Digital Sound & Music: Concepts, Applications, & Science, Chapter 4, last updated 6/25/2013
65
Figure 4.41 Comparison of delays, 0.5682 ms (top) and 2.2727 ms (bottom)
Room mode operates by the same principle as comb filtering. Picture a sound being sent
from the center of a room. If the speed of sound in the room is 1000 ft/s and the
room has parallel walls that are 10 feet apart, how long will it take the sound to
travel from the center of the room, bounce off one of the walls, and come back to
the center? Since the sound is traveling 5 + 5 =10 feet, we get a delay of
. This implies that a sound wave of frequency = 50
Hz sound wave will be combed out in the center of the room. The center of the
room is a node with regard to a frequency of 50 Hz.
For the second harmonic, 100 Hz, the nodes are 2.5 feet from the wall. The
time it takes for sound to move from a point 2.5 feet from the wall and bounce
back to that same point is 2.5 + 2.5 = 5 feet, yielding a delay of . This is
half the period of the 100 Hz wave, meaning a frequency of 100 Hz will be combed out at those
points. However, in the center of the room, we still have a delay of , which
is the full period of the 100 Hz wave, meaning the 100 Hz wave gets amplified at the center of
the room.
The other harmonic frequencies can be explained similarly.
4.4 References
In addition to references cited in previous chapters:
Davis, Don, and Eugene Patronis. Sound System Design and Engineering.
3rd
ed. Burlington,
MA. Focal Press/Elsevier, 2006.
Everest, F. Alton and Ken C. Pohlmann. Master Handbook of Acoustics.
5th
ed. New York:
McGraw-Hill, 2009.
MATLAB
Exercise:
Creating Room
Modes in
MATLAB
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