If I don't want Pi to be calculated, what should I do?

To make Pi inert, you can wrap it with Hold[] or HoldForm[].

Dt[0.04 Cos[10 HoldForm[Pi] x] Cos[50 HoldForm[Pi] t]]

Some details :

Hold[exp] prevents exp to be evaluated whatever exp is.

HoldForm is equivalent to Hold except that it is not visible in OutputForm.

If you do not want to change every Pi manually, you can do :

 With[{Pi = HoldForm[Pi]},
    Dt[0.04 Cos[10 Pi x] Cos[50 Pi t]]
    ]  

You can retrieve the numerical value of an expression containing some HoldForm[Pi] with ReleaseHold wrapped around the whole expression.