Lecture Notes: Wave Reflection and Inversion

Introduction to Wave Reflection

• All types of waves, including light waves, reflect.
• Example: A wave pulse moving to the right along a spring attached to a wall.

Reflection from Fixed End

• Observation: When the wave pulse reaches the wall, it reflects back.
• Key Point: The reflected pulse is inverted (upside down).
  • A crest sent towards the wall reflects back as a trough.
• Live Demo:
  • A crest sent to a fixed end is reflected as a trough.
  • This represents wave inversion upon reflection from a fixed end.

Reflection from Free End

• Setup: A ring on a post allowing movement up and down.
• Prediction: Will the wave reflect if the end is not fixed?
• Observation:
  • The wave does reflect.
  • The reflection is not inverted.
  • A crest sent towards the free end reflects back as a crest.
• Live Demo:
  • A rope tied to a slinky allows free end movement; a crest sent reflects as a crest.
  • No inversion occurs in free-end reflection.

Explanation of Fixed End Reflection

• Inversion Explanation:
  • When the wave hits the wall, the spring pulls up on the wall.
  • Newton's Third Law:
    • The wall exerts an equal and opposite force, pulling the spring down, leading to inversion of the wave.

Explanation of Free End Reflection

• Non-Inversion Explanation:
  • The free end moves up, pulling the rest of the spring up with it.
  • Newton's First Law:
    • An object in motion stays in motion if no net force acts on it.
  • The end maintains its upward velocity, reflecting the wave without inversion.

Summary

• Reflection occurs at both fixed and free ends.
• Fixed ends cause wave inversion, whereas free ends do not.
• Understanding the interaction of forces at the reflecting point explains the behavior of the wave's reflection.

Next Steps

• Using this understanding to make further predictions about wave behavior in different scenarios.