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A waveguide system for radiating sound waves. The system includes a low loss waveguide for transmitting sound waves, having walls are tapered so that said crosssectional area of the exit end is less than the cross-sectional area of the inlet end. In a second aspect of the invention, a waveguide for

A waveguide system for radiating sound waves. The system includes a low loss waveguide for transmitting sound waves, having walls are tapered so that said crosssectional area of the exit end is less than the cross-sectional area of the inlet end. In a second aspect of the invention, a waveguide for radiating sound waves, has segments of length approximately equal towhere l is the effective length of said waveguide and n is a positive integer. The product of a first set of alternating segments is greater than the product of a second set of alternating segments, in one embodiment, by a factor of three. In a third aspect of the invention, the first two aspects are combined.

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1. A waveguide system for radiating sound waves, comprising:a low loss acoustic waveguide having means for supporting standing waves without substantial attenuation for transmitting sound waves, said waveguide comprisinga first terminus adapted to be coupled to a source of sound waves;a second termi

1. A waveguide system for radiating sound waves, comprising:a low loss acoustic waveguide having means for supporting standing waves without substantial attenuation for transmitting sound waves, said waveguide comprisinga first terminus adapted to be coupled to a source of sound waves;a second terminus adapted to radiate said sound waves to the external environment;a centerline running the length of said waveguide;walls enclosing cross-sectional areas in planes perpendicular to said centerline;wherein said walls are tapered such that the cross-sectional area at said second terminus is less than the cross-sectional area at said first terminus. 2. A waveguide in accordance with claim 1, wherein said cross-sectional areas progressively decrease as a function of distance from said first terminus. 3. A waveguide system in accordance with claim 1, wherein the cross-sectional area at said second terminus is less than one half the cross-sectional area at said first terminus. 4. A waveguide system in accordance with claim 3, wherein the cross-sectional area at said second terminus is on the order of one seventh of the cross-sectional at said first terminus. 5. A waveguide system for radiating sound waves, comprising:a low loss acoustic waveguide for transmitting sound waves, said waveguide comprisinga first terminus adapted to be coupled to a source of sound waves;a second terminus adapted to radiate said sound waves to the external environment;a centerline running the length of said waveguide;walls enclosing cross-sectional areas in planes perpendicular to said centerline;wherein said walls are tapered such that the cross-sectional area at said second terminus is less than the cross-sectional area at said first terminus,wherein said cross-sectional areas progressively decrease as a function of distance from said first terminus,wherein said cross-sectional areas vary according to a formula A(y)=A inlet  where A is the cross-sectional area, A inlet is the cross-sectional area at said first terminus, y is the distance measured from said first terminus, and where x is the length of the waveguide, and AR is the cross-sectional area at said first terminus divided by the cross-sectional area at said second terminus. 6. A waveguide system for radiating sound waves, comprising:a low loss waveguide having means for supporting standing waves without substantial attenuation for transmitting sound waves, said waveguide comprisinga first terminus adapted to be coupled to a source of said sound waves;a second terminus adapted to radiate said sound waves to the external environment;a centerline;walls enclosing cross-sectional areas in planes perpendicular to said centerline;a plurality of sections, along the length of said centerline, each of said sections having a first end and a second end, said first end nearer said first terminus and said second end nearer said second terminus, each of said sections having an average cross-sectional area;wherein a first of said plurality of sections and a second of said plurality of sections are constructed and arranged such that there is a mating of said second end of said first section to said first end of said second section; andwherein the cross-sectional area at said second end of said first section has a substantially different cross-sectional area from that at the first end of said second section. 7. A waveguide system in accordance with claim 6, wherein said average crosssectional area of said first section is substantially different from the average crosssectional area of said second section. 8. A waveguide in accordance with claim 7 wherein the cross-sectional area of said second section is substantially constant. 9. A waveguide in accordance with claim 6 wherein the cross-sectional area of said first section is substantially constant. 10. A waveguide system in accordance with claim 6 wherein there are an even number of sections. 11. A waveguide system in accordance with claim 10 wherei n a product of the average cross-sectional areas of a first set of alternating sections is approximately three times the product of the average cross-sectional areas of a second set of alternating sections. 