Waves and wave motion.
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In physics, waves are classified as
either mechanical waves or
electromagnetic waves.
Examples of mechanical waves
include, water waves, waves on a
rope or slinky and sound waves. All
mechanical waves must have a
medium to travel through.
Electromagnetic waves make up
the electromagnetic spectrum and
include radio waves, micro-waves,
visible light and infra-red waves.
Electromagnetic waves do not
require a medium to travel, they
can travel through a vacuum, at a
speed of 3 x 108 m/s.
Travelling mechanical waves.
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“ a travelling mechanical
wave is a disturbance
carrying energy through a
medium without any
overall motion of that
medium”.
Waves can be seen as a
means of transferring
energy from one place to
another.
Periodic waves.
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A disturbance in a
medium caused by a
series of identical
wave pulses is known
as a periodic wave.
Transverse and longitudinal waves.
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A transverse wave is a
wave where the direction of
the vibration is
perpendicular to the
direction in which the wave
travels. (e.g. waves on a
rope, water waves, E.M.
waves)
A longitudinal wave is a
wave where the direction of
vibration is parallel to the
direction in which the wave
travels. (e.g. compressions
on a spring, sound waves)
Terms used to describe periodic travelling
waves.
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The top of the wave is called a
crest, the bottom of the wave is
called a trough.
The maximum distance of any
particle of the medium from the
undisturbed position is called the
amplitude (A). Measured in
metres.
The disturbance produced by one
complete vibration of the source is
called an oscillation or cycle( i.e.
one crest and one trough.)
The distance from any point on
one cycle to the corresponding
point on the next cycle is called
the wavelength () i.e. trough to
trough or crest to crest. Measured
in metres.
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Vibrating
source
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The number of cycles
passing a point per
second is called the
frequency ‘f’ of the
wave. Frequency is
measured in units called
hertz (Hz).
1 Hz = 1 cycle per
second.
The distance travelled by
any point on the wave in
one second is the
velocity of the wave ‘c’,
measured in metres per
second.
c = fλ
Wave phenomena
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Reflection
Refraction
Diffraction
Interference
Polarisation
The Doppler Effect.
When discussing the
various properties
of waves, we will use the
idea of wave fronts.
Wave fronts are a series of
parallel lines drawn to represent
a number of waves. The
parallel lines are drawn to
represent the position of an advancing
wave. The lines are formed by joining
points that are in phase, such as the
crests.
Reflection of waves.
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When a wave front
strikes an obstacle, it
is reflected.
The angle of
incidence equals the
angle of reflection.
i° = r °
N
i r
Refraction of waves.
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When waves travel from
one medium to another,
they change speed.
If the waves passes the
inter-face at an angle
other than 90 ° then the
wave will be refracted.
Refraction is the
change in direction of a
wave as it passes from
one medium to another.
Diffraction of waves
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When a wave front strikes an
obstacle or a gap, it tends to
spread out in the region behind
the obstacle or gap..
The extent to which the wave
spreads out depends on the size
of the obstacle or gap in terms of
the wavelength ‘λ’ of the wave.
The greater the wavelength of the
wave compared to the width of the
obstacle, the greater the extent to
which the wave spreads out.
The diffraction of
sound waves explains
why an open door will
allow a noise form
outside to be heard
throughout the room. As
the sound wave passes
through the opening of
the door, it is diffracted
and spreads out in all
directions behind the
door.
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Diffraction is the
spreading out of a
wave when it meets
an obstacle or gap in
its path.
When a wave passes through a narrow gap it is
diffracted and spreads out. For a wave of a given
wavelength, the narrower the gap through which the
wave passes, the greater the diffraction will be.
Polarisation of waves.
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Polarisation occurs
when the plane of
vibration of a wave is
restricted to one
plane only.
Only transverse
waves can be
polarised.
Vertically
polarised
Horizontally
polarised.
All electromagnetic waves,
including visible light are
made up of an electric
component and a magnetic
component which vibrate
at right angles to each other.
A source of white light will
consist of a number of waves
vibrating in all directions.
Polaroid sunglasses work by
coating the lenses of the glasses
with a material which will only
allow light of one plane of vibration to pass through. All other waves
are absorbed. Light which has been polarised in such a way is
said to be plane polarised.
If two pieces of polaroid material are held perpendicular
to one another, no light can pass through.
Light
Source
Polaroid A
Polaroid B
Interference of waves.
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What happens when two or more waves meet at a point
?
