Fixed boundary condition

Definition

A fixed boundary condition occurs when the end of a medium is fixed in place, preventing any displacement of the medium at that point. This results in the reflection of waves with an inversion of their phase.

5 Must Know Facts For Your Next Test

1. A wave encountering a fixed boundary undergoes a phase shift of $\pi$ radians, or 180 degrees.
2. At a fixed boundary, the displacement of the wave is always zero.
3. Fixed boundary conditions are often used to model physical constraints in real-world systems, such as the ends of a vibrating string tied down.
4. The reflected wave at a fixed boundary has an inverted amplitude compared to the incident wave.
5. Fixed boundaries affect both transverse and longitudinal waves similarly by imposing zero displacement.

Review Questions

• What happens to the phase of a wave when it reflects off a fixed boundary?
• How does a fixed boundary condition affect the displacement of a wave at that point?
• Explain how fixed boundary conditions are applied in real-world scenarios.

Related terms

Free Boundary Condition: Occurs when the end of a medium can move freely, allowing maximum displacement and no phase inversion upon reflection.

Node: A point along a standing wave where the wave has minimum amplitude due to destructive interference.

Antinode: A point along a standing wave where the amplitude reaches its maximum due to constructive interference.