Introduction to Computer Music: Volume One

12. What are standing waves?

A particular pattern of constructive and destructive interference is called a standing wave, which is essential to the way string instruments produce sound, but very undesirable in the listening environment of an electronic studio.

The characteristic mode of vibration of a string with one fixed end is the standing wave pattern. In a normal reflection of a sound wave from a hard surface, the phase of the reflected wave is not changed. With a wave induced in a string with a fixed end, the wave reflects from the fixed end out of phase with the incident wave, creating patterns of constructive interference at certain resonant frequencies. Nodes and antinodes on the resultant string correspond to points of minimum (node) and maximum (antinode) vibrations. Air columns in both closed and open tubes also exhibit standing wave properties. In this case, the nodes and antinodes refer to the minimum (node) and maximum (antinode) pressure in the tube. Woodwind instruments are examples of half- or quarter-wave resonators that produce multiple standing waves. The differences are whether the tube is open at both ends (flute, including the embouchure hole) or closed at one end, such as the oboe or clarinet.

Standing waves in rooms can cause certain resonant frequencies to be either unduly enhanced (pressure nodes) or completely disappear (presure antinodes). Offset from those, displayed below, are air displacement nodes and antinodes, points of maximum or minimum movement of the medium. Pressure nodes are displacement antinodes and visa versa (for a more complete explanation, please follow the Hyperphysics link below). For that reason, it is always a good idea to listen to your work from a few different spots in the studio, since we have not completely eliminated our standing wave potential.


Below is a picture of a closed tube with a loudspeaker at one end. The pellets in the tube form the nodes and antinodes of a standing wave from a sine wave played through the speaker. Exhibit built and designed by the WonderLab Exhibit Team led by Don Marvel, Bloomington, Indiana.


For a very detailed discussion of the physics of standing waves (with excellent graphics) see:
http://hyperphysics.phy-astr.gsu.edu/hbase/waves/standw.html#c4

 

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