The general types and properties of WAVES - an introduction including transverse
waves, longitudinal waves and calculations
IGCSE AQA GCSE Physics Edexcel GCSE Physics OCR GCSE
Gateway Science Physics OCR GCSE 21st Century Science Physics
Doc Brown's school physics revision notes: GCSE
physics, IGCSE physics, O level physics, ~US grades 8, 9 and 10
school science courses or equivalent for ~14-16 year old students of
physics
including
ripple tank experiments illustrating reflection, refraction and diffraction, all
of these are explained with lots of diagrams
Sub-index for this page
(a) Introduction to waves
- what are they?
(b)
Everyday examples of waves
(c)
The technical description and properties
of a TRANSVERSE WAVE and equation
(d)
The technical description and properties
of a LONGITUDINAL WAVE
(e)
Comparing and contrasting examples of transverse and longitudinal waves
(f)
More on the properties of waves - reflection, refraction,
diffraction
(g)
REFLECTION of waves and scientific model
(h)
REFRACTION of waves and scientific model
(i)
DIFFRACTION of waves and scientific model
(j)
WAVE CALCULATIONS - formulae and how to solve wave problem
questions
(k)
Experiments with water waves
in a RIPPLE TANK
(l)
Another investigation
of waves using a tensioned wire and signal generator
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(a) Introduction to waves - what are they?
Be able to describe that waves transfer energy and information without
transferring matter.
Waves are vibrations of a material e.g.
sound or oscillations of an electromagnetic field e.g. visible light.
Waves have energy and can transfer it from
one place to another.
This means waves can carry
information by changing the energy of the wave in a sequential way to
transfer 'data' from one place to another, but waves cannot transfer
the matter of the medium its is moving though - the medium can be
gas, liquid or solid.
Electromagnetic radiation
does not need a medium, it can travel through vacuum as well
as transparent gases (e.g. air), liquids (e.g. water) or solids
(e.g. glass).
Infrared and visible light beams in
fibre optic cables can carry enormous amounts of information often as
telephone calls or the networks of the internet - the information is
converted to binary code and the 'pulsed code' is imposed on, and
transferred by, the visible or infrared carrier wave.
When the signals reach your
mobile phone or computer, they are decoded and presented in an
audio-visual way.
When your TV receives the signal, its just
coded data in the electromagnetic wave, energy is transferred, but no material substance arrives!
However, if energy itself
wasn't transmitted, no effect could be produced on the TV screen without
something from the receiver!
Similarly, when ripples on water cause
floating objects to bob up and down, energy is needed to do this, but
neither the floating object or the water itself actually move in the
direction of the transverse waves - but energy is transferred from one
location to another.
Note the floating
The most dramatic transfer of energy
involves seismic earthquake waves, both transverse and longitudinal, yet the effects
are transmitted and felt miles from the epicentre and no part of the earth's
crust moves in the direction of the seismic waves but it may move violently
from side to side, up and down or compressed/decompressed.
When sound waves vibrate your ear drum no
air moves from the TV, person or musical instrument to your ear, yet energy is
transferred, carried by vibrations, through the medium of air, otherwise, what
could cause your ear drum
to vibrate!
You need to know the two formulae for waves
relating them to wavelength, frequency, speed and distance travelled and
calculations and problem solving based on them.
speed = distance / time
and speed = wavelength x frequency
Know the differences between longitudinal and transverse waves by referring to
sound, electromagnetic and seismic waves.
You need to understand that in a
transverse wave the oscillations are perpendicular (at 90o) to the direction of
energy transfer, but in a longitudinal wave the oscillations are parallel to
the direction of energy transfer ie direction of forward wave movement.
Shaking a slinky spring from
side to side (at 90o to stretched out spring) in a regular
rhythm produces a transverse wave of energy pulses.
Similarly wave ripples on water and all
electromagnetic radiation waves oscillate at 90o to the direction
the wave is travelling.
Pulling and pushing on a slinky
spring in a regular rhythm produces pulses of energy transmitted as a longitudinal wave
down the stretched out spring.
Similarly a
sound wave is pulses of energy travelling through a medium - the 'compressions' and
'rarefactions' are in the same direction as the wave movement.
More on examples of waves in the next
section
TOP OF PAGE and
sub-index
(b) Everyday examples of waves
A wave can be described as a regular
disturbance that transfers energy.
This uniform pattern of movement allows the
wave to transfer energy in various forms at a particular frequency.
To transfer
this energy the particles vibrate or the bulk material oscillates in some way,
but the particles or material stay in the same place - only the energy 'moves'!
This description is fine for example ..
1. When you drop a stone in a pond you see
ripples on the surface of the water as the kinetic energy of the
impact is transferred in all directions as water waves. If the ripple meets
a floating object, that object just bobs up and down as the ripples pass by
- the object is not carried along. This is an example of a transverse
wave, the vibrations/oscillations at 90o to the direction of
wave movement - more details later.
Waves crashing on the seashore or
battering a pier, is a good examples of waves transferring energy!
2. When you play a musical instrument the
sound of the notes, that is the energy of the vibration (string or reed
etc.), is transferred to your ear by the particles of air
vibrating-oscillating to and fro in line with the direction of the sound
wave is travelling - this is an example of a longitudinal wave - more
details later. The air does NOT move along in the direction of the waves, only the sound energy is
transferred.
3. However these descriptions of waves don't
completely fit electromagnetic radiation e.g. radio, microwave,
infrared, visible light, uv, X and gamma rays. In this case the energy is carried by photons, which have
wave properties, but they do actually move from one place to another e.g.
from the Sun to Earth or reflected light by which you see objects. BUT, they
still transfer energy e.g. infrared radiation transfers thermal energy from
the Sun to the Earth's surface, visible light energy triggers a response on
a photographic plate or a photosensitive electronic photocell.
The first two examples, 1. and 2. above, require a medium e.g. air or
water, but electromagnetic radiation can travel through a vacuum as well as
transparent materials like air, water or glass.
However, the vibrations-oscillations of the photons due to their wavelike properties
occur at 90o to the direction of travel, so they are transverse
waves.
TOP OF PAGE and
sub-index
(c) The technical description and properties
of a TRANSVERSE WAVE and equation
The above diagram gives an idea of
a transverse wave where the oscillations/vibrations (disturbance) are at 90o to the
direction the wave moves.
-
electromagnetic radiation waves,
ripples-waves on water, shaking a slinky spring or rope from side to side,
earthquake waves of the S-waves type.
TOP OF PAGE and
sub-index
(d) The technical description and properties
of a LONGITUDINAL WAVE
The oscillations/vibrations of a longitudinal wave are in the same
direction as the wave is moving.
The disturbance of the medium is
parallel to the direction the wave is moving.
Know and understand why longitudinal waves show areas
of compression and rarefaction.
The above diagram shows the compression and
decompression (rarefaction) of a longitudinal sound wave, illustrated
'visually' by the pushing pulling of a slinky
spring (see below 'picture' below).
The 'to and fro' effect is due to the
particles of the medium being compressed to give a point of maximum particle
density (maximum pressure), squashed up to give a compression.
At the
same time, further along the wave, the arrangement of particles is stretched out
to give a point of minimum density (or minimum pressure) called a rarefaction.
You can appreciate this by the way the
vertical lines and spaced out or compressed together - the vertical lines
represent the relative density of particles in the medium (gas, liquid
or solid).
Also, the diagram above illustrates
longitudinal sound waves travelling at the same speed where wave B has twice the
frequency and half the wavelength of wave A. You can deduce this because in wave
B the distance between two compression or two rarefactions is halved, so twice
as many waves will pass a given point in the same time.
The diagram above illustrates a slinky spring
'pulsed' with longitudinal waves. It also illustrates in a way what happens to
the air when a sound wave passes through it and the ground with one of the
types of earthquake wave (the compressional P waves), which go right through the
Earth to the other side of the world!)
Examples of longitudinal waves:
Sound waves - e.g. from your
vocal chords or musical instrument
Earthquake P-waves - that can
go right through the Earth
Slinky spring - 'pushed and
pulled' to send pulses of energy along it.
TOP OF PAGE and
sub-index
(e)
Comparing and contrasting examples of transverse and longitudinal waves
-
You need to understand that in a
transverse wave the oscillations are perpendicular (at 90o) to the direction of
energy transfer, but in a longitudinal wave the oscillations are parallel to
the direction of energy transfer ie direction of forward wave movement.
-
Transverse wave
-
-
Longitudinal wave
-
-
Shaking a slinky spring from
side to side produces a transverse wave, as ripples on water and all
electromagnetic radiation.
-
Pulling and pushing on a slinky
spring produces pulses of energy transmitted as a longitudinal wave like a
sound wave travelling through a medium ie the 'compressions' and
'rarefactions' are in the same direction as the wave movement.
-
When your TV receives the signal its just
coded data in the electromagnetic transverse waves, no material substance arrives!
Or does it? Can't photons behave like little bullets?
-
However, if energy itself wasn't transmitted
or no effected could be produced by the TV receiver!
-
Similarly, when ripples on water cause
floating objects to bob up and down, energy is needed to do this, but
neither the floating object or the water itself actually move in the
direction of the transverse waves.
-
The most dramatic transfer of energy
involves
earthquake waves, both transverse and longitudinal, yet the effects
are transmitted and felt miles from the epicentre and no part of the earth's
crust moves in the direction of the seismic waves but it may move violently
from side to side, up and down or compressed/decompressed.
-
When sound waves vibrate your ear drum no
air moves from the TV, person or musical instrument etc., yet energy is
transferred through the medium of air, otherwise, what causes your ear drum
to vibrate!
The general points
and behaviour of waves is discussed above and below are dealt with in more
detail on separate pages -
see the waves index at the end.
TOP OF PAGE and
sub-index
(f) More on the properties of waves - reflection, refraction,
diffraction
(all dealt with in more
details for specific examples like light or sound)
All waves undergo reflection, refraction and
diffraction and a general description of them is explained below.
Appreciate and understand that all three
wave effects can be successfully modelled in the way described in the manner
described below and predictions can be made on the basis of these models.
What can happens when waves meet a boundary between two media?
When waves meet an interface between two
materials there are three possible outcomes.
The outcome depends on the properties of
the wave and the nature of the two materials involved.
(i) The wave, its energy, is absorbed
by the second material, so the energy store of the 2nd material is increased -
this usually equates to increasing the thermal energy store of the 2nd
material.
Soft materials easily absorb sound wave
energy.
Rough matt black surfaces absorb most of
visible light that's why they look black!
Infrared radiation from the Sun heats up
surfaces.
(ii) The wave is reflected back off
the second material without losing any significant energy. In this case there is
little wave energy absorbed or transmitted.
If the surface is particularly
smooth-shiny and flat, very little wave energy is absorbed and you can
observe a high quality reflected image e.g. looking at yourself in a silver
surfaced mirror!
In the case of sound you get echoes.
If the surface is rough, much of the wave
energy is absorbed or scattered in all directions.
(iii) The wave is transmitted through
the second material without being absorbed and the waves may change direction
(refraction).
This can happen if the material is transparent and
the waves can continue passing through the 2nd material
You see this by the 'bent' image at the
'wrong' angle when observed putting a stick in water.
Refraction effects are used in the
lenses of optical equipment like reading glasses and cameras.
(iv) There are situations where waves
partially meet a barrier and bend round corners or pass through a gap in a
barrier and then spread out - radiating from the gap.
These effects are called diffraction and does not involve passing from one medium to another.
You can hear sound round a corner -
that's due to a combination of reflection and diffraction effect.
(v) You should be aware that in some
situations (some already mentioned) you may get a combination of effects.
e.g. when a light beam in air then
passes through a glass block, some rays refract at the interface and
others are reflected.
What actually happens at an interface
depends on the wavelength/frequency of the wave and the properties of
the materials the waves strike.
The five points (i) to (v) are now discussed in detail using the scientific
models of waves in sections (g) to (i) below.
TOP OF PAGE and
sub-index
(g)
REFLECTION of waves and scientific wave model
TOP OF PAGE and
sub-index
(h)
REFRACTION of waves and scientific wave model
-
Waves travel at different speeds in
different materials and this can result in a change of direction as the
waves pass through a boundary from one material to another.
-
To explain
how waves will be refracted at a boundary in terms of the change of speed and
direction, we need diagrams!
-
The scientific model explaining refraction of waves at a boundary between two media
-
The above diagram
illustrates the phenomena of refraction by considering what happens to
waves e.g. visible light or water waves.
-
You can think of the
parallel lines as representing a series of crests of waves eg think
of waves on the sea or ripples in a pond on throwing a stone in or
ripple tank experiments in the school laboratory.
-
The vertical dotted line is NOT a
wavefront, but as already mentioned in reflection, it is an important
imaginary construction line at 90o to the media boundary to help
measure what we call the angles of incidence and refraction - see diagram of
refraction below.
-
Refraction A: When waves passing
through a less dense medium, hit a boundary interface, and enter a
more dense medium, the waves 'bend towards the normal' i.e. refraction
occurs.
-
*
-
This happens because on
entering the more dense medium, the waves are slowed down causing the change
in wave direction at the boundary interface. Diagram above and left of diagram below. Diagram
B is discussed later, but it is the opposite situation to refraction A.
-
Comparing refractions A and B
-
The above diagram illustrates the
scientific model of the wave theory of refraction.
-
You can also see that in refraction A the wavelength
is decreased as well as the velocity.
-
The frequency does NOT change.
-
wave speed
= frequency x wavelength, in 'symbolic shorthand'
v = f x
λ (see
wave calculations)
-
If the frequency (f) does not
change, then the velocity (v) is directly proportional to wavelength
(λ).
-
The bigger the change in speed the
bigger the change in direction - the greater the angle of refraction.
-
You see this effect in ripple tank
experiments when you abruptly go from deeper water to shallower
water the waves will change direction towards the normal.
-
The waves slow down in shallower
water and if they hit the shallower water at an angle, refraction
will occur.
-
The waves slow down in shallower
water because of increased friction with the bottom surface of the ripple tank.
-
In this example the refraction has
nothing to do with density, but is caused by increased friction -
increase in the 'drag' effect.
-
You can observe this in a ripple tank by
placing a rectangular plate in to the water at an angle to the waves and you
can see these changes in wavelength and speed. BUT, by using a
stroboscope you can show the frequency does not change.
-
Effect
of decreasing speed.
-
For examples see
Reflection,
refraction and diffraction of visible light, examples with diagrams and explanations
-
Refraction B: When
waves from a more dense medium, hit a boundary interface, and enter a
less dense medium, the waves 'bend away from the normal' ie refraction
occurs.
-
*
-
This happens because on
entering the less dense medium, the waves can speed up causing the change in
wave direction at the boundary interface. Diagram above and right of diagram below. Diagram
refraction A has been previously discussed, but here refraction B is
the opposite situation to refraction A.
-
Comparing refractions A and B
-
The above diagram illustrates the
scientific model of the wave theory of refraction.
-
You can also see that in refraction B the wavelength
has increased as well as the velocity.
-
The frequency does NOT change.
-
wave speed
= frequency x wavelength, in 'symbolic shorthand'
v = f x
λ (see
wave calculations)
-
If the frequency (f) does not
change, then velocity (v) is directly proportional to wavelength
(λ).
-
The bigger the change in speed the
bigger the change in direction - the greater the angle of refraction.
-
You see this effect in ripple tank
experiments when you abruptly go from shallower water to deeper
water the waves will change direction away from the normal.
-
The waves speed up in deeper
water and if they hit the deeper water at an angle, refraction will
occur.
-
The waves speed up in deeper water because
of decreased friction with the bottom surface of the ripple tank.
-
In this example the refraction has
nothing to do with density, but is refraction caused by decrease in friction -
reduction of the 'drag' effect.
-
You can observe this in a ripple tank by
placing a rectangular plate in to the water at an angle to the waves and you
can see these changes in wavelength and speed. BUT, by using a
stroboscope you can show the frequency does not change.
