly the same volume but double
the frequency. (Perhaps you should use a ruler to keep your diagrams neat and
make sure you label the diagrams).
Draw a sound wave. Then draw a second with exactly the same frequency but
double the volume.
Example 4
Explain how sound levels are measured and use your knowledge of physics to
explain why ear defenders should be worn by a worker in a noisy factory.
Example 5
The table gives the speed of sound in different materials.
Material
Air
Tissue (like skin or muscle)
Jelly
Speed of Sound m/s
340
1500
1450
transmitter
AND receiver
jelly
baby’s head
An expecting mother is given an ultrasound scan. A pulse is transmitted at a
frequency of 60 kHz.
The pulse travels through the mother’s skin and muscle and is reflected by the
baby’s head. The transmitted pulse takes 1.3 × 10−4 s to be received after it has
been reflected.
Calculate the depth of the baby’s head.
Use your knowledge of physics (and information from the table above) to explain
why jelly is put between the probe and the mother’s skin.
Light
Light travels through air at 3 × 108 𝑚/𝑠 in straight lines. This is much faster than the
speed of sound in air. As a result, for example when a fire work explodes, we see the
light of the flash before we see the sound of the explosion. (The speed of light is so fast
that we see the flash almost instantly!)
1. Refraction



When light passes from one medium (substance) to another it instantaneously
changes speed.
As it passes from air into glass (for example) it instantaneously
slows down at the surface.
As it passes from glass into air it instantaneously speeds up at
the surface.

This change is speed is called refraction

As a result of this change in speed light also changes direction
as it passes from one medium into another.

When light passes from one substance, we measure the angle of the incident ray to
a line drawn at 90° to the surface called the normal. We call this angle the angle of
incidence.

We measure the angle of the refracted ray in the same way. We call this the angle
of refraction.

The angle in air is always larger than the angle in another medium, such as glass or
water.
2. Lenses
We can make lenses which make the light change direction in a particular way
Convex Lens
 A convex lens causes rays of light to converge to a
focus.
 If the rays enter the lens in a parallel beam, the
distance from the lens to the focus is called the
focal length of the lens.
 Some lenses refract light more than others. We
say that they are more powerful.
 The power of a lens, P is measured in units called
dioptres, D

The more powerful a lens, the shorter its focal length.

The Power and frequency of a wave are linked by the equation:
𝑃=
1
𝑓
f = focal length in metres
P = lens power measured in dioptres
Concave lens
 A concave lens causes rays of light to spread out or
diverge.
 Although the concave lens doesn’t have a focus, we
can draw lines backward to find an imaginary
focus.


We say that the focal length of the concave lens is
negative.
If a lens has a negative power or focal length it is
a concave lens.
Measuring focal length of a convex lens
 Hold a lens between a distant object and a screen. Move the lens back
and forth until a sharp image is formed of the distant object.
 Measure the distance between the screen and the
lens – this is the focal length.
 (A distant object is used so that the rays of light
coming from it enter the lens in a parallel beam!)
3. Ray diagrams
We can draw diagrams to work out where a lens will form an image and what the
image will be like – if it is magnified for example, or if it is inverted (upside down).
 It is a good idea to draw your ray diagrams on graph paper as the following ray
diagram is.
 Be careful with your drawing; a small change in the angle of the undeviated ray can
lead to quite a big change in the final position of the image. And PLEASE... use a
sharp pencil.
EYES
Our eyes have a lens that focuses light onto the retina which is covered in lots of light
sensitive cells. We only see things clearly when light from them is focused on the retina.
The lenses in our eyes can change shape to focus light from near or distant objects.
1. Normal vision
Light from
a near
object
Fat, powerful
lens
Light from
a distant
object
thin, less
powerful lens
2. Long sight
The lens in the eye of a long sighted person is not powerful enough so the focal length
is too long.
 Although distant objects can be seen clearly, near objects appear blurred.
 This is because light from close objects focuses behind the retina.
 A convex lens is used to correct this eye defect
Light focused
behind the
retina
Correcting
convex lens
3. Short sight
The lens in the eye of a short sighted person is too powerful enough so the focal
length is too short.
 Although near objects can be seen clearly, distant objects appear blurred.
 This is because light from distant objects focuses in front of the retina.
 A concave lens is used to correct this eye defect
Light focused
in front of the
retina
Correcting
concave lens







However, only part of the ray refracts, the rest is reflected
The angle of refraction in the air is larger than the angle
of incidence in the material.
If the angle of incidence is small the ray is partially reflected and
partially refracted.
As the angle of incidence increases the brightness of the reflected
ray increases and the refracted ray gets dimmer.
As the angle of incidence increases, so does the angle of
refraction.
At a certain angle, called the critical angle, the angle of refraction
90°.
(The refracted ray is parallel to the surface of the medium).
partially
refracted
ray
𝜃𝑚𝑎𝑡
When light travelling inside a medium such as glass or water, it
refracts at the surface as it passes into air.
𝜃𝑎𝑖𝑟
Total internal reflection
partially
reflected
ray


At angles larger than the critical angle, the angle of refraction
would be larger than 90° which means it would go back into the
medium.
The light is all reflected back into the medium and no light us
refracted. This is called total internal reflection.
1. The fibre optic
Light can travel along a fibre optic by a process of repeated total
internal reflections.
Light signals can be transmitted along fibre optics as an alternative to
using electric signals in copper wires.
There are several advantages to this:
 Because no light escapes the edges of the fibre optic there is very
little energy lost so few amplifiers are needed, even on a very long
fibre optic. (In copper wires electric energy is transferred to heat so
regular amplifiers are needed).
 A fibre optic has a huge signal capacity – a single fibre
can carry many TV channels or telephone lines.
 Fibre optics are secure because no signal escapes out of the edges.
 Fibre optics are much cheaper than copper wires and are lighter
and more flexible.
2. The fiberscope (endoscope)
A fiberscope allows a doctor to see inside a patient without the need
for surgery (It also allows engineers to see inside pipes, aircraft etc).



