Download Properties of waves

Qatar International School
Science Department
Section3; Properties of waves
3.1 General wave properties.
UHS 3a
Describe what is meant by wave motion as illustrated by vibration in ropes,
springs and by experiments using water waves.
Use the term wavefront.
Give the meaning of the term wavefront.
We know what we mean by a wave, such as a wave on water, but it is not easy to give
a scientific definition of what we mean by a wave. A wave or wave-motion means
‘the transfer of energy through a medium by vibration of the medium’ there are two
important points here; the vibration and the movement of energy.
e.g. a sound wave; the air vibrates and sound energy moves.
e.g. a wave in a slinky spring or (tight rope) we shake one end of the slinky (putting in
kinetic energy) and a ‘vibration’ moves along the spring. We call this vibration a
wavefront.
e.g. waves on water, we can use a ripple tank to see water waves. As we disturb the
water, we cause wavefronts to move away from the disturbance.
Definition of wavefront.
The set of points reached by a wave at the same instant as the wave travels through a
medium. The medium means what ever the wave is moving through, e.g. if a sound
wave is moving in air, then air is the medium.
The lines formed by ripples on
a pond, as the wave spreads
through the pond correspond to
circular wave fronts.
The distance between any
wavefront and the next is called
the wavelength (see below)
Disturb water here
wavefronts here
Distinguish between transverse and longitudinal waves and give suitable
examples.
There are two types of waves; transverse and longitudinal waves.
A transverse wave is when the vibration of the medium is perpendicular to the
direction of the wave movement. E.g. waves on water, light waves.
A longitudinal wave is when the vibration of the medium is parallel to the direction of
the wave movement. E.g. sound waves.
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Give the meaning of speed, frequency, wavelength and amplitude.
Recall and use the equation v = f λ.
Speed of a wave means distance/time (like any other object). Symbol v, units m/s.
Frequency means how many waves there are in one second. The equation is number
of waves divided by time. Symbol f, units /s or Hz.
Wavelength is the length of one wave. Wavelength is also equal to the distance
between one wavefront and the next. Symbol λ, units m.
Amplitude is the height of one wave Symbol a, units m..
Time period (or period) is the time for one wave. Symbol T, units s.
The wave equation states v = f λ or in words speed = frequency x wavelength.
Another useful equation is period = 1
in symbols T = 1
Frequency
f
λ
a
λ
a
λ
Worked example.
Given the speed of sound in air is 330m/s and the wavelength of a certain sound is
1.0m, calculate the frequency of the sound. Can this sound be heard by a human?
Answer;
Use v = f λ where v = 330 and λ =1
330 = f x 1 so f = 330Hz.
This sound can be heard, because it is in the audible range (20 to 20000 Hz).
Example.
Find the speed and Period of a wave which has frequency 200Hz and a wavelength
0.5m.
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Describe the use of water waves to show (i) reflection at a plane surface
(ii) refraction due to a change of speed (iii) diffraction produced by wide and
narrow gaps.
We can see waves on the surface of water by using a ripple tank. We can see three
wave effects, and you should be able to recognize or draw the three diagrams below.
Note the most common requirement in IGCSE is to do the diffraction diagrams, these
are also the easiest diagrams. But you need to know the difference between the wide
and narrow gap diagrams.
Diffraction in water waves.
Diffraction through a narrow gap
Through a narrow gap
(about equal to the wavelength).
λ
λ
Waves are circular after passing
through the gap. Wavelength is the
same as before the gap (λ in the
diagram is the same before the gap
as after the gap). Note that the
wavefronts become longer as the
wave spreads out.
Diffraction through a wide gap.
Through a wide gap
(much larger than the wavelength).
Waves are straight in the region between
the lines after passing through the gap.
There are diffraction effects only at the
edge of the waves. Wavelength is the same
as before the gap (λ in the diagram is the
same before the gap as after the gap). Note
the straight part does NOT become longer,
but the curved part can become longer.
Example.
Draw the diffraction of the waves through the gaps shown below.
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Reflection.
Water waves follow the law of reflection, angle of incidence equals angle of
reflection. As shown in the diagram below. The wavelength is the same before and
after the reflection. The first diagram shows the incident waves changing direction
after being reflected. This may be enough to answer the IGCSE question. However if
you are required to show a wave which is partly incident and partly reflected this is
more complicated and is shown below the first diagram.
Diagram showing the bent wave fronts which are partly reflected while still having a
part of the wave moving towards the reflecting surface. (without labels)
Wavelength is the same as before
the reflection (λ in the diagram
below is the same before the gap as
after the reflection). Note that the
wavefronts are the same size before
and after the reflection.
