Try turning off the right recirc fan and then re-engaging it. The "OFF" light goes out but the duct noise typically decrease. In about 80% of the a/c it drops the air conditioning duct noise in half. Keep in mind it's not something to do on the ground, or right after takeoff. The additional air pressure only comes back after landing. I used to know, but can't remember, if switching electrical power or shutting an engine down reactivates the fan.
Run the cabin temp slightly cooler(71-72 F/22 C) prior to attempting.
I avoid this technique on full/short/sweaty/daytime/combinations thereof flights.
Unfortunately the loudest a/c often seem to be in the 20% were it doesn't decrease the duct noise.
Cockpit noise? Aircraft design (767/757 +++ ) helps. Next is reduction in KIAS. With fuel issues dictating .78-.79 crz and higher alts = lower KIAS (250-260 KIAS at altitude) the 757 cockpit, especially after R recirc fan cycling, is very quiet.