We already knew Waveboard was bringing Google Wave to both the desktop and the iPhone with two dedicated clients, but you’ll be interested to know the iPhone app is now live on the App Store and available for less than a buck (iTunes link).
As you can tell from the short demo video below, the app does exactly what you think it does: it displays ‘waves’ and lets you search historical ones, start new ones and manage your contacts. It also opens external links in a custom browser without the need to leave the app. Waveboard also supports push notifications through a workaround (you need both the Prowl iPhone app and the Mac version of Waveboard), although they did say the next iteration will have proper push notifications.
Update: commenters are pointing out that the app functions merely as a viewer for what you can see when visiting the Google Wave service from your iPhone. To an extent, this is definitely true – there is, after all, no Google Wave API yet – but there a couple of features that you won’t get in the web version like the integrated browser window and a ‘shake’ function for logging out or reloading waves, with more features underway according to the developer behind the tool. Of course, it’s entirely up to you if you want to shell out a dollar for the app rather than simply installing a Safari bookmark on your iPhone for free instead.
(Hat tip to AppsFire)