Some people like single-sided for portable headphones. One less cable hanging around. I have a single sided headphone and sometimes I feel like it's pulling me to the left side. There's the issue of having to run the wire through the headband some and terminating at the other driver. Shouldn't have any audible effects though.
It depends on whether you think people can discern differences on the nano second scale audibly. In copper wire the propogation speed varies from about .6c to .75c (c=speed of light) - so approximately 1 ns per 6 inches of wire (75% of the speed of light)
So, in theory - yes, you're looking at 1.2-1.6 nanosecond delays. Whether that is an audible amount, is entirely another question.
IIRC, a delay of about 10 us between the channels was found to be audible. The exact threshold of audibility can be argued (blind tests can be created if there is interest), but it might be reasonable to assume that no one can hear a <100 ns delay. By the way, some DACs have a few tens of ns inter-channel delay, probably one ~24 MHz clock cycle. Of course, all the above is probably dwarfed by acoustic delays, considering that even a difference of 0.5 mm between the distances to each ear adds an ITD of more than 1 us.
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