WAVES AT MEDIA
BOUNDARIES
Section 9.2
Key Terms
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Media Boundary
Free-end Reflection
Fixed-end Reflection
Transmission
Standing Wave
Node
Antinode
Fundamental Frequency/First Harmonic
Harmonics
Overtone
Media Boundaries
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Wave speed depends on the properties of the
medium through which the wave is travelling.
All media have boundaries.
 The
location where two media meet.
Free-End Reflections

If a wave travels from a more dense medium to a
less dense medium, it will travel more quickly in the
more dense medium.
 Wave
moving towards the boundary will be reflected
with the same orientation and amplitude
Fixed-End Reflection

As a wave moves towards a fixed boundary, it will
reflect.
 Reflected
pulse has the
same shape as the
incoming pulse, but its
orientation is inverted.
Amplitude

When a wave encounters a boundary that is not
strictly free-end or fixed-end, the wave will split in
two.
 One
wave is reflected
 Energy
 The
other is transmitted.
 Energy

“bounces back”.
passes into new medium.
Amplitude of the two waves may not be equal, but
the sum of the amplitudes will be equal to that of
the original wave.
Media Boundaries
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Not all difference in media boundaries are as
dramatic as fixed-end or free-end.
 Water
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 Air
If a wave travels from a medium in which the speed
is faster (more dense) to a medium in which the
speed is slower (less dense), the wave particles can
move more freely
 Energy
is transferred
into new medium
 Reflected wave has
same orientation
Media Boundaries
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The opposite is also true.
 Air
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 Water
If a wave travels from a medium in which the speed
is slower (less dense) to a medium in which the
speed is faster (more dense), the wave particles
cannot move as freely
 Energy
is transferred
into new medium
 Reflected wave has
inverted orientation
Standing Waves
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Suppose a series of waves is sent down a string that
is fixed at both ends.
 At
a certain frequency, reflected waves will
superimpose on the stream of incoming waves to
produce waves that appear stationary
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The locations in which the particles of the medium
do not move are nodes.
The locations in which the particles of the medium
move with the greatest speed are antinodes.
Standing Wave
Standing Waves

Waves interfere according to principle of
superposition.
 Waves
are moving continuously
 At the antinodes, the amplitudes of the troughs and
crests are double that of the original wave.
 At the nodes, the amplitudes are the same but one is a
crest and the other is a trough.
 Interference
pattern appears to be stationary because it is
produced by otherwise identical waves travelling in opposite
directions.
Standing Waves Between Two Fixed Ends
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Standing waves can be predicted mathematically.
 Consider
a string with two fixed ends
 Standing
wave with nodes at both ends.
 The shortest length of the string, L, is equal to one half of the
wavelength.
 The frequency of the wave that produces this simplest
standing wave is called the fundamental frequency

First harmonic
 All
standing waves to follow require frequencies that are
whole-number multiples of the fundamental frequency.

Additional standing wave frequencies are known as the nth
harmonic of the fundamental frequency
Harmonic (n)
Overtone
0
First
Fundamental
f1
1
Second
First
f2
2
Third
Second
f
3
Fourth
Third
Symbol
Number of Nodes Between
Ends
f0
Diagram
Harmonics and Overtones
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Harmonics consist of the fundamental frequency of
a musical sound as well as the frequencies that are
the whole-number multiples of the first harmonic.
When a string vibrates with more than one
frequency, the resulting sounds are called
overtones.
 Similar
to harmonics, however the first overtone is equal
to the second harmonic.
Calculations with Standing Waves
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The length of the medium is equal to the number of
the harmonic times half the standing wave’s length.
For a media with a combination of fixed and free
ends (node at one end and antinode at the other),
the equation is:
Summary
Homework
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Page 426
 Questions
1-5