Matt,
  thanks for suggesting smartctl. Ubuntu had loaded a GUI version. It looks
fine on all drives but the smallest (and therefore probably oldest) one. I
had to apt-get install smartmontools to get the command line version. The
GUI was returning almost immediately from the self test with no values for
any test parameters. The command line gave the data below. The error count
kept increasing when I re-ran it. It looks like the drive is trying to
start up and finding a smart mode error. If I just mount the volume (VFAT),
it does not make the sound and the directory appears to work correctly
(virtually nothing left on that drive, anyway). But when I unmount it, and
try to run tests, it starts making the sounds again every minute or so, and
the error count begins to go up again. I guess it is time to shred the
drive. remove it and throw it away.

Mike

=== START OF READ SMART DATA SECTION ===
SMART overall-health self-assessment test result: UNKNOWN!
SMART Status, Attributes and Thresholds cannot be read.

SMART Error Log Version: 1
Warning: ATA error count 9953 inconsistent with error log pointer 5

ATA Error Count: 9953 (device log contains only the most recent five errors)
        CR = Command Register [HEX]
        FR = Features Register [HEX]
        SC = Sector Count Register [HEX]
        SN = Sector Number Register [HEX]
        CL = Cylinder Low Register [HEX]
        CH = Cylinder High Register [HEX]
        DH = Device/Head Register [HEX]
        DC = Device Command Register [HEX]
        ER = Error register [HEX]
        ST = Status register [HEX]
Powered_Up_Time is measured from power on, and printed as
DDd+hh:mm:SS.sss where DD=days, hh=hours, mm=minutes,
SS=sec, and sss=millisec. It "wraps" after 49.710 days.

Error 9953 occurred at disk power-on lifetime: 8634 hours (359 days + 18
hours)
  When the command that caused the error occurred, the device was in an
unknown state.

  After command completion occurred, registers were:
  ER ST SC SN CL CH DH
  -- -- -- -- -- -- --
  04 51 00 07 4f c2 10  Error: ABRT

  Commands leading to the command that caused the error were:
  CR FR SC SN CL CH DH DC   Powered_Up_Time  Command/Feature_Name
  -- -- -- -- -- -- -- --  ----------------  --------------------
  b0 da 00 00 4f c2 10 08  17d+09:09:16.032  SMART RETURN STATUS
  b0 d0 01 00 4f c2 10 08  17d+09:09:12.992  SMART READ DATA
  ec 00 01 00 00 00 10 08  17d+09:09:12.976  IDENTIFY DEVICE
  ec 00 01 00 00 00 10 08  17d+09:09:12.976  IDENTIFY DEVICE
  ca 00 01 a4 88 03 f0 08  17d+09:02:49.152  WRITE DMA


-- 
But he lives on in a Horcrux named Siri