Although the the Spectrogram function or the SpectrogramArray allow to calculate the spectrogram of this sound I don’t known the options such as ColorFunction used to generate the spectrogram of the Sound object.
The Spectogram function is much newer than sound object. That is, the sound object isn’t making it’s spectogram with the Spectogram function.
I don’t think we can find what options for Spectogram were used to generate the spectogram in sound object because I don’t think that Spectogram is used to generate the spectogram in sound object. But we can create a color function to try and reproduce the same effect.
By sampling the color used is RGBColor[{52, 48, 207}/256]. Playing around gives a reasonable approximating ColorFunction: