Grounding the shield on the cable at the "source" produces the least noise (hum). That is the reason for the "direction".
Don, I'd be interested in the science on which you base this pronouncement ;--))
Clio, the cable you describe is either:
(1) the old (pre-shotgun) coax that was used to connect all the early RCA enabled equipment; a 'hot' conductor in the center with a 'ground' conductor/shield around it, much like today's CATV cable, OR
(2) some current manufacturers (like Nordost, I think) are offering air-dielectric single-ended interconnects that use teflon tubing and no shield.
The reason for floating the shield is because if connected to ground at BOTH ends, it can conduct a current -- such current can be the music signal, but it can also include that created by nearby electromagnetic sources (power cords, transformers) or by airborne radio waves. If you disconnect the shield at one end, it can still drain interference to the ground end, but it can no longer conduct the 'minus' half of the music signal.
In "pre-shotgun" days, one of the biggest problems people had (with the old coaxial interconnect) was with their record players -- especially after the introduction of stereo, which meant having TWO parallel coaxial interconnects (with shields connected at both ends) creating a nice BIG loop antenna, enabling you to hear both your record AND a local radio broadcast at the same time!!
BTW, the term "shotgun" simply refers to the fact that instead of having a single center conductor (for the 'hot' signal) and a signal conducting shield surrounding it, the new "shotgun" cable had TWO signal conductors in the center (doubled barreled shotgun ;-) with a floating, non-conducting protective shield surrounding them.
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