Manipulate with variable number of sliders plus variable number of functions

Question

I'm trying to setup a Manipulate where I have a variable number of sliders similar to this one, where every slider controls a function. In my case, there will be an additional slider which sets the number of functions.

I've tried with

Manipulate[
  Block[{},
    Manipulate @@ 
      {Plot[Table[Cos[2\[Pi]Subscript[h, i]x], {i, 1, n}], {x, 0, 1}], 
       Sequence@@Table[{Subscript[h, i], 0, 1}, {i, n}]}], 
  {{n, 1, "Waves"}, 1, 4, 1}]

but that does not work. I hope I have been successful in explaining my problem.

For instance this is partially working, except I can not add controls on functions, i.e. Subscript[h,i] in a nested manipulate

Manipulate[
  Block[{
    trange = {t, 0, tmax},
    plotrange = {{0, xmax}, {-1, 1}},
    aspectratio = 1/xmax,
    f = Table[Cos[2 \[Pi] i t], {i, 1, n}]
    },
    Plot[Evaluate[f], Evaluate[trange], PlotRange -> plotrange, 
    AspectRatio -> aspectratio]
    ],
  {tmax, 0.1, 1},
  {xmax, 0.1, 1},
  {n, 1, 4, 1}
]

Answer 1

In your construction, it will evaluate {Plot[...],..} first and then apply Manipulate. Plot[..] will become empty graphics since it didn't know about Subscript[h,1]. The following will be the better construction for this purpose:

Manipulate[
 With[{controls = Sequence @@ Table[{Subscript[h, i], 0, 1}, {i, 1, n}], 
       func = Table[Cos[2 \[Pi] Subscript[h, i] x], {i, 1, n}]}, 
       Manipulate[Plot[func, {x, 0, 1}], controls, Paneled -> False]], 
 {n, 1, 10, 1}]