Consider a pulse moving through a medium - perhaps through a
rope, a slinky or even a telephone cord. What happens to the
pulse when it reaches the end of that medium? The answer depends
on whether the medium is fixed in space or free to move at its
end. For example, if the pulse is moving through a rope and the
end of the rope is held firmly by a person, then it could be said
that the pulse is approaching a fixed end. On the other hand, if
the end of the rope is lying on the floor such that it is free to
move up or down when the pulse reaches its end, then it could be
said that the pulse is approaching a free end.
The animation below depicts a pulse moving through a medium
which is free to move at its end.
The animation depicts a boundary behavior phenomenon. The
pulse reflects off the free end and returns with the same
direction of displacement which it had before reflection. That
is, a pulse with an upward displacement will reflect off the end
and return with an upward displacement. Sometimes it is said that
the pulse is not inverted. This behavior of non-inversion
will always be observed when the end of the medium is free to
move. This behavior of non-inversion is also observed when the
medium is connected to another less heavy or less dense medium.
In the latter case, when the pulse reaches the end of the medium,
a portion of the pulse will reflect off the end and return with
the same direction of displacement; it is not inverted.
Since the medium beyond the end is less dense and less heavy, it
fails to fix the medium's end and thus allows it to move; in this
sense, the end of the medium behaves as a free end.
In conclusion, a pulse reaching the end of a medium does
not become inverted whenever it either
reflects off a free end,
or is moving in a more dense medium and reflects off a
less dense medium.
