Standing Waves: Superposition That Stays Put

Lesson notes

Key points

• When two identical waves travel in opposite directions on a string, their superposition forms a standing wave.
• Nodes are points that never move, while antinodes swing with maximum amplitude, halfway between nodes.
• Mathematically, adding the two waves gives 2A sin(kx) cos(ωt): a fixed spatial shape whose size oscillates in time.
• Adjacent nodes are always half a wavelength apart, which is how you measure wavelength in a lab.

Definitions

Standing wave

Pattern from two equal waves moving oppositely; points oscillate in place, no net energy transport

Takeaway: Standing waves: fixed nodes, oscillating antinodes, nodes λ/2 apart.

Standing waveNodes and antinodesSeparable formNode spacing λ/2