Physics: Difference between revisions - Bose Portable PA Knowledge

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:* Cylindrical waves do not lose intensity with distance as fast as spherical waves. They lose only half their intensity with each doubling of distance. Thus if the sound intensity is 100 units at 10 feet, it will be 50 units at 20 feet, 25 units at forty feet, and so on. We hear this reduction of level with distance as modest in comparison with the spherical-wave source. With such a source, if we set the correct level in the audience and then move closer, we hear the level as increasing only modestly. In fact, you can walk right up next to a cylindrical-wave source and never have the feeling that it is too loud. These properties will turn out to be of major importance to the problems of amplified music.

:* Plane waves theoretically lose no sound intensity with distance. Thus if the sound intensity is 100 units at 10 feet from the source, it will be still be 100 units at 20 feet, 100 units at forty feet, and so on. From this perspective, plane waves would be ideal for music performance because musicians and audience would get the same sound level.

For the reader interested in understanding the underlying physics of these differences, imagine a sound-intensity-meter in front of each kind of source, at a distance of say ten feet. Furthermore, imagine that at this distance, each source produces the same level. Now, consider a small area of the sound wave at the location of the meter.

:* As the spherical wave spreads out, the wave must expand over the surface of a sphere. When the sphere doubles in diameter, the small area of the sound wave must expand over a proportionately larger area at the doubled distance. As a result the intensity of the original area of sound wave diminishes. Since the area of a sphere increases as the square of the radius, increasing the distance from the source by a factor of two (doubling the distance and therefore the radius) means reducing the sound intensity by a factor of four (two squared).

:* As the cylindrical wave spreads out, the wave must expand over the surface of a cylinder. When the cylinder doubles in diameter, the small area of the sound wave at the closer distance must spread over a proportionately larger area at the doubled distance. As a result the intensity of the original area of sound wave is reduced. Since the area of a cylinder increases proportionately with only the radius (rather than as the square of the radius), increasing the distance from the source by a factor of two (doubling the radius) means reducing the sound intensity by only a factor of two.

:* As the plane wave progresses, the wave does not expand. When the wave reaches a distance that’s double the original, the small area of the sound wave at the closer distance hasn’t spread at all, and as a result the intensity of the original piece of sound wave is the same.

Figure x. A spherical-wave source, including virtually all existing loudspeakers, retains only one quarter of its intensity with each doubling of distance from the source. This is perceived as a rapid falloff of loudness with increasing distance. A cylindrical-wave retains half of its intensity with each doubling of distance from the source. This is perceived as a modest falloff of loudness with increasing distance. A plane-wave source loses no sound intensity with each doubling of distance from the source; in other words, the loudness is unchanged with increasing distance.

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 :* Cylindrical waves do not lose intensity with distance as fast as spherical waves. They lose only half their intensity with each doubling of distance. Thus if the sound intensity is 100 units at 10 feet, it will be 50 units at 20 feet, 25 units at forty feet, and so on. We hear this reduction of level with distance as modest in comparison with the spherical-wave source. With such a source, if we set the correct level in the audience and then move closer, we hear the level as increasing only modestly. In fact, you can walk right up next to a cylindrical-wave source and never have the feeling that it is too loud. These properties will turn out to be of major importance to the problems of amplified music.
 :* Plane waves theoretically lose no sound intensity with distance. Thus if the sound intensity is 100 units at 10 feet from the source, it will be still be 100 units at 20 feet, 100 units at forty feet, and so on. From this perspective, plane waves would be ideal for music performance because musicians and audience would get the same sound level.
+For the reader interested in understanding the underlying physics of these differences, imagine a sound-intensity-meter in front of each kind of source, at a distance of say ten feet. Furthermore, imagine that at this distance, each source produces the same level. Now, consider a small area of the sound wave at the location of the meter.
+:* As the spherical wave spreads out, the wave must expand over the surface of a sphere. When the sphere doubles in diameter, the small area of the sound wave must expand over a proportionately larger area at the doubled distance. As a result the intensity of the original area of sound wave diminishes. Since the area of a sphere increases as the square of the radius, increasing the distance from the source by a factor of two (doubling the distance and therefore the radius) means reducing the sound intensity by a factor of four (two squared).
+:* As the cylindrical wave spreads out, the wave must expand over the surface of a cylinder. When the cylinder doubles in diameter, the small area of the sound wave at the closer distance must spread over a proportionately larger area at the doubled distance. As a result the intensity of the original area of sound wave is reduced. Since the area of a cylinder increases proportionately with only the radius (rather than as the square of the radius), increasing the distance from the source by a factor of two (doubling the radius) means reducing the sound intensity by only a factor of two.
+:* As the plane wave progresses, the wave does not expand. When the wave reaches a distance that’s double the original, the small area of the sound wave at the closer distance hasn’t spread at all, and as a result the intensity of the original piece of sound wave is the same.
 Figure x. A spherical-wave source, including virtually all existing loudspeakers, retains only one quarter of its intensity with each doubling of distance from the source. This is perceived as a rapid falloff of loudness with increasing distance. A cylindrical-wave retains half of its intensity with each doubling of distance from the source. This is perceived as a modest falloff of loudness with increasing distance. A plane-wave source loses no sound intensity with each doubling of distance from the source; in other words, the loudness is unchanged with increasing distance.