the turn around time is a day or two now. i just received a new Google account from my university as we're switching to gmail and i applied for a Wave account and had the invite the next day.
on the other hand, i invited some friends with my main account and it took 2 - 3 days for my invite to them to go through. i suspect that Google is starting to ramp up trying to handle much bigger traffic and that anyone who applies is now being accepted quickly.
i plan to have all of the students in one of my online classes use Google Wave this semester. i am also prepared to abandon it quickly. heh.
when you get an invite from another person, it seems like it takes a while before Google gives you invites to send out to others. when i got an invite from Google, the invites were included to send out and invite friends. do you have invites to send out?
and, i don't think you'll get the invite from Google if your account is already using it.
I've played with it, and still find myself wondering how or why I would use it. It seems to me, for now at least, that it's a great tool for the uber-geek, software developers, etc., but not much good for the average "Joe consumer."
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i am doing some research with 2 colleagues and we are collecting data and trying to get some research written based upon the data being collected. we're finding Wave is extremely beneficial in this type of project-based collaboration as it saves us from having a zillion emails going back and forth with attachments here and there, etc. -- Wave allows us to have everything in one place and for discussions to take place pretty easily.
that being said, i think Wave is a bit slow for my preferences. hopefully that comes around pretty soon.