Some questions about the mixed function space

Hello everyone , i am working on the fenics 2019.1,and i have some questions about the mixed function space. For example, to solve the time-dependent wave equation (second time derivative) ,i reduce the time derivative order .Let
1699863335313, ww can get a system of first order equations about u and \phi (for the time derivative), I wonder if i need define a mixed function space to solve the first order system.

u_elem            = FiniteElement("P", mesh_s1.ufl_cell(), 2)
phi_elem              = FiniteElement("P", mesh_s1.ufl_cell(), 2)
elem                = MixedElement([u_elem, phi_elem])
Vh                   = FunctionSpace(mesh_s1, elem) 

Or, could i solve this system only on a FunctionSpace?

In my opinion using a MixedElement would be the natural choice in this case.