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A resonator for damping pressure waves or instabilities in a system supported by acoustic energy wherein the resonator adopts the use of counter-bored openings on the downstream side of the resonator within the flow path of the system. The resonator includes a first member and a second member where

A resonator for damping pressure waves or instabilities in a system supported by acoustic energy wherein the resonator adopts the use of counter-bored openings on the downstream side of the resonator within the flow path of the system. The resonator includes a first member and a second member where the second member includes a plurality of openings therethrough with each hole having a counter-bore on its upstream side. The first member has a size substantially smaller than the diameter of said flow path and a first plurality of openings therethrough. The openings are in fluid communication with the flow path. The second member has a size generally equal to the first member and a second plurality of openings therethrough, which openings are in fluid communication with the flow path.

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I claim: 1. A method of damping pressure waves supported by acoustic energy in a system having a flow path, the method comprising the steps of: providing a resonator having a first member and a second member defining a volume therebetween; locating the resonator in the system so that the first memb

I claim: 1. A method of damping pressure waves supported by acoustic energy in a system having a flow path, the method comprising the steps of: providing a resonator having a first member and a second member defining a volume therebetween; locating the resonator in the system so that the first member is upstream of the second member within the flow path; forming a first plurality of openings through the first member; forming a second plurality of openings through the second member to have a geometry thereby establishing a first acoustic inertance and a first rate of mass flow of air through the resonator; and changing the geometry of the second plurality of openings to reduce the first acoustic inertance to a second acoustic inertance without increasing the mass flow of air through the resonator. 2. The method of claim 1 further comprising the step of: determining a location of the maximum acoustical energy within the flow path of the system; and locating the resonator proximate the location. 3. The method of claim 2 wherein the step of changing the geometry includes the step of counter-boring at least one hole within the second plurality of openings. 4. The method of claim 2 further comprising: forming each of the second plurality of openings to include a cylindrical upstream portion having a first diameter and a first length; and forming each of the second plurality of openings to include a cylindrical downstream portion having a second diameter and a second length wherein the first diameter is greater than the second diameter. 5. The method of claim 4 further comprising the steps of: selecting a predetermined lower limit for the second length; and forming the first length so that the second length is not less than the predetermined lower limit. 6. The method of claim 2 further comprising: forming each of the second plurality of openings to have a cylindrical downstream portion; and counter-boring each of the second plurality of openings. 7. The method of claim 2 further comprising the steps of: determining a size for each of the first plurality of openings; determining a size for each of the second plurality of openings; forming the first plurality of openings in the first member so that a surface area of the first member between any two of the first plurality of openings is maximized; and forming the second plurality of openings in the second member so that a surface area of the second member between any two of the second plurality of openings is maximized. 8. A method of damping pressure waves supported by acoustic energy in a system having a flow path, the method comprising the steps of: providing a resonator having a first member and a second member defining a volume therebetween; forming a first plurality of openings through the first member; forming second plurality of openings through the second member; counter-boring an upstream portion of at least one of the second plurality of openings so that the upstream portion has a diameter that is greater than a downstream portion of the at least one of the second plurality of openings; and locating the resonator in the system so that the first member is upstream the second member in the flow path. 9. A method of damping pressure waves supported by acoustic energy in a system having a flow path, the method comprising the steps of: providing a resonator having a first member and a second member defining a volume therebetween; locating the resonator in the system so that the first member is upstream the second member in the flow path; forming a plurality of first openings through the first member; forming a plurality of second openings through the second member, wherein at least one of the second openings comprises a second opening upstream portion and a second opening downstream portion, wherein a second opening upstream portion cross section is greater in area than a second opening downstream portion cross section. 10. The method of claim 9, further comprising forming the second opening upstream portion with a circular cross section, and forming the second opening downstream portion with a circular cross section. 11. The method of claim 9, further comprising inserting a device into at least one of the second openings and securing it therein in order to reduce the second opening downstream portion cross section. 12. The method of claim 11, further comprising forming a plurality of second openings by drilling, and comprising forming the second opening upstream portion and the second opening downstream portion by inserting and securing in at least one of the second openings a device with a hole therethrough.