can someone correct me if i'm wrong, but i believe if you solder a small value cap (e.g. 0.001uF) between the output and ground, you can kill some of the high pitch hum...
A capacitor wired as you suggest forms a kind of passive low pass filter and will remove some of the top end noise in theory. To quote something i was just reading on the net:
'A filter in which a capacitor provides a path to earth, therefore presents less attenuation to low-frequency signals than high-frequency signals and is a low-pass filter.'
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