I often see (without hearing) helicopters in the downtown brooklyn area. If this aircraft flies above ~600 feet, noise should be little to no concern.

You need to live in a quieter area. Too much noise pollution in NYC.

In a suburb of Portland Oregon I routinely hear helicopters up to about 2000 feet. I hear many planes at over 5000 ft. When jets take off from PDX and climb over my house I can easily hear them at about 16,000 feet.

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Depending on the weather I hear aircrafts at 32,000 to 40,000 ft. Trough closed windows (double paned isolating stuff) at night. Mostly traffic from/to Paris, France and from/to Asia, which goes over here.

There will be a difference between a hovering helicopter and one travelling at cruising speed. I assume you experience more of the latter while I the former.