12. A waveguide system in accordance with claim 6 wherein said walls are tapered such that the cross-sectional area of said second end of said first section is less than the cross-sectional area of said first end of said first section. 13. A waveguide system in accordance with claim 6 wherein said walls are tapered such that the cross-sectional area of said second end of said second section is less than the cross-sectional area of said first end of said second section. 14. A waveguide system in accordance with claim 6 wherein said walls are tapered such that the cross-sectional area at said second ends of said first section and of the second section are less than the cross-sectional area at said first ends of said first section and of said second section. 15. A waveguide system in accordance with claim 6, wherein said waveguide is constructed and arranged to form a standing pressure wave having a wavelength substantially equal to the effective length l of said low loss waveguide, said standing pressure wave having nulls, and wherein said mating is positioned so that it coincides with one of said pressure nulls. 16. A waveguide system in accordance with claim 6, wherein said waveguide is constructed and arranged to form a standing volume velocity wave having a wavelength substantially equal to the effective length l of said low loss waveguide, said volume velocity standing wave having nulls, and wherein said mating is, positioned so that it coincides with one of said volume velocity nulls. 17. A waveguide system for radiating sound waves, comprising:a low loss waveguide for transmitting sound waves, said waveguide comprisinga first terminus adapted to be coupled to a source of said sound waves;a second terminus adapted to radiate said sound waves to the external environment;a centerline;walls enclosing cross-sectional areas in planes perpendicular to said centerline;a plurality of sections, along the length of said centerline, each of said sections having a first end and a second end, said first end nearer said first terminus and said second end nearer said second terminus, each of said sections having an average crosssectional area;wherein a first of said plurality of sections and a second of said plurality of sections are constructed and arranged such that there is a mating of said second end of said first section to said first end of said second section; andwherein the cross-sectional area at said second end of said first section has a substantially different cross-sectional area from that at the first end of said second section,wherein said waveguide is constructed and arranged to form a standing pressure wave having a wavelength substantially equal to the effective length I of said low loss waveguide, said standing pressure wave having nulls, and wherein said mating is positioned so that it coincides with one of said pressure nulls,wherein said wavelength is substantially equal to where n is an integer greater than one. 18. A waveguide system for radiating sound waves, comprising:a low loss waveguide for transmitting sound waves, said waveguide comprisinga first terminus adapted to be coupled to a source of said sound waves;a second terminus adapted to radiate said sound waves to the external environment;a centerline;walls enclosing cross-sectional areas in planes perpendicular to said centerline;a plurality of sections, along the length of said centerline, each of said sections having a first end and a second end, said first end nearer said first terminus and said second end nearer said second terminus, each of said sections having an average crosssectional area;wherein a first of said plurality of sections and a second of said plurality of sections are constructed and arranged such that there is a mating of sai d second end of said first section to said first end of said second section; andwherein the cross-sectional area at said second end of said first section has a substantially different cross-sectional area from that at the first end of said second section,wherein said waveguide is constructed and arranged to form a standing volume velocity wave having a wavelength substantially equal to the effective length l of said low loss waveguide, said volume velocity standing wave having nulls, and wherein said mating is positioned so that it coincides with one of said volume velocity nulls,wherein said wavelength is substantially equal to where n is an integer greater than one. 19. A waveguide system, for radiating sound waves, comprising:a low loss waveguide for transmitting sound waves, said waveguide comprisinga first terminus adapted to be coupled to a source of said sound waves;a second terminus adapted to radiate said sound waves to the external environment;a centerline;walls enclosing cross-sectional areas in planes perpendicular to said centerline;a plurality of sections, along the length of said centerline, each of said sections having a first end and a second end, said first end nearer said first terminus and said second end nearer said second terminus, each of said sections having an average crosssectional area;wherein a first of said plurality of sections and a second of said plurality of sections are constructed and arranged such that there is a mating of said second end of said first section to said first end of said second section; andwherein the cross-sectional area at said second end of said first section has a substantially different cross-sectional area from that at the first end of said second section,wherein said waveguide has a resonant frequency, said frequency having an associated wave length λ, and wherein the length of each of said plurality of sections is approximately equal to where n is an integer. 