At the Earth surface the radius of curvature of the wave front is 150,000,000 km,

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A light bulb is a source of a spherical wave. If
you are 5 ft away from the bulb and walk another
5 ft away the light intensity decreases by a
factor of 22 4.
At the Earth surface the radius of curvature of
the wave front is 150,000,000 km, The intensity
is the same everywhere, and the wave is
practically flat. It is a spherical wave on the
scale of the Solar system, though.
In terms of intensity of sunlight, it is about
the same as going from Venus to mars
2
If there are big waves and ripples on the water
surface, which are going to run faster?
For some kinds of waves the wave speed of a
simple harmonic wave depends on the wave
length. This phenomenon is called
dispersion. Example for large waves on the
surface of deep water
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Combining of two waves to form a composite wave
is calledInterference
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When two (or more) waves of the same kind
propagate through the same region, they produce a
composite wave. This phenomenon is called
interference. It is constructive, when the
waves reinforce each other. It is destructive,
when they reduce each others amplitude.
Usually the disturbances (displacements) the
waves produce are added algebraically. This is
called superposition principle.
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Superposition principleadding two square waves

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Superposition principle adding two harmonic waves

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Superposition of pulsesConstructive Interference
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Superposition of pulses Destructive Interference
For a moment it the string becomes a straight
line no disturbance is seen. Does the energy of
wave motion disappear? Where does it go? How can
the two waves go on after that?
Two kinds of energy in the wave motion potential
depends on deflection of the string from the
straight line kinetic depends on velocity of
motion of the string. In the very moment, when
the string becomes straight, it is actually
moving very fast - high K.
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http//www.kettering.edu/drussell/Demos/superposi
tion/superposition.html
10
When there are two interfering waves with close
but different frequency the result of the
interference is the beats. They are perceived as
a wave with an average frequency, but with a
slowly oscillating amplitude.
http//www.kettering.edu/drussell/Demos/superposi
tion/superposition.html
http//webphysics.ph.msstate.edu/jc/library/15-11/
index.html
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When there are two interfering waves with close
but different frequency the result of the
interference is the beats. They are perceived as
a wave with an average frequency, but with a
slowly oscillating amplitude.
The resulting composite wave
http//webphysics.ph.msstate.edu/jc/library/15-11/
index.html
12
When there are two interfering waves with close
but different frequency the result of the
interference are beats. They are perceived as a
wave with an mean frequency, but with a slowly
oscillating amplitude.
slowly oscillating amplitude
mean frequency
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What about wave shapes?Are all periodic waves
(not pulses) harmonic?
Harmonic waves are simplest kind of waves.
Other periodic waves (rectangular, triangular
etc.) and even wave pulses can be represented as
sums of harmonic waves with frequencies, which
are multiples of the basic one (higher
harmonics), and different amplitudes.
Fourier decomposition.
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Fourier decomposition.
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A harmonic wave is the simplest kind of wave.
Real waves may have ugly profiles. It is often
convenient to present those complex waves as sums
of simple harmonic waves with frequencies, which
are multiples of the same basic frequency.
Fourier decomposition.
http//www.kettering.edu/drussell/Demos/Fourier/F
ourier.html
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Limits of applicability of the superposition
principle.
Superposition principle suggests that disturbance
of the composite wave is an algebraic sum of the
disturbances produced by the individual waves.
This is NOT true, when the amplitudes of the
individual waves are so large that they change
the properties of the medium through which they
propagate.One can tell that the second wave
propagates through a different medium due to the
perturbation made by the first wave. The
interference does not result in algebraic
addition then.

As the amplitude grows, the string gets more
stretched, the tension force increases and so
does the wave speed. A wave with a higher
amplitude goes faster!
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Waves breaking at a sea shore
Waves break when their amplitude becomes
comparable with the sea depth.Bigger waves
break further away from the shore.
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Two waves may interfere constructively and add
algebraically far from the shore 1.The
amplitude of the composite wave with the larger
amplitude becomes comparable with the depth
further away from the shore 2-4. Therefore the
composite wave would break sooner than any of the
two constituent waves.The breaking wave is not
any more a sum of the two constituent waves the
superposition principle is violated, when the
amplitude becomes large compared with the depth.
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Interference in two dimensions