A first bundle of fibre optics
called the light guide transmits
light into the patient (from a
cold source so no damage is
done to the patient’s insides).
The second bundle transmits
reflected light from inside the
patient to the eyepiece or
camera so the doctor can see
the patient’s insides.
The fiberscope is flexible so that it can move
around the inside of the patient’s body without
causing damage.
Example 1
Draw and label a diagram showing a ray of light being refracted through a
rectangular prism.
Example 2
A school boy can clearly see the writing in his jotter but when he looks at the clock at
the back of the room it appears blurry. Name and explain the eye defect he has and
describe how it could be corrected. You should include diagrams in your explanation.
Example 3
A lens has a focal length of -5 cm. Calculate the power of the lens. State what type
of lens it is and explain how you know this. Draw a diagram showing light passing
through the lens and its focal point.
Example 4
Use your knowledge of physics to explain in as much detail as you can how light
travels through an optic fibre. Describe one use of the optic fibre and state its
advantages.
Example 5
Complete the ray diagram to find the position and nature of the image that is formed.
The Electromagnetic Spectrum
When white light passes through a triangular prism, the light is
split into all the colours that make up white light. These
are:
Red, Orange, Yellow, Green, Blue, Indigo and Violet
1. Beyond the visible
 Before red and beyond violet are invisible “colours” that are also part of white light.
 The whole range of “colours” is called the electromagnetic spectrum.
 All the waves in the electromagnetic spectrum travel at the speed of light.
Radio
Waves
Microwaves
Infrared
Visible
light
Ultra
Violet
X-rays
 As the frequency increases the wavelength decreases
 Radio waves have the longest wavelength
 Gamma rays have the highest frequency
 As the frequency of a wave increases its energy also increases.
Gamma
Rays
2. Sources, detectors and uses of the electromagnetic spectrum
Type of
Radiation
Radio Waves
Sources
Detectors
Effects on body
Uses
o Sparks
including
lightning,
o a.c. currents,
o stars
o Radio Antenna
o No significant
effects on body
Micro Waves
o Field Effect
Transistors,
o MASERS,
o Magnetron
o Cosmic
Background
Radiation
(from Big
Bang)
o All hot objects
including stars
o Dish antenna
o No significant
effects
demonstrated
o Communication
(radio and TV signals
carried by radio
waves)
o RADAR
o MRI
o Car Remote Locking
o Communication
(mobile phones and
satellite TV)
o GPS
o Black bulb
thermometers
o Thermopiles
o Thermocouples
o Burns
o Can cause eye
damage (esp
IR close to
Visible Light)
o Sun and Stars
o Blacklights
(passing
electric current
through (eg)
mercury
vapour
o UV lasers and
LEDs
o High voltage Xray tubes
o Stars and
Galaxies
o Fluorescent dyes
o Photodiodes
o UV film (like
photo film)
o Causes blood
vessels near
surface of skin
to enlarge
o Sunburn and
skin cancer
o Production of
Vitamin D in
body
o Risk of cancer
o Radioactive
decay
o Pulsars,
Quasars
neutron stars
and black holes
(all types of
star)
o Photographic
film,
o Geiger counter
o Scintillation
Infrared
Ultra Violet
X Rays
Gamma Rays
o Photographic
film,
o Geiger counter
o Scintillation
(small flashes for
each X Ray
detected)
o Radiation burns
to skin
o Radiation
sickness
o Risk of cancer
o Thermograph
cameras (night
vision and medical
uses)
o Muscle therapy
o Detecting underlying
layers in artwork
o Remote Controls
o Killing bacteria and
viruses (sterilization)
o ID marking (using
fluorescent ink)
o X-ray photos
(medical and
industrial)
o Computerized
tomography (more
detailed than normal
X-ray photo
o Radiotherapy
o Sterilization and
pasteurization
o Treat caner (by
killing cancerous
cells)
o Scanning shipping
containers
o Gauge metal
thickness etc
Example 1
Draw a diagram to show the electromagnetic spectrum. Make clear on your diagram
which radiation has:
 the highest frequency.
 the longest wavelength.
 the most energy.
Example 2
Microwaves are used to transmit signals across the country using
microwave repeater links, between dish aerials on the tops of tall
buildings and pylons
 Give reasons why microwaves are used for this purpose.
 Use your knowledge of diffraction to explain why the
maximum range of these signals is just 40 km.
Example 3
Infrared radiation also has a range of uses.
 What is another name for infrared
 Name some electronic detectors of infrared.
 Describe one medical and one non-medical use of infrared.
Example 4
Describe how an X-ray photo is taken. Explain what is used as a detector and how it
works. Explain the position of the X-ray machine and detector in relation to the
broken leg. Explain any safety precautions that should be taken and why.
Example 5
Another type of x-ray photograph is called a CAT scan. Explain what is meant by
CAT scan, explain the advantages of a CAT scan and explain why CAT scans are not
always used by doctors.