Transcript 4.5 Wave properties

Waves
Topic 4.5
Wave Properties
Wave Behavior
 Reflection in one
dimension
This diagram shows a
pulse travelling along a
string
This diagram shows the
pulse after it has been
reflected
Notice
 The pulse keeps its shape
 It is inverted
 It has undergone a 180o
phase change
 Or  change in phase
 This is because the instant the
pulse hits the fixed end, the rope
attempts to move the fixed end
upwards
 It exerts an upwards force on the
fixed end
 By Newton’s third law, the wall
will exert an equal but opposite
force on the rope
 This means that a disturbance
will be created in the rope which,
however is downwards and will
start moving to the left
 If the end of the rope is not
fixed but free to move the
situation is different
 Most of the pulse would carry
on in the same direction, some
would be reflected but the
reflected pulse is in the same
phase as the original pulse
 There is a change of direction,
but no inversion here
 Similar situations
occur in springs
and columns of air
Wave Behaviour
• Reflection in two
dimensions
 Light is shone from above
a ripple tank onto a piece
of white card beneath
 The bright areas
represents the crests
 The dark areas represent
the troughs
 These wavefronts can be
used to show reflection
(and refraction and
diffraction and
interference) of water
waves
Normal
Angle of
incidence
=
Angle of
reflection
The Law for Reflection
• The angle of incidence is equal
to the angle of reflection
• Also - The incident ray, the
reflected ray and the normal lie
on the same plane
• Use this rule for any ray or wave
diagram involving reflection from
any surface
• For circular waves hitting a flat
reflector, the reflected waves
appear to come from a source,
which is the same distance
behind the reflector as the real
source is in front of it
• Also a line joining these 2
sources is perpendicular to the
reflecting surface
O
I
• If a plane wave is incident on a
circular reflector then the waves
are reflected so that they
–Converge on a focus if the
surface is concave
–Appear to come from a
focus if the surface is
convex
Echos
• In the case of sound, a source of
sound can be directed at a
plane, solid surface and the
reflected sound can be picked up
by a microphone connected to
an oscilloscope.
• The microphone is moved until a
position of maximum reading on
the oscilloscope is achieved.
• When the position is recorded it
is found that again the angle of
incidence equals the angle of
reflection.
Wave Behaviour
• Refraction
• The speed of a wave depends
only on the nature and properties
of the medium through which it
travels.
• This gives rise to the
phenomenon of refraction
• Refraction is the change of
direction of travel of a wave
resulting from a change in speed
of the wave when it enters the
other medium at an angle other
than right angles.
• In a ripple tank this is achieved
by using a flat piece of plastic,
giving two regions of different
depth
• As the wave passes over the
plastic it enters shallow water
and slows down.
• As v = f ,
• if v decreases
• And f is constant (the source
hasn’t changed)
•  must also decrease
• So the waves get closer together
• If the waves enter the shallow
area at an angle then a change
in direction occurs.
Shallow water
• This is because the bottom of the
wavefront as drawn, hits the
shallow water first so it slows,
and hence travels less distance
in the same time as the rest of
the wavefront at the faster speed
travel a larger distance!
• If the waves enter the deep area
at an angle then a change in
direction occurs
Deep water
• This is because the
top of the wavefront
hits the deep water
first so it speeds up,
and hence travels
more distance in the
same time as the rest
of the wavefront at the
slower speed travel a
smaller distance!
Refraction for light
Refracted ray
Partial reflection
Partial reflection
Incident ray
Refracted ray
Incident ray
Snell’s Law
• Snell discovered that for
any two media
• Sin 1 / Sin 2 = constant
• Also v1 / v2 = the same
constant
• Where 1 is the angle of
incidence in the 1st
medium, v1 is the velocity in
that medium
• And 2 is the angle of
refraction in the second
medium, v2 is the velocity
• The constant is 1n2
• Therefore
1 n2
=
sin 1
sin 2
= v1
v2
• This law enable us to define a
property of a given optical
medium by measuring 1 and 2
when medium 1 is a vacuum
• The constant is then the property
of medium 2 alone and it is
called the refractive index (n).
• We usually write
• n = (Sin i) / (Sin r)
• n is also a ratio of the speeds in
the 2 mediums i.e. n = cvacuum /
vmedium
Using Refractive Index
• Refractive index is written for
materials in the form of light
entering from a vacuum or air
into the material.
• The refractive index of a vacuum
or air is 1
• It can also be shown that, for two
mediums (1 and 2)
• n1 sin 1 = n2 sin 2
• Care needs to be taken when
dealing with light leaving a
material
Combining them!
• Rearranging
• n2/n1 = sin 1 / sin 2
• But n1 = 1
• n2 = sin 1 / sin 2
n2 sin 1

n1 sin  2
• Therefore anb = nb / na
Refraction of
Sound
• A sound wave is also able to
be refracted.
• This is due to the fact that
the speed of sound is
affected by temperature and
the medium through which it
travels.
Diffraction
• Diffraction is the spreading out of
a wave as it goes passed an
obstacle or through an aperture
• When the wavelength is small
compared to the aperture the
amount of diffraction is minimal
• Most of the energy associated
with the waves is propagated in
the same direction as the
incident waves.
• When the wavelength is
comparable to the opening then
diffraction takes place.
• There is considerable sideways
spreading, i.e. considerable
diffraction
• Diffraction also takes place when
a wave moves passed an
obstacle
• If the wavelength is much
smaller than the obstacle, little
diffraction takes place
• If the wavelength is comparable
to the obstacle size, then
diffraction takes place
Using Huygens’ Principle
• Remember that Huygens'
idea was to consider every
single point on the wavefront
of the wave as itself a source
of waves.
• In other words a point on the
wavefront would emit a
spherical wavelet or
secondary wave,of same
velocity and wavelength as
the original wave.
• Therefore as a wave
goes through a gap or
passed an obstacle the
wavelets at the edges
spread out.
• Huygens’ construction
can be used to predict
the shapes of the wave
fronts.
• The new wavefront would then
be the surface that is tangent
to all the forward wavelets from
each point on the old
wavefront.
• We can easily see that a plane
wavefront moving undisturbed
forward easily obeys this
construction.
The Principle of Linear Superposition
• Pulses and waves (unlike
particles) pass through each
other unaffected and when
they cross the total
displacement is the vector
sum of the individual
displacements due to each
pulse at that point.
• Try this graphically with two
different waves
Interference
• Most of the time in Physics we
are dealing with pulses or waves
with the same amplitude.
• If these cross in a certain way we
will get full constructive
interference, here the resultant
wave is twice the amplitude of
each of the other 2
+
=
• If the pulses are 180o () out of
phase then the net resultant of
the string will be zero. This is
called complete destructive
interference.
+
=
Home fun
• Design a simulation
of wave
characteristics
• Presentation Next
Lesson