When a wave crosses a boundary between two media, it is partially transmitted and partially reflected. The amount depends on the boundary - a hard boundary reflects the wave out of phase, while a soft boundary reflects it in phase. Reflection follows the law that the angle of incidence equals the angle of reflection. Refraction occurs when a wave crosses into a medium with a different wave speed, causing it to change direction according to Snell's law. Diffraction spreads waves out when they pass through an opening or obstacle. Superposition combines overlapping waves constructively or destructively based on their phase difference.

1. Topic 4 – Oscillations and Waves
4.4 Wave Properties

2. Reflection and Transmission
● When a wave crosses a boundary between 2
media the wave will be partly reflected and
partly transmitted.
● The amount of reflection and transmission
depends on the nature of the boundary.
● If the wave is able to move at the boundary then the
reflected wave will be in phase. (A Soft Boundary)
● If the wave is fixed at the boundary then the
reflected wave will be out of phase. (A Hard
Boundary)

3. Reflection and Transmission
● As waves move from one
medium into another the wave
is partially transmitted and
partially reflected.
● If the boundary is from low
density to high density then
this is a hard boundary and
the reflected wave suffers a
phase change.
● If the boundary is from high
density to low density then
this is a soft boundary and the
reflected wave is reflected in
phase.
θi
θR
θr

4. The Law of Reflection
● The angle of incidence always equals the angle
of reflection.
θi
θR

5. Changing Media
● As waves move from one medium into another their
wavespeed will change.
● Transverse waves usually have more resistance to
propagation in dense materials
● The wave will therefore usually travel slower in more
dense materials.
● The refractive index (1
n2
) is the ratio of the speeds to
the wave in medium 2 to that in medium 1
● The absolute refractive (n2
) index is that when medium
1 is a vacuum, i.e. c
n2
.

6. Refractive Indices
● The refractive indices of some common
materials are shown below.
● Calculate the speed of light in these materials
Material n v x108
ms-1
Air 1.0003
Water 1.333
Perspex 1.49
Crown Glass 1.52
Diamond 2.42

7. Changing Media
● When a wave crosses a boundary between two
media at an angle other than the normal it will
change direction.
● This is called refraction
● The amount of refraction is predicted by Snell’s
law: sin θi
sinθr
=
vi
vr
=
nr
ni

8. Refraction
● When light crosses from a
less optically dense
medium into an more
optically dense medium
the light refracts towards
the normal.
● When light crosses from a
more optically dense
medium into an less
optically dense medium
the light refracts away the
normal.
θi
θr

9. Refraction and Critical Angle
● The use of a semi-circular block of medium
allows the effect of moving from a high
optical density to a low optical density to be
studied.
● Any ray that enters the block along a radius
will strike the curved surface normally and
hence will not refract.
● As light exits a material into air or the
vacuum it will refract away from the normal.
● At some angle of incidence, the refracted
ray will be directly along the flat surface of
the block.
● This is known as the critical angle θc
.
● The refractive index of the medium can
hence be determined.
θc
sinθi
sinθr
=
nr
ni
ni=
nr sinθr
sinθi
n=
1sin 90
sinθc
n=
1
sinθc

10. Diffraction
● When a plane wave
encounters a gap in a
barrier then the waves that
pass through will become
curved at the edges and
spread out.
● This is called diffraction.
● This is the phenomenon
that allows sound to
“travel around corners”
● The amount of diffraction
depends on the ratio of the
width of the gap and the
wavelength.

11. Diffraction
● If the gap width (d) is
much larger than the
wavelength then the
wave passes through
with only small
diffraction.

12. Diffraction
● If the gap width (d) is
larger than the
wavelength then the
wave passes through
with only more
diffraction.
● The wave ends start
to noticeable curve

13. Diffraction
● If the gap width (d) is
slightly wider than the
wavelength then the
wave passes through
with a lot of
diffraction.
● The wave looks more
curved than straight

14. Diffraction
● If the gap width (d) is
exactly the same
width as the
wavelength then the
wave passes through
and forms perfectly
circular waves.
● There are now no
shadows

15. Examples of Diffraction
● Water waves are
often seen diffracting
as they enter a
harbour.
● Sound can be heard
around a corner due
to diffraction

16. Examples of Diffraction
● Light also diffracts but this
is much less noticeable
than sound because of the
short wavelength of light.
● Often the image suffers
chromatic aberration
● Different colours of light
have different
wavelengths so are
diffracted by different
amounts.
● This colour splitting is
known as dispersion

17. Superposition
● Two waves that exist in the
same space are able to
propagate through each
other.
● When the two waves
interact, the resultant wave
form is that formed by the
superposition of the two
waves.
● Superposition is the vector
addition of the two
amplitudes.

18. Superposition
● If the two waves are in
phase at the interaction,
then the amplitude
increases.
● This is constructive
superposition.
● If the two waves are out
of phase at the
interaction, then the
amplitude is zero.
● This is destructive
superposition.

19. Superposition and Harmonics
● Musical Instruments
rarely produce pure
notes.
● Usually additional
harmonics are
audiable.
● If the fundamental
frequency of a string
instrument is f, then
the harmonics are:
● 2f, 3f, 4f etc.