-
Effect
of increasing wave speed
-
For examples see
Reflection,
refraction and diffraction of visible light, examples with diagrams and explanations
-
If the waves hit the
interface at an angle of 90o (perpendicular) to the
interface between the two mediums, there is still a change in speed and
wavelength, but there is NO change in direction, NO refraction and the wave frequency remains
the same. See diagrams below where the waves strike the boundary along,
or parallel to, the normal.
-
-
A: When the waves pass from a less dense
medium to a more dense medium the waves decrease in velocity at the media
boundary and the
wavelength also decreases.
-
B: When the waves pass from a more dense
medium to a less dense medium the waves increase in velocity at the media
boundary and the
wavelength also increases.
-
In both cases the frequency remains
unchanged and in both cases no refraction takes place.
-
You can observe this in a ripple tank by
placing a rectangular plate in to the water parallel to the waves and you
can see these changes in wavelength and speed. BUT, by using a stroboscope
you can show the frequency does not change.
-
-
The effect of increasing or decreasing
friction in a ripple tank - effectively decreasing speed and wavelength or
increasing speed and wavelength,
TOP OF PAGE and
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(i)
DIFFRACTION of waves and scientific wave model
-
-
The scientific model of
the diffraction of waves through a gap
(or bending round a corner)
-
Diffraction is the effect
of waves spreading out when passing through a gap or passing by a barrier.
In effect, waves go round corners! and it doesn't matter if its sound, light
or water waves - they all diffract and bend round corners! The effect is so
small with light (tiny wavelength), you don't notice it, but you see water
waves bending around the walls of a harbour and you can hear sounds from
round a corner.
-
You should appreciate that
significant diffraction only occurs when the wavelength of the wave is of
the same order of magnitude as the size of the gap or obstacle.
-
A: There is a relatively small
diffraction effect when waves pass through a wide gap that is much bigger
than the wavelength of the wave.
-
B: You get the maximum spreading
or diffraction when the waves pass through a gap of similar size to the
wavelength of the incident waves.
-
You can see these effects with transverse
water waves at the seaside as waves hit the protective walls of a harbour
BUT you need a very tiny slit to observe diffraction with light waves
because of their tiny wavelength.
-
Excluding satellite TV and
radio, if it wasn't for diffraction you would never get a radio
signal down in a valley - the radio waves bend over the hills!
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(j)
WAVE CALCULATIONS - formulae and how to solve wave problem
questions
Examples of wave calculations
Q1
A wave has a speed of 0.25 m/s and a wavelength of 5.0 cm.
(a) Calculate the frequency of the wave
f = v ÷ λ
5.0 cm ≡
5/100 m = 0.05 m
Therefore frequency = 0.25/0.05 =
5.0
Hz
(b) Calculate the period of the wave.
period = 1 / frequency = 1 / 5 =
0.20 s
Q2 The
frequency of sound in air at room temperature and pressure is 343 m/s.
The musical note middle C has a frequency of 262 Hz.
Calculate the wavelength of the middle C sound.
λ
= v ÷ f
wavelength = 343 ÷ 262 =
1.31 m (131 cm, 3
s.f.)
Q3
A set of ocean waves has a frequency of 0.50 Hz.
If the average distance between the
crests of the waves is 10 m, what is the average speed of the ocean waves?
v = f x
λ
speed (m/s) = frequency (Hz) x wavelength
(m)
speed = 0.5 x 10 =
5.0 m/s
Q4
The time period of a radio electromagnetic wave is 5.0 x 10-5 seconds
(a) What is the frequency of the radio
wave?
period = 1 / frequency
f = 1 / period = 1 /
(5.0 x 10-5) =
2.0
x 104
Hz
(b) If the 'speed of light' is 3.0 x 108
m/s, calculate the wavelength of the radio wave in m.
λ
= v ÷ f = 3.0 x 108 / 2 x 104 =
1.5 x 104 m
(c) If the distance from the radio
station to your radio is 200 km, how long does it take the signal to reach
you?