Same diagram as above, but with explanatory labels.
λ
Reflective
surface
After reflection wavefronts are at 900
to direction arrow after reflection
direction arrow after reflection
λ
Before reflection wavefronts are at 900 to
direction arrow before reflection
direction arrow before reflection
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Refraction.
As a wave moves into shallower water its wavelength becomes
less. (Or it becomes larger as it enters deeper water). When we
draw the refraction diagram the wavefronts are closer in the
shallower water, and this means the wave direction changes, so
the wave bends as it goes into shallow water. (It will bend the
other way entering deep water, but almost all exam questions
ask about wave moving from deep to shallow).
Steps in drawing the diagram are shown in the example below.
Worked example.
On the diagram to complete the wavefronts shown, also show the next few wavefronts
after the water wave enters shallow region of water in a ripple tank.
First we complete the direction arrow of
the wave after it enters the shallow water.
We choose the angle of refraction, but
choose an angle about half way between
the perpendicular and the original direction
as shown in step 1.
Then draw the new wavefronts in the
shallow region at 900 to this direction line
to complete the diagram as shown in step 2.
Step 1 - direction
Step 2 - wavefronts
Note that the direction of the new wave is the first step, and after that
the wavefronts automatically take on the new direction if you correctly
draw them at 900 to this new direction arrow.
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Science Department
Interpret reflection, refraction and diffraction using wave theory.
Wave theory just means learn the table below. For each wave effect, that is reflection,
refraction and reflection, you need to know the effect on speed, frequency and
wavelength (these are the properties of a wave called wave properties).
You have two choices, either memorize the table or remember how the table is
completed.
To complete the table there are three steps.
1. The frequency never changes.
2. Use the diagrams above to see if the wavelength changes (the wavelength is
the distance between the wavefronts, see page 1).
3. use v = f λ (you now know if λ changes and if so then v changes in the same
way; if λ increases so does v, if λ decreases so does v).
Wave property
frequency
wavelength
Stays the same
Stays the same
Stays the same
Stays the same
Stays the same
Decreases
speed
Wave effect
reflection
diffraction
refraction
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Stays the same
Stays the same
Decreases
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3.2 Light
3.2(a) Reflection of light.
Describe the formation, and give the characteristics, of an optical image by a plane
mirror.
Use the law angle of incidence = angle of reflection.
Formation of an image by a mirror.
When light hits a mirror it will reflect, but if it enters your eye you see it AS IF it
came from a straight line.
The object means the original object that the light actually comes from. The image
means what we see, even though the light came from the object it looks AS IF it came
from the image.
Characteristics of an image formed by a mirror.
A mirror will always give a virtual image. The image is as far behind the mirror as the
object is in front. It is the same size as the object, and is laterally inverted (this means
the left becomes the right).
In summary the image is
 virtual
 upright
 same size as the object
 same distance behind the mirror as the image is in front.
 Laterally inverted.
The law of reflection
The angle of reflection equals the angle of incidence. In symbols, i = r
The meaning of ‘real’ and ‘virtual’ when referring to an image.
A real image is one where the light actually passes through the image.
A real image could appear on a screen.
A virtual is one where the light does not actually passes through the image.
A virtual could not appear on a screen.
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Perform simple constructions, measurements and calculations.
We use the law of reflection to find the position of an image, and we always describe
it with the characteristics above. A construction just means an accurate drawing.
The diagram on the right shows rays from each end of an
object obeying the law of reflection as they enter the eye
of a observer. The solid lines show the actual path of the
light, while the dotted lines show where the light
APPEARS to have come from (the eye sees light AS IF it
came in a straight line).
Each ray has been drawn as shown below.
Angle of
Incidence
Incident ray
i
mirror
Angle of
reflection
r
reflected ray
Normal (900 to the mirror)
Examples.
Draw a construction to find the position of the image of man B seen by man A in each
diagram below.
A
r
B
r
B
r
A
r
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3.2(b) Refraction of light.
Describe an experimental demonstration of the refraction of light.
Use the terminology for the angle of incidence i and angle of refraction r.
Experimental notes.
1) ray box.
We can use a light box to create a ray of light. A ray means a beam of light which is
approximately parallel so it travels in a straight line. A bulb will give out light in all
directions but we simply shield the light in a box and only allow light to go in one
direction. We can draw a light ray as a straight line on a ray diagram.
