Something like this should work (though there will be no audible sound in the case of your data since it is just a straight line) -- note that the timeseries data is of the form

{{t1,a1},{t2,a2},...,{tn,an}}

rather than the reversed form that you gave.

So with this understanding and your date example one does

timeSeries = TimeSeries[
  Transpose[{{0.0001, 0.0074, 0.0147, 0.0220, 0.0293, 0.0366, 0.0439, 
     0.0512}, {0.0006, 0.0407, 0.0808, 0.1210, 0.1611, 0.2013, 0.2415,
      0.2816}}]
  ]

and then

ListPlay[timeSeries, SampleRate -> 1000]

Here is a different example with random amplitudes at random times:

times = Flatten[{0, Sort@RandomReal[{0, 5}, 100], 5}] 

randomTS = 
 TimeSeries@
  Table[{times[[i]], 10 RandomReal[{-1, 1}]}, {i, 1, Length[times]}] 

ListPlay[randomTS, SampleRate -> 8000] 

David & Vitaly,

Thank you very much for your suggestions, I have been using David's solution in the above post. Unfortunately, the solution proposed by Vitaly below was taking far too long given that I have datasets that are approx 21000000 points long.

Following on from this method, is there a way to obtain the SpectrogramArray of this? I cannot work out how to ensure that the non-uniform spacing of the points is considered.

Many thanks,

Daniel