Answer: The resultant displacement at that point is equal
to the algebraic sum of the individual displacements at
that point. (Principle of superposition)
If waves from coherent sources meet and interfere with
each other an interference pattern is produced.
Coherent sources are sources which have the same
frequency and are in phase with each other.
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Interference occurs when
two or more waves meet.
The amplitude of the
resulting wave is equal to
the algebraic sum of the
amplitudes of the
interfering waves.
Depending on the point at
which waves meet and
interfere, the resultant
amplitude will either be
greater or less than the
initial amplitudes.
Constructive interference occurs when
two waves meet and the amplitude of the
resulting wave is greater than the
amplitudes of the individual waves.
Destructive interference occurs when two
waves meet and the amplitude of the
resulting wave is less than the amplitudes
of the individual waves.
Interference patterns.
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If two or more
coherent waves meet
and interfere, then an
interference pattern
is produced.
Diagram shows the
interference pattern
produced in a ripple
tank, by two coherent
point sources.
The Doppler Effect.
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The Doppler Effect is the
apparent change in
frequency due to the
relative motion between
source and observer.
For sound waves the
Doppler effect produces a
change in pitch.
For light waves a change
in colour is produced.
Stationary and moving source.
Crest 1
Crest 1
Crest 2
Crest 2
Crest 3
Crest 3
A
B
S
A stationary source S emits
a wave of given wavelength and frequency.
The wave is emitted in all directions from a
point source, with equally spaced wave fronts
movie
A
S1 S2 S3
B
A moving source S emits a wave of given
wavelength and frequency. The
emitted wave fronts are no longer
equally spaced but begin to ‘bunch up’ in
front of the moving source.
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For a stationary observer
in front of a moving
wave source (source and
observer moving closer),
the wavelength of the
wave appears to be
decreasing.
The speed ‘c’ of the
wave remains constant.
The frequency appears
to be increasing.
f’ = f c
c-u
a stationary observer
behind a moving wave source
(source and observer moving
apart), the wavelength of the
wave
appears to be increasing.
The frequency appears to be
decreasing.
 f’ = f c
c+u
where,
f ' = observed frequency
f = actual frequency at source
c = speed of the wave
u = speed of the source or observer
Examples of the Doppler Effect.
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Any moving source of
sound or light waves will
produce the Doppler
Effect for a stationary
observer. The faster the
source is moving, the
greater the effect.
Formula 1 racing cars,
passing ambulance or fire
engine.
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Applications of the
Doppler Effect include
Garda speed guns
and the Red Shift of
stars.
Standing (stationary) waves.
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If a rope is fixed at one end and vibrated
at the other, a wave is produced and
travels along the rope. When this wave
meets the fixed end it is reflected and
travels back along the rope.
If a second wave has been produced it
will meet and interfere with the reflected
wave.
At particular frequencies of vibration a
standing wave is produced on the rope.
The rope appears to have points of
maximum vibration and points which
appear to be at rest.
Terms used to describe standing waves.
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A standing wave is produced
when two coherent waves of
the same amplitude but
travelling in opposite directions
meet.
A point of maximum
displacement (caused by
constructive interference), is
called an anti-node.
A point of no displacement
(caused by destructive
interference), is called a node.
anti-node
node
Inter-nodal distance
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For a standing wave, the
distance from one node
to the next is equal to half
a wavelength.
The distance from an
anti-node to the next antinode is half a
wavelength.
Node to anti-node is one
quarter wavelength.
Λ/2
λ/2
Sound as a wave motion.
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Every sound is produced
by a vibrating source.
The vibrating source
causes air molecules to
vibrate and the vibration
travels from air molecule
to air molecule.
When this vibration
causes the ear drum to
vibrate, the human ear
detects the vibration as a
sound.
The human vocal chords
vibrate to produce the sound
of your voice.
The bell jar experiment!
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Sound travels as a
longitudinal wave.
Sound waves can
undergo all of the wave
phenomena such as
reflection, refraction,
etc…
Sound must have a
medium in which to
travel, sound cannot
travel in a vacuum.
If the air is removed from
the bell jar the sound of the
ringing bell fades although it
continues to ring..
Reflection of sound.
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The existence of echoes
verifies the fact that sound
can be reflected, when it
strikes an obstacle.
The reflection of sound waves
in large halls or arenas can
enhance the production of
sound or make it very difficult
to hear.
The study of the reflection
and absorbance of sound
waves is called acoustics.
Refraction of sound.
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Refraction is the changing of direction of waves on
entering a different medium, due to a change in speed.
