Standing Waves

Whenever a travelling wave reaches a rigid boundary, it reflects back into the medium and interferes there with the still-arriving incident wave; if the incident and reflected waves happen to have exactly equal amplitude and frequency but travel in opposite directions, their superposition produces a distinctive fixed pattern -- one that does not itself advance forward or backward through the medium at all -- called a stationary wave, or standing wave. This section works out the mathematics of exactly where this pattern's zero-displacement points (nodes) and maximum-displacement points (antinodes) form, catalogues the general characteristics that set stationary waves apart from ordinary travelling waves, applies the theory to the discrete set of natural frequencies (harmonics and overtones) a string clamped at both ends can …