The speed formula is v = d / t,
so t = d / v
= (200 x 1000) / (3.0 x 108) =
6.7 x 10-4
s
Q5 A water wave has a frequency of 0.50 Hz
and a wavelength of 150 cm.
(a) Calculate the speed of the wave in
m/s.
v = f x
λ = 0.50 x (150/100) =
0.075 m/s
(b) If the frequency of this wave
triples, what will be its wavelength? and what assumption have you made?
If you assume the speed stays the
same, the wavelength will be a third of 150 cm, 50 cm or
0.50 m,
because frequency x wavelength (f
x λ) is a constant for a constant speed.
(c) If the frequency of the original wave
doubles, and the wavelength of the wave quadruples, what will be the new
speed of the wave?
v = f x
λ, putting in the factors gives 2 x (1/4) = 0.5, so the new
speed will be 0.5 x 0.075 =
0.038 m/s (2 sf)
Q6
Suppose an airliner sends out a microwave radar signal of wavelength of 1.20 cm.
The microwave reflects off another
aircraft and the echo is detected after a time lapse of 6.0
µs.
The
speed of electromagnetic radiation = 3.00 x 108 m/s.
(a)
What is the frequency of the microwave beam?
speed =
wavelength x frequency
f = v ÷ λ = 3.00
x 108 ÷ (1.20 / 100) =
2.50 x 1010
Hz
(b)
What is the distance between the two aircraft?
s = d / t,
d = s x t = 3.00 x 108 x 6.0 x 10-6 = 1800 m
(total distance including echo)
distance
between aircraft = 1800 ÷
2 = 900 m
(µ
is micro = 10-6, and total distance is halved because it
involves 'there and back')
Q7
A satellite is 75 km above the Earth's surface. (speed of light 3.00 x 108
m/s)
What is the shortest time that a
microwave signal would take to reach the satellite from the Earth's surface?
s = d / t, t = d / s = (75 x 1000)
/ (3.00 x 108) =
2.50 x
10-4
seconds
Q8
A red light wave has a wavelength of 7.0 x 10-7 m. (speed of light
3.00 x 108 m/s)
What is the frequency of the light wave?
v = f x λ * f = v / λ
= 3 x 108 / (7.0 x 10-7 m) =
4.29 x
1014
Hz (3 sf)
Q9
Need Q using kHz, X-rays, gamma etc.
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sub-index
(k) Experiments with water
waves
in a
RIPPLE TANK
The humble ripple tank is an excellent way
for students to experimentally investigate waves.
Introduction - common points for all
three wave experiments described
The apparatus consists of:
A transparent tank of water - so you can
clearly observe the waves.
A paddle or dipper is suspended over and into the
water of the ripple tank.
A small
electric motor that is slightly off-set from symmetrical rotation is used to
oscillate the paddle/dipper - this
gives the 'to and fro' rocking action of the paddle sending waves from left
to right.
The vibration generator can have a
built in signal generator so that you can directly set the
frequency of paddle oscillation i.e. frequency of the ripple waves.
A variable power supply allows you to vary the rate
of 'to and fro' oscillation of the paddle that produces the water waves -
this allows a fixed wave frequency to be created AND the ability to vary the
water wave frequency. You might even have a 'sophisticated' frequency
generator to work the humble paddle!
A stopwatch is essential, plus a small
cork, white paper, ruler, pencil, strobe light of variable frequency, graph
paper stuck on card.
(Note: My diagrams are simplified and
don't show the full detail of a good quality ripple tank set-up - could
anybody send me a good image of a really good set-up? properly acknowledged
of course.)
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sub-index
(i) How to measure the
frequency of a water wave
Here
you place a small cork on the water and start the wave generator to make the
cork bob up and down.
Choose a start point e.g. the top of a bob, start the stopwatch
and time 10 complete oscillations or 'bobs'.
Divide the time by 10 gives you a good average time for
one
period.
Then, a simple calculation ...
Frequency = 1 / period = ? Hz.
You can of course do the calculation directly: Frequency (Hz) =
10 / total time (s)
Repeat with different frequencies.