When sound waves travel from air of one temperature to
air of a different temperature, they can be diffracted.
Sound travels faster in warm air than in cold air.
On a warm day sound waves are diffracted upwards
since the waves travel faster in the warmer air closer to
the ground.
On a cold day, the waves closer to the ground travel
slower and so the waves are refracted downwards.
This refraction of sound waves explains why sounds can
be heard more clearly on a cold night.
Diffraction of sound.
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Sound waves can be
diffracted when they meet
and obstacle with a gap
in it, such as a wall with
an open door or window.
Sound can pass through
an open door and spread
out into the region behind
the open door.
Because of the diffraction
of sound, it is possible to
hear around corners.
Note: The width of doorways
and windows is close to the
wavelength of audible
sounds, and so the diffraction
is considerable.
Interference of sound.
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To demonstrate that
sound travels as a
wave it can easily be
shown to undergo
both diffraction and
interference.
To demonstrate the interference of sound.
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Set up the apparatus as shown.
Turn on the signal generator.
Walk slowly form A to B.
The loudness of the sound can
be heard to increase and
decrease regularly while
moving from A to B.
This is because of the coherent
sources producing both
constructive and destructive
interference between A and B,
producing an interference
pattern.
Interference produced is
evidence that sound is a wave.
Loudspeakers.
Signal generator
Reduction of noise by destructive interference.
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Large background noises such as those produced by
exhaust systems or air conditioning units can be
greatly reduced using destructive interference.
A sample of the problem noise is picked up by
microphone and a sound wave of the same frequency
and amplitude is produced electronically.
The crests of this wave coincide with the troughs of
the noise and the troughs of the wave coincide with
the crests of the noise.
The wave is then emitted by loudspeaker into the
region where the noise exists and destructive
interference occurs.
The noise can thus be eliminated and a region of
almost silence is produced.
Speed of sound.
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The speed of sound depends
on the medium through which
sound travels.
In general sound travels faster
in a denser medium.
In a gas such as air, the speed
of sound increases with
increasing temperature.
The change in the speed of
sound as it passes from cooler
air to warmer air causes
refraction and explains why
sound can be heard more
clearly on a cold night than on
a warm day.
Material
Approx
speed of
sound.
(m/s)
Air (0°C)
Water
Copper
Steel
331
1500
3400
4800
Temperature
(°C)
Approx
speed of
sound.
(m/s)
0
20
100
331
344
384
Characteristics of notes.
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Vibrating objects will
often produce sounds
with frequencies which
are multiples of a given
frequency. These
frequencies are called
overtones.
If ‘f’ denotes a given
frequency, then ‘2f’ is the
first overtone, ‘3f’ the
second overtone, etc…
The main characteristics of a note are loudness, pitch
and quality.
• The loudness of a given note depends on the
amplitude of the wave producing it. The greater the
amplitude the louder the note.
• The pitch of a given note depends on the frequency
of the wave producing it. The higher the frequency,
the higher the pitch.
• The quality of a note is what distinguishes the same
note played on two different instruments.
• The quality of a given note depends on the number
and strength of overtones which an instrument
produces. Different instruments produce different
overtones. A tuning fork or a signal generator can
produce a pure note of just one frequency.
Frequency limits of audibility.
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For a sound wave to be
audible its frequency
must be between 20Hz
and 20,000 Hz.
The upper limit
decreases with age.
Frequencies above
20,000 Hz are called
ultrasonic and cannot be
heard by humans.
Dogs and bats can hear
sounds up to 35,000 Hz.
Natural frequency and resonance.
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An object that is free to
vibrate will tend to do so at
a preferred frequency,
called its natural frequency
of vibration.
If a periodic force is applied
to a vibrating body, with a
frequency close to or near
to the natural frequency of
vibration of the body, the
body will vibrate with a very
large amplitude.
This phenomenon is called
resonance.
Resonance is the response of
a body to a frequency equal to
or very close to the natural
frequency of vibration of the
body.
Pushing a child on a swing is
an example of resonance.
The child must be pushed at
a frequency close to the
natural frequency of the
swing, in order for the child
to swing higher and higher.
Resonance.
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The frequency of a pendulum
depends on its length. Barton’s
pendulums can be used to
demonstrate resonance.
Opera singers can produce high
pitched notes which resonate
with a drinking glass and cause it
to shatter.
The wire on a sonometer can be
made to resonate with a given
tuning fork.
Building can collapse due to
resonance produced by
earthquakes.