(455) Phase difference in standing waves [IB Physics SL/HL]

Standing Waves and Phase Difference

• Standing waves result from the superposition of two waves interacting back and forth.

• This interaction creates nodes and anti-nodes, giving the appearance of waves oscillating up and down.

Key Concepts of Phase Difference

• Nodes: Points in a standing wave that do not move; occur at regular intervals.

• In Phase: Points within the same node are all in phase (phase difference of 0 radians).

  • Example: All points between one node and the next are in phase since they move in the same direction (up or down).

• Adjacent Nodal Regions: Points in different nodal regions show a phase difference of 180° (or π radians).

  • Example: Points from one region (A) to the next region (B) are π radians out of phase.

Application Example

• Case Study: A string closed at both ends oscillating in the second harmonic displays additional nodes in the pattern.

  • Points labeled P and Q within the same nodal region ensure that they are in phase, meaning the phase difference is 0 radians.

Summary

• In standing waves:

  • Any points within the same nodal region are in phase with a phase difference of 0 radians.

  • Points between adjacent nodes (or nodal regions) are out of phase by 180° (π radians).

• Understanding these concepts is critical to analyzing standing waves and their properties.