Build a standing wave

Equal-amplitude waves of the same frequency travelling in opposite directions can form a standing wave. Its fixed pattern of oscillation amplitude differs from the travelling profiles that produce it.

Take two waves in the same region and oscillation direction, with the same wavelength and speed but opposite propagation directions. At every position and instant, add their signed displacements. The result is also called a stationary wave.

Add the profiles through a cycle

Each component in this supplied model has amplitude 2.0 mm, wavelength 0.80 m and period T = 0.20 s. The view covers x = 0 to 0.80 m.

• At t = 0, the resultant displacements at x = 0, 0.20, 0.40, 0.60 and 0.80 m are 0, +4.0, 0, -4.0 and 0 mm.
• At t = T/4 = 0.050 s, the whole resultant profile is at equilibrium. The two component profiles are not both zero; they cancel point by point.
• At t = T/2 = 0.100 s, the nonzero resultant displacements have reversed sign.

Identify amplitude, nodes and antinodes

A node has zero displacement at all times and therefore zero oscillation amplitude. The fixed nodes here are x = 0, 0.40 and 0.80 m. An antinode has the greatest oscillation amplitude: here 4.0 mm at x = 0.20 and 0.60 m.

Amplitude describes the full oscillation, not the displacement in one frame. At T/4, an antinode passes through equilibrium at its greatest speed; it has not become a node.

Points within one loop oscillate in phase. Points in neighbouring loops oscillate in antiphase: when one loop moves up, the next moves down. The nodes separating them do not oscillate.

The ideal standing pattern has no net time-averaged energy transport along it. Energy is still present and exchanges locally. Real driven demonstrations need an energy input to replace losses; this does not turn the fixed node pattern into travelling crests.

The graphical model explains formation. The string and microwave experiments and air-column experiment show how the pattern can be observed and measured.