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Waves
By Neil Bronks
Some definitions…
Crest
1) Amplitude – this is
height of the wave.
Trough
2) Wavelength () – this is the
distance between two
corresponding points on the
wave and is measured in metres:
3) Frequency – this is how many waves pass by
every second and is measured in Hertz (Hz)
Some definitions…
Transverse waves are
when the displacement
is at right angles to the
direction of the wave…
e.g.Light
Longitudinal waves
are when the
displacement is
parallel to the
direction of the wave…
e.g.Sound
The Wave Equation
The wave equation relates the speed of the wave to its
frequency and wavelength:
Wave speed (v) = frequency (f) x wavelength ()
in m/s
in Hz
in m
V
f

Diffraction
Diffraction is when waves spread out from the edge of a gap.
More diffraction if the size of the gap is similar to the wavelength
More diffraction if wavelength is increased (or frequency decreased)
Sound bends better around corners
Uses of Total Internal Reflection
Optical fibres:
An optical fibre is a long, thin, transparent rod made of glass
or plastic. Light is internally reflected from one end to the
other, making it possible to send large chunks of
information
Optical fibres can be used for communications by sending e-m signals
through the cable. The main advantage of this is a reduced signal loss.
Also no magnetic interference.
It is important to coat the strand in a material of low n.
The light can not leak into the next strand.
Detection
• Waves invisible to
the eye have to be
detected using
special apparatus
• IR (Infra-Red) is
a heat wave so a
blackened
thermometer bulb
UV Light
• Ever walked into a nightclub
• White cloth washed in optical
brighteners glows in UV light
Coherent Waves
• Same Frequency
• In Phase
Or Constant phase
difference
Phase difference in
measured in
degrees of a circle
Interference is where 2 coherent waves meet.
The resultant is the algebraic sum of the 2
waves at any point.
+
=
Constructive
Interference
To Remember this we simplify it a little
Equation
• sin  = /d
• d sin  = 

d


• When more than one
wavelength difference
• d sin  = n
MEASUREMENT OF THE WAVELENGTH
OF MONOCHROMATIC LIGHT
n=2
Metre
stick
n=1
Laser
θ
x
n=0
Diffraction
grating
D
Tan θ = x/D
n=1
n=2
Polarization of Light
Normally all e-m waves (Transverse) oscillate
in all perpendicular planes at once.
Polarization leaves only one plane of oscillation
Sound is a longitudinal wave and so can not be
Polarised
Standing Waves
When two coherent waves of the same amplitude traveling in
opposite directions meet the waves combine to form a
stationary wave
We draw this as the two extremes
n
A

Real Standing Waves
Strings
/2
Closed
Tubes
/4
Open
Tubes
/2
MEASUREMENT OF THE SPEED
OF SOUND IN AIR
Tuning fork
λ=4(l1+0.3d)
d
l1
Graduated
cylinder
Tube
Water
Harmonics
Whole number multiples of the fundamental
frequency that happen at the same time as
the fundamental.
Formula for stretched string
1 T
frequency 
2l 
1
f
l
L=length
T=tension
=mass/unit length
f T
INVESTIGATION OF THE
VARIATION OF FUNDAMENTAL
FREQUENCY OF A STRETCHED
STRING WITH LENGTH
Tuning
Fork
Paper rider
l
Sonometer
Bridge
Musical Notes
Music waves have a regular
shape where noise is irregular
Three Qualities – called the characteristics
1. Pitch - This is frequency of the wave.
2. Loudness - this is the amplitude of the
wave.
3. Timbre or Quality - The wave shape that is
mainly due its overtones.
Resonance
• Transfer of energy between two
objects with the same, or very
similar, natural frequency.
Barton’s Pendulum
String
Doppler Effect
The apparent change in frequency due to
the motion of the observer or the source
• Hence the change in pitch as a car passes
• Used by the Gardai in to detect speeding cars
Summary - Sound as a Wave
Interference proves sound is a wave.
If we twist a
tuning fork near
our ear it goes
loud and soft.
The two prongs
of the fork are
interfering with
each other.
Threshold of Hearing
• The absolute threshold of hearing
(ATH) is the minimum sound level of a
pure tone that an average ear with
normal hearing can hear in a noiseless
environment at 1kHz.
Limits of Audibility
• The top and bottom
values of the range are
known as the limits of
audibility.
•
For the human ear, the
lower limit is approximately
20 Hz and the upper limit is
20,000 Hz. In other words,
our ears are supposed to be
able to hear sound with
frequencies that are
greater than 20 Hz and less
than 20,000 Hz.
High Tension
Voltage
X-Rays
• Electrons jump from the
surface of a hot metal –
• Thermionic Emission
Accelerated by high voltage they smash into tungsten
The electrons excite orbiting electrons to high energy
orbits-see next few slides for details
These fall back emitting high frequency waves.
Most of the electron energy is lost as heat.-about 90%
X-rays very penetrating, fog film, not effected by fields.
The Problem
• If you shine light on the surface of
metals electrons jump off
e
e
e
e
e
Polished Sodium Metal
• Electrons emitted
• This is The PHOTOELECTRIC EFFECT
A charged Zinc plate
is attached to an
Electroscope
When a U.V. lamp is
shone on the plate
the leaf collapses as
all the electrons
leave the surface of
the zinc
Einstein’s Law
So we define the Photoelectric effect as:-
Electrons being ejected from the surface of a metal by
incident light of a suitable frequency.
Uncle Albert used Plank’s theory that as energy came in
packets all energy 1 photon to 1 electron
A small packet would not give the electron enough energy to
leave
Low frequency light had too small a parcel of energy to get the
electron free.
Energy of each
photon = h.f
Photo-Electric Effect
Electron
Energy
f0=Threshold
Frequency
Frequency of
light
Energy of incident photon =
h.f = h. f0+ KE of electron
Work Function,
Energy to release Electron
Energy
left over
turned
into
velocity
Reflection
Wave bouncing off
a solid object
Refraction
Waves changing
speed and direction
due to change in
density of medium
Echo
Frequency
stays the
same
Better with
long
wavelength
Sound round
corners
Spreading from
slit
Interference
Two coherent
waves meeting
combine wave at
any point is the
algebraic sum of
the two waves
Proves
things are
waves
Constructive
and
destructive
Polarisation
Reduces transverse
waves to one plane
of oscillation
Difference
between
transverse and
longitudinal
Snow
sunglasses
Diffraction
spreading of a wave
around an obstacle
or on the emergent
side of a slit.
Hear people
across a lake