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Notes
Superposition and Interference
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Physics Tool box
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Constructive Interference: refers to when waves build up each other, resulting
in the medium having larger amplitude.
Destructive interference: occurs when waves diminish one another and the
amplitude of the medium is less than it would have been for either of the
interfering waves acting alone.
Superposition: the simple algebraic sum of the values of a wave.
Node: : a point that remains at rest
Antinode: point midway between the nodes where maximum constructive interference occurs.
When waves are combined, only certain allowed frequencies can exist on systems with boundary conditions. It is
the understanding of this behaviour that demonstrates why a large array of musical instruments can produce he
sounds they generate. When two sound waves having nearly the same frequency interfere, we hear a variation in the
loudness of the tone (called beats). The beat frequency corresponds to the rate of alternation between constructive
and destructive interference between the waves.
Superposition and Wave interference
In nature most interesting wave phenomena cannot be
produced by single travelling waves, Instead, we need to
analyse the interactions of multiple traveling waves. The
analysis of the combination of these multiple travelling waves
requires the application of the Superposition Principle.
When two or more traveling waves
are moving through a medium, the
resultant value of the wave function
at any point is simply the algebraic
sum of the values of the wave
functions of the individual waves.
One of the amazing consequences of the superposition
principle is that two traveling waves can actually pass through
each other without being destroyed or even altered.as seen on
the image on the right.
Wave interference is the phenomenon that occurs when
two waves meet while traveling along the same medium. The
interference of waves causes the medium to take on a shape
that results from the net effect of the two individual waves upon
the particles of the medium. This type of interference is probren
down into two types
Constructive Interference
is a type of interference that occurs at any location along the medium where the two interfering waves have a
displacement in the same direction. In this case, both waves have an upward displacement; consequently, the
medium has an upward displacement that is greater than the displacement of the two interfering pulses. Constructive
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interference is observed at any location where the two interfering waves are displaced upward. But it is also
observed when both interfering waves are displaced downward.
Destructive interference
is a type of interference that occurs at any location along the medium where the two interfering waves have a
displacement in the opposite direction. The consequence of a destructive interference is a final displacement that is
less than the displacement of the two interfering pulses.
When we have a single generator producing two vibrating point sources, the created waves will have the same
wavelength, amplitude and phase ( the particular point in the cycle of each wave is the same). As these wave move
from their point souses they will interfere. Sometimes crest to crest and trough to trough, and at other times crest to
trough. This will create patterns of contrastive and destructive interference. As the waves move out from the sources,
a symmetrical pattern will be produced, creating nodal lines (areas of destructive interference where the point remains
at rest) and areas of constructive interference.
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You will notice that the nodal lines appears to be straight lines, but actually they are curved lines following a
hyperbolic path. When the frequency of the sources is increased the wavelength also decreases thus bringing the
nodal lines closer together (also increasing the number).
Node: a point that remains at rest
Antinode: point midway between the nodes where maximum contructive interference occurs.
Standing Wave
If two waves with identical wavelengths and amplitudes are traveling in the opposite directions, the resulting
interference patterns will produce some interesting interactions. A standing wave, such as the one shown in Figure
below , is an oscillation pattern with a stationary outline
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that results from the superposition of two identical waves traveling in opposite directions.
Example
If the wavelength of the wave generated is 0.25 m, and the frequency of generated wave is 4 Hz, what is the
waves speed?
Solution:
v f
  4 Hz  0.25m 
 1.0
m
s
Example
The distance between two successive nodes in a vibrating rope is 20cm. The frequency of the source is 40 Hz.
What is the wavelength? What is the speed of the nodes?
Solution:
The distance between any two successive nodes is
Therefore
1
  20cm
2
  40cm
v f
  40 Hz  40cm 
 1.6  102
cm
s
Mechanical Resonance
1

2
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Superposition and Interference
Extra Notes and Comments
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