Light bends when it goes from one medium to another (medium means the material
light is moving in, e.g. air or glass). The bending effect is called refraction. We can
use a light ray from a ray box to see this. Note most diagrams do not draw a ray box,
we start with a parallel ray of light.
Diagram of a ray box.
Bulb gives light in
all directions
Box shields
light and
stops it going
in most
directions
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light ray comes out of
the hole in one direction
There is a hole in
the box on one
side only
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2) Optical pins.
An optical pin is a pin used to trace a light ray. We can look at several optical pins
and if they appear to be in a straight line then they fall on the same ray of light. This
may be a straight ray, or a ray bending (refraction).
IGCSE questions on optical pins usually require you to draw the position of pins on
a diagram, the idea is to draw the pins as far apart as possible. You may be asked to
give some methods of making the experiment with pins as accurate as possible (or
reducing errors, which means the same thing). Answers include; view the base of the
pin, make sure the pins are vertical, use thin pins, put the pins far apart.
The experimental demonstration referred to is shown below, using a glass block.
The angle of incidence is the angle between the incident light ray and the normal,
called i, and the angle of refraction is the angle between the refracted ray and the
normal. Both angles are also shown below.
Describe the passage of light through parallel sided transparent material.
A parallel sided transparent material simply means a rectangular glass or plastic
block. We can use a ray box and see the light ray directly, or we can view optical
pins.
Normal (900) to
surface of the block
Incident ray
i
r
Glass block
Light ray comes out of
the block parallel to the
original incident ray.
Recall and use the definition of refractive index n in terms of speed.
Recall and use the equation n = sin i /sin r.
We have studied how light bends when it crosses the boundary between one medium
and another. The amount of refraction is measured by the refractive index, symbol n.
You need to know two equations for refractive index
Refractive index = speed of light in air
speed of light in the medium
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Refractive index =
sin i
sin r
=
sin angle of incidence
sin angle of refraction
Worked example.
If the angle of incidence is 450 and the angle of refraction is 300, calculate the
refractive index of the medium. Calculate the speed of light in the medium (speed of
light in air is 300 000 000 m/s.
Answer; Refractive index = sin i
sin r
=
sin 45 = 1.41
sin 30
Refractive index =
speed of light in air
=
300 000 000
speed of light in the medium
speed in the medium
so, speed of light in the medium = 300 000 000 /1.41 = 212 000 000 m/s.
Example.
On the diagram below draw a normal and label angle of incidence and refraction. Use
a protractor to measure the angle of incidence and refraction, and then calculate the
refractive index of the glass. Complete the diagram by drawing the ray after it passes
out of the block on the lower face. Draw on your diagram suitable positions for four
optical pins used to trace the ray.
Glass block
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Give the meaning of critical angle.
Describe internal and total internal reflection.
The critical angle refers to a situation where light is inside a glass block and trying to
leave (i.e. going from more dense to less dense medium). The light will refract as
shown in the diagram above and in diagram 1 below. Note there is a weak reflected
ray, some light s reflected from the inside of the block, this is reflected off the inside
of the block and so it is called internal reflection.
If the angle of incidence increases, we reach a situation shown in diagram 2 where the
refracted ray has an angle of refraction equal to 900. In this case the angle of incidence
is called the critical angle, because it is the change over point between diagram 1 and
3.
Definition of critical angle; The critical angle (C) is the angle of incidence which
gives an angle of refraction 900.
If the angle of incidence increases any more it is impossible for the light to refract
(since the angle of refraction would be greater than 900 so the light would not leave
the glass) and so all the light reflects. This is called Total Internal Reflection (TIR).
This is shown in diagram 3.
Diagram 1
Diagram 2
Diagram 3
C
r = 900.
Refraction at 900 and
internal reflection
Refraction and
weak internal
reflection
No refraction,
total internal reflection
(TIR)
Describe the action of optical fibres.
An optical fibre uses TIR to guide a ray of light along the fibre. As each reflection is
TOTAL internal reflection, no light is lost regardless of how many reflections there
are.
T.I.R.
T.I.R.
T.I.R.
Optical fibre
Light enters
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Light leaves
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Science Department
State the approximate value of the speed of electromagnetic waves.
Use the term monochromatic.
The speed of light in air or in vacuum is 300 000 000 m/s or 3 x 108 m/s you need to
memorise this number. All electromagnetic waves have the same speed in a vacuum.
Worked example.
State the speed of xrays moving in air.