20. A waveguide system for radiating sound waves, comprising:a low loss waveguide having means for supporting standing waves without substantial attenuation for transmitting sound waves, said waveguide comprisinga first terminus adapted to be coupled to a source of said sound waves;a second terminus adapted to radiate said sound waves to the external environment;a centerline, running the length of said waveguide;walls enclosing cross-sectional areas in planes perpendicular to said centerline;a plurality of sections, along the length of said centerline, each of said sections having a first end and a second end, said first end nearer said first terminus and said second end nearer said second terminus;wherein a first of said plurality of sections and a second of said plurality of sections are constructed and arranged such that there is a mating of said second end of said first section to said first end of said second section;wherein the cross-sectional area of said first section increases from said first end to said second end according to a first exponential function andwherein the cross-sectional area at said second end of said first section is larger than the cross-sectional area at said first end of said second section. 21. A waveguide system in accordance with claim 20, wherein said crosssectional area of said second section increases from said first end to said second end t according to a first exponential function. 22. A waveguide system in accordance with claim 20, wherein said crosssectional area of said second section increases from said first end to said second end according to a second exponential function. 23. A waveguide system or radiating sound waves, comprising: a low loss waveguide having means for supporting standing waves without substantial attenuation for transmitting sound waves having a tuning frequency, said frequency having a corresponding wavelength, said waveguide comprising a centerline, running the length of said waveguide;walls enclosing cross-sectional areas in plan es perpendicular to said centerline;a plurality of sections, along said centerline, each of said sections having a length of approximately one fourth of said wavelength, each of said sections having an average cross-sectional area;wherein the average cross-sectional area of a first of said plurality of sections is different from the average cross-sectional area of an adjacent one of said plurality of sections. 24. A waveguide system in accordance with claim 23 wherein the cross-sectional area of said first section is substantially constant. 25. A waveguide system in accordance with claim 24 wherein the cross-sectional area of said adjacent section is substantially constant. 26. A waveguide system in accordance with claim 23 wherein a product of said average cross-sectional areas of a first set of alternating sections is approximately three times a product of said average cross-sectional areas of a second set of alternating sections. 27. A waveguide system for radiating sound waves, said waveguide having segments of length approximately equal towhere l is the effective length of said waveguide and n is a positive integer, each of said segments having an average cross-sectional area, wherein a product of the average cross-sectional areas of a first set of alternating segments is greater than two times a product of the average cross-sectional areas of a second set of alternating segments. 28. A waveguide system in accordance with claim 27 wherein said product of said average cross-sectional areas of said first set of alternating segments is approximately three times said average cross-sectional area of said second set of alternating segments. 29. A waveguide m accordance with claim 27, wherein one of said segments has an average cross-sectional area greater than the cross-sectional area of either of the adjacent segments. 30. A waveguide for radiating sound waves, constructed and arranged to form standing pressure waves and standing volume velocity waves,said volume velocity standing wave having a wavelength substantially equal to the effective length I of said waveguide, said volume velocity standing wave having volume velocity nulls;said pressure standing wave having a wavelength substantially equal to the effective length l of said waveguide, said pressure standing wave having pressure nulls,said pressure nulls occurring between said volume velocity nulls;said volume velocity nulls and said pressure nulls delimiting a plurality of segments of said waveguide, each of said segments having an average cross-sectional area; andwherein a product of the average cross-sectional areas of a first set of alternating segments is greater than two times a product of the average cross-sectional areas of a second set of alternating segments. 31. A waveguide in accordance with claim 30 wherein said product of said average cross-sectional areas of said first set of alternating segments is approximately three times said average cross-sectional area of said second set of alternating segments. 32. A waveguide in accordance with claim 30, wherein one of said segments has an average cross-sectional area greater than either of the adjacent segments.