Scaling of fft, when analyzing an audio file

I am trying to understand what the appropriate scaling factor is for the fft. I have an audio file split into four different segments, and I am trying to look at the different frequency behavior of each segment. I have seen some conflicting information about scaling by dt (1 / sampling frequency), or by the length of the individual segments. Obviously, the general plot behavior is the same for each case (so maybe it doesn't matter), but I don't understand what the scaling here does.

Answer 1

[Chunru]

For random signal, abs(fft(x))^2 / N is the estimate (biased) of the power spectrum and its unit is power per normalized frequency (which means fs is corresponding to the normalized frequency of 1). abs(fft(x))^2/(N*fs) is the power spectrum with the unit of power/Hz.