Transcript Topic 4.5

Waves
Topic 4.5
Wave Properties
Wave Behaviour
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
Fixed vs Free-end Reflection
 The inversion 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 fixed end will exert
an equal but opposite force on the rope
 This means that a disturbance will be created
in the rope which is “downwards” and will
start moving to the left
Fixed vs Free-end Reflection
 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
Wave Behaviour
Reflection in two
dimensions
Reflection
Wavefronts incident upon a boundary…
Reflected waves
Incident waves
Normal
Angle of
incidence
=
Angle of
reflection
The Law for Reflection
• The angle of incidence is equal to the
angle of reflection
-keep in mind that angles are measured with
respect to the normal at point of contact
• 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
Incident
wavefronts
Reflected
wavefronts
(semi circles)
Incident
wavefronts
Reflected
wavefronts
Wave Behaviour
Refraction
• The speed of a wave depends only on the
nature and properties of the medium through
which it travels.
• 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.
• Remember: 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
• The constant is…the ratio of the wave
velocity in the two media v1 / v2
• 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
• Therefore
• Or… n1 sin 1 = n2 sin 2
• Where n is the index of refraction of the media
• For light and optics…
nvacuum = 1 (also taken as the value in air)
• 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
Diffraction
• Diffraction is the spreading out of a wave as
it passes an obstacle or through an aperture
(an opening)
• When the wavelength is small compared to
the aperture the amount of diffraction is
minimal. When the wavelength is
comparable to the size of the opening then
diffraction effects are significant.
• 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 is significant
Huygens’ Principle
• Christian Huygens' idea was to consider
every single point on the wavefront of the
wave as the source of a new wave
disturbance.
• 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.
Huygens’ Principle
• Therefore as a wave goes through a gap or
passed an obstacle the wavelets at the
edges spread out the wave energy.
• Huygens’ construction can be used to predict
the shapes of the wave fronts.
• Huygens’ Principle
• 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 of the
medium is the vector sum of the
individual displacements due to each
pulse at that point.
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.
+
=