This application relates to the design of acoustic treatment to mitigate buzz saw noise from a gas turbine engine. 
Gas turbine engines are known, and typically include a fan delivering air into a bypass duct, and into a compressor.  The air in the compressor is compressed and passed into a combustion section where it is mixed with fuel and ignited.  Products of this combustion pass downstream over turbine rotors, driving them to rotate.  The turbine rotors in turn drive the fan and compressor rotors. 
Gas turbine engines having a fan as described above are typically utilized to drive aircraft.  During take-off and climb for commercial aircraft, a problem called “buzz saw noise” can be a significant contributor to noise in the passenger cabin.  Buzz saw noise is produced when supersonic flow interacts with the fan.  This interaction produces shocks that propagate upstream.  The shocks eventually evolve into sound that is emitted from the inlet.  This sound is then transmitted through the fuselage and into the cabin of the aircraft where it is perceived as a buzz saw like noise by the passengers. 
Near the fan, the shocks are characterized by a wave pressure pattern.  This wave is composed of tones at the blade passage frequency and its harmonics.  Due to small blade-to-blade geometric variations, the spacing between neighbouring shocks ceases to be circumferentially uniform as they propagate upstream. 
Ultimately, when these shocks evolve into sound, the sound is characterized by multiple tones at engine-order harmonics.  Due to this characteristic, buzz saw noise may also be known as multiple pure tone noise.  Buzz saw noise typically assumes its largest magnitude when the fan tip relative Mach number is approximately 1.2. 
Gas turbine engines are treated with acoustic liners to attenuate fan noise.  In some cases, those acoustic liners have been designed to mitigate buzz saw noise, but they have been deeper than the liners described by the present invention.