I am a beginner in acoustics and there are severals problems I am currently struggling while I was reading the first chapter of "Theory of Vortex Sound" (available on Google books).
The Attempt at a Solution
For Q2 and 3, as underlined in the first picture, if the velocity and pressure doesn't go like 1/r , the integral will diverge as r-> inf. However, there are no 1/r terms in U0cos(wt)
I am not sure how to proceed, since the variable y is contained in two terms within the dirac delta,I don't know how to eliminate it.
BTW, I googled sth that might be helpful for Q4.
(From P.115-116 of https://books.google.co.uk/books?id=1x_RvffW-hcC&printsec=frontcover&dq=handbook+of+acoustics&hl=en&sa=X&ved=0ahUKEwin8Ler7uDWAhVKDxoKHe_nDiQQ6AEIMjAC#v=onepage&q&f=false )
Thanks very much!!