Answer; 3 x 108 m/s
Monochromatic
The word monochromatic means one frequency. The only colours of visible light
which are monochromatic are the three primary colours; red, green or blue. All other
colours are a mixture of colours.
We often use monochromatic light in an experiment to avoid diffraction, you may
come across an IGCSE question stating ‘red light enters the block’ this just means we
do not get dispersion. The light will act as shown in the diagrams above, which are
actually using monochromatic light.
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3.3 Sound.
Describe the production of sound by vibrating sources.
Describe the longitudinal nature of sound waves.
Describe compression and rarefaction.
When a guitar makes a sound the string vibrates. When a drum makes a sound the
drum skin vibrates. When we speak our vocal cords vibrate. When we hold a ruler on
the desk and make it vibrate we hear a sound. All sound is created by a vibration.
The vibration of the object causing sound causes the air near to the object to vibrate as
areas of high and low pressure as shown below. This is a LONGITUDINAL wave
made up of areas of high called compressions and low pressure called rarefactions.
Example a vibrating ruler causing high and low pressure.
Ruler moves upwards
causing high pressure
in the air above the
ruler (compression)
vibrating ruler moves
upwards and down
desk
Ruler moves downwards
causing low pressure in the air
above the ruler (rarefaction)
Relate the loudness and pitch of sound waves to amplitude and frequency.
We can use a vibrating ruler to see the effect of amplitude and frequency on the sound
we hear. If we make the ruler short it vibrates faster, this is HIGH FREQUENCY and
we hear a HIGH PITCH SOUND.
If we hit the ruler harder it vibrates more, this is HIGH AMPLITUDE and we hear a
LOUD SOUND.
We can see the same effect with any other instrument such as a guitar, a thin string
vibrates faster and gives a high pitch, plucking the string harder causes a larger
amplitude and gives a louder sound.
In General;
HIGH FREQUENCY = HIGH PITCH SOUND.
LARGE AMPLITUDE = LOUD SOUND.
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State the approximate range of audible frequencies.
We can use a signal generator and a speaker to create sounds of different frequency.
Very high pitch and very low pitch sounds can not be heard. A healthy young person
can hear a wider range of sound than an older person due to damage to the ear through
out life. A typical healthy person can hear sound between 20Hz and 20000Hz. You
need to be able to state these values.
Describe an experiment to determine the speed of sound in air.
State the order of magnitude of the speed of sound in air, liquids and solids.
Show an understanding that a medium is required in order to transmit sound
waves.
Experiment to measure the speed of sound.
To calculate speed we need distance and time. Sound is fast so we need to use a large
distance or the time is too short to measure. Light travels so fast we can ignore the
time it takes for light to travel the distance involved in the experiment.
Two people stand far apart, and measure the distance between them. One makes a
sound by banging wooden sticks (or firing a gun etc.). As the other person sees the
movement he starts the stopwatch, when he hears the sound he stops the stopwatch.
This gives the time for sound to travel from one person to the other.
Use speed = distance/time to calculate the distance.
Man with a stopwatch
starts timing when he
sees sticks come
together, stops when he
hears sound of sticks.
Man with sticks,
when he bangs
them it makes a
sound.
Light travels to the eye (almost) instantly
sound travels to the ear much more slowly
Large distance. E.g. 100m or more
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Sound and different mediums
The medium means the material which sound (or any wave) is passing through.
Sound can travel through a gas (e.g. air) or through a liquid (e.g. when swimming
under water you can still hear) or through a solid (e.g. we can hear through a wall).
Most objects travel more easily through air, but sound is the reverse; sound travels
faster through solids (5000m/s) and slowest through gas (330m/s).
This is because the strong bonds in a solid transmit the vibrations easily.
In lower school we see an experiment where we suck out air from a big jar with an
alarm in clock inside. We see the sound get quieter. If all the air is removed we hear
no sound at all because sound can not move through a vacuum, note light can do so
(e.g. light from the sun passes through space to reach Earth).
Big jar
Alarm clock making sound. As air is
removed the sound gets quieter showing
sound needs a medium to move through.
To vacuum pump (sucks air)
Describe how the reflection of sound may produce an echo.
When a sound wave hits a solid object it can reflect in the same way as a light wave
reflects from a mirror. If we hear the reflected sound we call it an echo. Often we will
hear the original sound directly then a few seconds later we hear the echo as the sound
reflects from a distant object like a building. The reflection moves a longer distance
and so takes longer to reach us compared to the direct sound. Example, this is very
common when watching fireworks.
firework
Reflected sound takes more
time as it travels a longer
distance
Direct
sound
building
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