Real-time Parameters
Legend
Wave Parameters
Boundary Settings
Pulse Settings
Display Settings
Reflection Laws
What is Wave Reflection?
Wave reflection occurs when a wave encounters a boundary or obstacle and bounces back. The behavior of the reflected wave depends on the type of boundary. At a fixed end (hard boundary like a wall), the reflected wave is inverted (phase change of π). At a free end (soft boundary like an open end), the reflected wave remains upright (no phase change). This principle applies to all types of waves including strings, sound waves, and electromagnetic waves.
Fixed End Reflection (Hard Boundary)
When a wave pulse reaches a fixed end, the boundary exerts an equal and opposite force on the string, causing the reflected pulse to be inverted. A crest (upward displacement) reflects as a trough (downward displacement), and vice versa. This π phase change occurs because the displacement at the fixed end must always be zero. The reflected pulse travels back with the same speed and shape but opposite polarity.
Free End Reflection (Soft Boundary)
At a free end, the string can move freely. When a pulse reaches the free end, it overshoots and creates a reflected pulse with the same orientation (no phase change). A crest reflects as a crest, and a trough reflects as a trough. The free end acts like a moving source that creates a new wave continuing in the same direction as the incident displacement.
Applications and Examples
Wave reflection is fundamental in many areas: Musical Instruments - string instruments rely on reflection at fixed and free ends to create standing waves and resonant frequencies; Architecture - room acoustics depend on sound reflection from walls; Optics - mirrors reflect light according to the same principles; Seismology - seismic waves reflect off geological boundaries; Communications - radio signals reflect off the ionosphere enabling long-distance transmission.
Visualization Guide
This interactive tool demonstrates wave reflection on a string. Select between fixed end (hard boundary) and free end (soft boundary) to see the difference in phase change. Click "Send Pulse" to launch a wave pulse from the left side. Watch as it travels to the boundary, reflects, and returns. Observe how the pulse inverts at a fixed end but stays upright at a free end. Adjust amplitude, width, and speed to experiment with different pulse characteristics. Use the animation speed control to slow down and study the reflection process in detail.