A druid loses her ability to speak while in animal form because she is limited to the sounds that a normal, untrained animal can make, but she can communicate normally with other animals of the same general grouping as her new form.
At 6th level, a druid can use wild shape to change into a Large or Tiny animal or a Small elemental. When taking the form of an animal, a druid's wild shape now functions as beast shape II. When taking the form of an elemental, the druid's wild shape functions as elemental body I.
So, the "vocal chord changes" don't prohibit her from speaking while Wild Shaped into an elemental. Therefore, it's off to the Elemental Body description...
... which says nothing about languages, one way or the other. Elementals can speak (granted, just their native tongue, but the can speak). Therefore, RAW would seem to imply that Wild Shaping Druids can continue to speak while in Elemental form.
A druid loses her ability to speak while in animal form because she is limited to the sounds that a normal, untrained animal can make, but she can communicate normally with other animals of the same general grouping as her new form
So, again, the 3.5 Druid can't speak while in Animal form.
At 16th level, a druid becomes able to use wild shape to change into a Small, Medium, or Large elemental (air, earth, fire, or water) once per day. These elemental forms are in addition to her normal wild shape usage. In addition to the normal effects of wild shape, the druid gains all the elemental’s extraordinary, supernatural, and spell-like abilities. She also gains the elemental’s feats for as long as she maintains the wild shape, but she retains her own creature type.
Elemental Form does note that it applies "the normal effects of Wild Shape". I would read "the normal effects" as covering the duration, HP regeneration, and gear melding; the inability to speak seems to be specific to Animal Form.
As I read them, RAW would allow a Druid to speak any languages she knows normally while Wild Shaped into an Elemental, but that Wild Shaping would not grant the elemental's native tongue.