2nd method
You can measure the frequency by
using a lamp shining down on the ripple tank and projecting shadows onto
a screen under the tank.
Mark a point on the middle of the
screen and switch on the wave generator.
Then count the number of waves
passing in a given time e.g. X waves in 20 seconds using a stopwatch.
Therefore the frequency is
X/20 Hz.
(ii) How to measure the
wavelength of a water wave
For this experiment you need a graph card at the back of the
tank.
Set the oscillator going to give a steady stream of water waves.
Direct the strobe light onto the ripple tank so several of the
waves are illuminated.
Adjust the frequency of the strobe light until the waves seem to
stand still.
At this point you can then measure the length of e.g. 10 waves
against the back projection of the graph card.
Just divide the total length by the number of waves to get an
average wavelength in cm ==> m.
You can repeat with different frequencies of the oscillating
paddle.
For variation on the method of measuring
wavelength see
measuring speed of a wave
See also
SOUND - how to measure the wavelength of
sound wave
(iii)
How to measure the
speed of a water wave
1st method to
measure the speed of water ripples
You
need two students for this experiment.
Place a large piece of white paper by the side of the tank.
Place a ruler on the paper alongside the tank.
Start the waves going and track the path of a crest on the paper
with the pencil.
The second student starts the stopwatch as the first person
starts marking with the tracking pencil.
Therefore you have time and distance data to calculate the speed
of the waves.
speed (m/s) = distance (m) / time (s)
Don't forget if the distance was measured in cm, divide by 100 to get metres!
In all these experiments where you are changing a variable,
keep all the equipment the same and do three repeats to get a good average.
For a fair test also watch for the variables you are not
testing for ..
e.g. keep the amplitude of the wave constant, keep the
'dipper' in the same position - immerse in same depth of water, use the same
depth of water in the tank.
2nd
method to measure the speed of water ripples
(also indirectly, the wavelength too)
You use the same apparatus set-up
described above, but coupled with a signal generator and employing
the use of a stroboscope and a screen below the tank.
By using a signal generator attached
to the paddle of the ripple tank, you produce water waves of a
particular frequency.
The lights are dimmed and turn on the
strobe light to see the wave pattern.
You alter the strobe light frequency
until waves seem to freeze on the screen under the tank - this because
the strobe light frequency matches the water wave frequency and al the
waves are lit at the same point in their cycle at the same time.
You measure the width of 10 crests
(or troughs) from the shadow lines and divide by 10 giving you the
length of one wavelength - you can place a ruler down on the screen
aligned with the direction of wave movement.
You now know the frequency (Hz) and
wavelength (convert to m) of the water waves and so ...
speed = frequency x wavelength =
v = f x
λ = ? m/s
Variation on the above method with
using a strobe light
By using a signal generator attached
to the paddle of the ripple tank, you produce water waves of a
particular frequency.
The lights are dimmed and broad
bright light is shone from above the tank to cast a shadow on the screen
below.
Again, you measure the width of 10
crests (or troughs) from the shadow lines and divide by 10 giving you
the length of one wavelength - you can place a ruler down on the screen
aligned with the direction of wave movement.
You now know the frequency (Hz) and
wavelength (convert to m) of the water waves and so ...
speed = frequency x wavelength =
v = f x
λ = ? m/s
TOP OF PAGE and
sub-index
(l) Another investigation
of waves using a tensioned wire and signal generator
A The set-up
A signal generator is connected to a vibration
transducer.
A longish piece of wire or string is fixed to the
vibration transducer and passed over a pulley wheel at the end of the
bench.
The other end of the wire/string is
connected to a hook system on which
you can add 'weights' to increase the tension on the wire/string.
B The procedure
You switch on the signal generator
and vibration transducer to set the
wire/string vibrating - the waves should oscillate up and down.
Adjust the frequency until you can get a
clear transverse standing wave (as in diagram B) and measure its
wavelength using the metre rule sighted behind the vibrating
wire/string.
Its easiest to measure the length
of as many half wavelengths as you can, calculate the average and
then double the average to get the full wavelength.
