Buzz in Rio Cali but not in Rio Chiba?

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I recently picked up two lightweight Rio flash players which run on disposable batteries so I could use them on a long airplane flight without the need for additional cords for charging - a 128 MB Rio Cali and a 256 MB Rio Chiba. I have used both payers with my Ety 4P and Ety 6 headphones, but the Cali seems to have this persistent, high pitched whine regardless of the level of volume. It only seems to be present with downloaded songs and not the FM tuner. Does anybody have any idea if this is a common trait for these types of units? Is there anything I can do to make this noise go away? Any suggestions or diagnostic procedures would be greatly appreciated. I do not normally use DAP's since I normally listen to CD's piped into a Headroom amp when I am mobile. Any help would be greatly appreciated. I am beginning to appreciate the convenience of DAP's in certain situations, and understand there is a trade-off in terms of sound quality vs. convenience.

Thanks,

--Ken