Radiation from a baffled piston
A circular piston in a large baffle is a good starting approximation for investigating the radiation of sound
from a loudspeaker mounted in an enclosure.
The far-field pressure radiated by a baffled piston depends on the radius of the piston a, the frequency
and the direction (with 0º being directly in front of the piston) according to the formula:
At low frequencies
(when ka is small) a loudspeaker radiates sound in all directions.
This behavior is primarily the reason why the location of a subwoofer doesn't really matter regarding the on-axis
location- you can place it anywhere and it will still fill the room with sound.
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Radiation of low frequency sound.
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3D omnidirectional radiation pattern.
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At medium frequencies
As the frequency gets higher, but assuming the speaker diameter does not change, the value of ka increases
and the speaker becomes directional. That is, the sound energy produced by the speaker becomes channeled into
a preferred direction and very little energy is radiated at other directions. The radiated sound is pretty much
contained within a cone of 55º from the center axis.
The radiated sound field is strongest right in front of the speaker and weakens as you move to either side
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Radiation of medium frequency sound.
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3D radiation pattern.
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At high frequencies
When ka becomes much bigger than 1 the sound field radiated by the loudspeaker becomes narrower and
side lobes appear. Now the main lobe of radiated sound is limited to about 20º on either side of the
central axis, and the pressure amplitude falls off rapidly as you move away from the central axis.
Notice that the sound waves in the side lobes have the opposite phase as the sound wave in the main lobe
and the side lobes have significantly lower amplitude than the main-lobe.
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Radiation of high frequency sound.
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3D radiation pattern.
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