What is the equivalent of audacity for iPad?
The currently-accepted answer, WavePad, seems to be sporadically unavailable on the App Store (at least in some regions). I haven’t found another suitable alternative. Also, some would not agree a proprietary product—especially one requiring payment to unlock all features—is actually an “equivalent” to open-source Audacity.
However, there is new reason to hope for Audacity on iPad: it appears the technical obstacles cited by the Audacity team for the lack of iPad support are disappearing.
As of this writing (April 2021), the Audacity FAQ includes the following:¹

Current versions of Audacity work internally with uncompressed audio to permit high quality editing with a wide range of effects. This requires more processing power and disk space than is available on most mobile devices. Also the wxWidgets interface library we use only has limited support for mobile operating systems and small screen resolutions.
Therefore, considerable rewriting of Audacity and its interface will be required before Audacity will work on portable music players like iPod, smartphones like iPhone, tablet computers like iPad or any of the Nexus devices running Android.
However, Audacity in principle does support a tablet PC running Windows (including Microsoft's &quot;Surface with Windows 8 Pro&quot; tablet)…

As of 2021, some new iPads and Macs now share the same Apple Silicon M1 processor; so, according to the FAQ answer above, there should no longer be a performance obstacle—iPad should now be more akin to the Windows tablet PC situation mentioned above. Storage, too, is no longer an issue: the highest-end M1 iPad configurations include terabytes of storage.
In fact, working with uncompressed data such as RAW images and video is one of the selling points Apple is emphasizing in its promotion of these new iPads, and companies such as Adobe have promised to deliver iPad versions of some of their pro creative apps.

¹ Here’s a link to the archived version of the FAQ concurrent with this writing, and a link to current version.