You can vary two things:
(i) Vary the weights added to
tension the string and measure the wavelength each time for a fixed
length of wire/string between the transducer and the pulley wheel.
(ii) Vary the length of the
wire/string between the transducer and the pulley wheel for a fixed
tension weight.
Obviously, you can do several
sets of results within the experimental framework of (i) and (ii).
Measurements and calculations
For each set of experiments you
should record
the frequency of the standing
wave (f in Hz)
the tension on the string/wire (T
in N)
the total length of the
wire/string (L in
m)
the wavelength (λ
in m)
and you can calculate the speed
too (v = f x
λ in m/s).
This gives you loads of data
to play with!
You should find that the wavelength
of the string wire measured varies with:
(i) The in tension on the
wire/string for a fixed length.
You should find the frequency
increases and wavelength decreases the greater the tension on
the wire/string.
The frequency is proportional
to the square root of the tension (f
1/√T).
Think of tightening the
tension on a guitar or violin string (fixed length) - the pitch
increases the more you tighten it up.
(ii) The length of the
wire/string for a fixed tension weight.
You should find that the
frequency increases and wavelength decreases the shorter the wire/string.
For a fixed tension weight,
the frequency of a stretched string is inversely proportional to
the length of the string (f
1/L).
Having measured the wavelength
(convert to m), and knowing the frequency (Hz) from
the generator, you can then calculate the speed of the wave in each
case.
speed = frequency x wavelength =
v = f x
λ = ? m/s
For more
see
measuring the speed of sound in air
TOP OF PAGE and
sub-index
Some general learning objectives
-
Know and understand that waves transfer energy.
-
Know and understand that waves may be either
transverse or longitudinal.
-
Know that
ALL
electromagnetic waves are
transverse (radio, microwave, infrared, visible light) as are waves on water
- eg ripples, sound waves are longitudinal and mechanical waves may be either
transverse or longitudinal.
-
Know that all types of
electromagnetic waves travel at the same speed through a vacuum (~
empty space) -
'the maximum speed of light' which is 3 x 108 m/s.
-
Know that electromagnetic waves form a
continuous spectrum.
-
You should know the order of
electromagnetic waves within the spectrum, in terms of energy, frequency and
wavelength.
-
You should appreciate that the
wavelengths vary from the minute 10-15 metres for extremely high
frequency gamma rays to more than 104
metres for very low frequency radio waves.
-
Know that waves are
reflected and refracted at boundaries between different materials and in
diffraction, can spread
out when passing the end of a barrier or through an opening.
-
Know and understand that light waves can be reflected,
refracted and diffracted.
-
Appreciate and understand that all three
wave effects can be successfully modelled in the way described in the
following sections.
TOP OF PAGE and
sub-index
WAVES - electromagnetic radiation, sound, optics-lenses, light and astronomy revision notes index
General
introduction to the types and properties of waves, ripple tank expts, how to do
wave calculations
Illuminated & self-luminous objects, reflection visible light,
ray box experiments, ray diagrams, mirror uses
Refraction and diffraction, the visible light
spectrum, prism investigations, ray diagrams explained
gcse physics
Electromagnetic spectrum,
sources, types, properties, uses (including medical) and dangers gcse physics
The absorption and emission of radiation by
materials - temperature & surface factors including global warming
See also
Global warming, climate change,
reducing our carbon footprint from fossil fuel burning gcse
chemistry
Optics - types of lenses (convex, concave, uses),
experiments and ray
diagrams, correction of eye defects
The visible spectrum of colour, light filters and
explaining the colour of objects gcse physics revision notes
Sound waves, properties explained, speed measure,
uses of sound, ultrasound, infrasound, earthquake waves
The Structure of the Earth, crust, mantle, core and earthquake waves (seismic wave
analysis)
gcse notes
Astronomy - solar system, stars, galaxies and
use of telescopes and satellites gcse physics revision notes
The life cycle of stars - mainly worked out from emitted
electromagnetic radiation gcse physics revision notes
Cosmology - the
Big Bang Theory of the Universe, the red-shift & microwave background radiation gcse
physics
IGCSE revision
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