"The public is excited."
Translation:Das Publikum ist begeistert.
In my opinion,die Bevölkerung refers to 'population' only. Das Volk means '(the people of) the nation' and bevölkern means 'to populate'. So die Bevölkerung refers specifically to people who live in some country or other place. I am not sure if it is a good idea to use the word in the meaning 'the audience'.
Das Publikum begeistert = 'The audience excites'.
Das Publikum ist begeistert = 'The audience is excited.'
In the latter sentence, the audience witnesses something that makes them excited. In the first sentence, someone else is excited by the audience; the audience is the cause of the excitement.