Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
47
Room mode when the
frequency of sound wave is 150 Hz,
3rd
harmonic
Room mode when the
frequency of sound wave is 200 Hz,
4th
harmonic
Distance between two walls L = 10 ft
Speed of sound c = 1000 ft/s
One loudspeaker is in the middle of the room
Figure 4.33 Room mode
Frequency Antinodes Nodes Wavelength Harmonics
2 1
2L 1st
harmonic
3 2
L 2nd
harmonic
4 3
2L
3

3rd
harmonic
k + 1 k
2L
k

kth
harmonic
Table 4.6 Room mode, nodes, antinodes, and harmonics
This example is actually more complicated than shown because there are actually
multiple parallel walls in a room. Room modes can exist that involve all four walls of a room
plus the floor and ceiling. This problem can be minimized by eliminating parallel walls
whenever possible in the building design. Often the simplest solution is to hang material on the
walls at selected locations to absorb or diffuse the sound.
The standing wave phenomenon can be illustrated with a concrete example that also
relates to instrument vibrations and resonances. Figure 4.34 shows an example of a standing
wave pattern on a vibrating plate. In this case, the flat plate is resonating at 95 Hz, which
represents a frequency that fits evenly with the size of the plate. As the plate bounces up and
down, the sand on the plate keeps moving until it finds a place that isn’t bouncing. In this case,
the sand collects in the nodes of the standing wave. (These are called Chladni patterns, after the
German scientist who originated the experiments in the early 1800s.) If a similar resonance
occurred in a room, the sound would get noticeably quieter in the areas corresponding to the
pattern of sand because those would be the places in the room where air molecules simply aren’t
moving (neither compression nor rarefaction). For a more complete demonstration of this
example, see the video demo called Plate Resonance linked in this section.
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