When a wave encounters a fixed boundary, only a reflected
pulse is generated
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The polarity of the reflected pulse is opposite that of the
incident pulse for a fixed boundary
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When a wave encounters the middle junction, both a
transmitted and a reflected pulse are generated
The polarity of the reflected pulse depends on the sign of
the reflection coefficient at the middle junction
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When crossing the middle junction from right to left, the
transmitted wave has a larger amplitude than the incident
wave because the coefficient of transmission from the right to the left
is greater than one. Though this effect seems counter-intuitive, it
works because the total energy in the waves is a constant,
rather than the amplitude of the waves.
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The wavelength of a pulse changes when going across the middle
junction, because the two halves have different velocities. The lower
velocity on the right-hand side gives a shorter wavelength.
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Finally, since this is a linear process, the waves can add both
constructively and destructively. However, the waves have
no lasting effect on each other; after passing through each other, they
are unchanged. This idea is the basis for Fourier
series methods, which represent any piecewise continuous function as a
series of many harmonic waves.
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