Standing Waves

A wave phenomenon resulting from the interference of soundwaves of the same frequency and kind travelling in opposite directions. Such waves are characterized by the absence of propagation and the existence of nodes or partial nodes and antinodes or loops, which have a fixed distribution in space.

Standing waves in a plucked string.

For example, if a string is stretched between two supports so that a wave sent down its length is reflected completely and sent back again in the opposite direction, a standing wave will result. Standing waves can be likewise observed in columns as well as in plates, rods and diaphragms that are parts of percussion instruments, and therefore constitute an important feature of musical instruments and other resonators. See: Resonance.

For a string of length L, fixed at both ends, or a column of air of length L, open at both ends, the natural modes of vibration have their wavelengths λn of oscillation (which correspond to frequencies in the harmonic series) as follows:

λn = 2L / n      n = 1, 2, 3, ....

Standing waves are commonly set up in rooms by low frequency sounds with long wavelengths. The sound wave that is reflected is nearly in phase with the original wave and thus a fixed spatial pattern of nodes and antinodes is created where the nodes are experienced as dead spots, i.e. points of nearly complete cancellation. The frequency of a standing wave in an enclosed room is called an eigenton.

Standing waves will contribute to higher Ambient Noise Levels and therefore are to be avoided in acoustic design, particularly in industry. They are also avoided in concert halls to ensure uniform frequency response and good diffusion.

Compare: Drone, Stationary Sound, Vibration.