Contrary to Hxcboatcaptain’s "The audience were rising to their feet," I’ve found an example treating ‘audience’ as singular in an Oxford ESL dictionary: "There was a large audience at the pop concert."

‘Audience’ like ‘crowd’, ‘committee’ & jury’ is considered a collective (group) noun and is singular.

As Yoong Liat pointed out, "some grammarians do consider the second sentence to be wrong as 'were' should be used with 'their' (both plural)." I would rework the subject in that sentence to agree with the verb thus "The audiences were rising to their feet." Now you might have a question on the plural of ‘audience’. This revised sentence can only be correct if we refer ‘audiences’ to different groups of audience at different locations or engagements. It might then be better to say "everywhere he (the orator) goes, the audiences were rising to their feet."