Clause in sentence

I believe it is a dependent adverbial clause..

That Wayne played the tuba modifies found it surprising.

Things have been done to this sentence.

There are actually three clauses here, with 3 predicates: find, (be) surprising, and play.
Find takes an infinitive object complement, and (be) surprising takes a tensed subject that-clause.

John found [[that Wayne played the tuba] to be surprising]
==> Extraposition
John found [it to be surprising [that Wayne played the tuba]]
==> to be-Deletion
John found it surprising [that Wayne played the tuba].

That Wayne played the tuba is the subject complement clause of to be surprising.
The dummy subject it gets inserted by Extraposition, and then to be-Deletion does the rest.

To answer the question, that Wayne played the tuba is all of the following:

• a subordinate clause (since it's not the main clause)
• a subject clause (since it's the subject of (be) surprising)
• a noun clause (since it's a subject, it acts as a noun)
• a tensed clause (since it has a tensed main verb played)
• a that-clause (since it uses the tensed clause complementizer that)
• an extraposed clause (since it was moved by Extraposition)

It is not, however, an adverbial clause of any kind.