I'm still uncertain what causes this problem but it is the quick walk around until the problem is addressed.
Edit: Water Elemental sound still breaks with DK voices unchecked. Also, I think his sound breaks when a mob he is targeting dies while he is A.) Casting and B.) Moving.
Edit 2: Found useful information, another temp fix. You can remove the pre casting sound completely of waterbolt for the water elemental. To shut it off completely...
Go to your Data folder in your WoW install folder (generally C:\Program Files (x86)\World of Warcraft\Data ) if you do not have a folder called "Sound" make one. In that folder make another called "Spells" (the total path will now be similar to C:\Program Files (x86)\World of Warcraft\Data\Sound\Spells ). Make a text document in the Spells folder and name it PreCastFrostMagicHigh and change it from a .txt to a .ogg file. Restart you World of Warcraft and there you go. No more pre casting sound for your Water Elemental! Remember both the folders and files are CASE SENSITIVE meaning you have to pay attention to capitalization.
Edit 3: A few people are mentioning the same problem with arcane. It is possible the sound that is invoked is made by the mage (like the frost bomb casting which uses the same sound) and not by the water elemental. It could more prevalent on frost mages because frost bomb has a cast time.
Edit 4: I've talked to a couple of mages on my realm and confirmed what they have said with another post here. It seems the sound loop appears to occur from the use of the mage bombs (NT, LB, FrB) and not from the water elemental.