Properties of Stationary Waves

Gathering the results derived above, a stationary wave has the following properties. (1) It is produced by the superposition of two IDENTICAL waves (equal amplitude, equal frequency), of either kind (transverse or longitudinal), travelling through a medium along the SAME path but in OPPOSITE directions. (2) If the two interfering waves are TRANSVERSE progressive waves (as on a stretched string), the resultant is a transverse stationary wave, with some points (NODES) permanently motionless and others (ANTINODES) oscillating with the greatest amplitude A, and points in between oscillating with amplitudes ranging continuously from 0 to A. (3) If the two interfering waves are LONGITUDINAL progressive waves (as in a pipe closed at one end), the resultant is a longitudinal stationary wave with the same node/antinode structure, but now nodes are points of minimum (zero) particle-displacement amplitude and antinodes are points of maximum (A) particle-displacement amplitude, along the length of the pipe. (4) The distance between two consecutive nodes is $\lambda/2$, and likewise between two consecutive antinodes is $\lambda/2$. (5) Nodes and antinodes occur alternately, so the distance between a node and its neighbouring antinode is $\lambda/4$. (6) The amplitude of vibration varies periodically in SPACE (from node to antinode to node...), while every particle (nodes aside) shares the SAME frequency of vibration in TIME. (7) Although every particle away from a node genuinely possesses energy (it is oscillating), there is NO net propagation of that energy along the medium -- the disturbance stays localised to where it was produced, and the wave's own velocity is effectively zero; this localisation of energy is precisely why we call it a 'stationary' wave. (8) All particles WITHIN one loop (i.e. between one pair of adjacent nodes) oscillate exactly in PHASE wi …