Reflection of a Pulse at a Fixed End

Consider a pulse moving through a medium - perhaps through a rope or a slinky. 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 fixed at its end.

The animation depicts a behavior which is referred to as inversion. The pulse becomes inverted upon reflecting off the fixed end. That is, a pulse with an upward displacement will reflect off the end and return with a downward displacement. This inversion behavior will always be observed when the end of the medium is fixed. This inversion behavior is also observed when the medium is connected to another more heavy or more 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 an inverted displacement. The heavier medium acts like a fixed end to cause the pulse to be inverted.

In conclusion, a pulse reaching the end of a medium becomes inverted whenever it either

• reflects off a fixed end,
• or is moving in a less dense medium and reflects off a more dense medium.

For more information on physical descriptions of waves, visit The Physics Classroom Tutorial. Detailed information is available there on the following topics:

The Nature of a Wave

The Speed of a Wave

Boundary Behavior

Reflection, Refraction, and Diffraction of Waves