Do DSP principles apply in the same way to both Audio and EM spectrums? All  of my DSP experience is very much centred in the EM spectrum and I've only ever processed EM-type signals in the past. 

I'm now doing quite a bit of work in ultrasound and the audio spectrum, but a lot of the techniques I'm using are used in the EM mainly. I'm reading a lot of EM papers about DSP at much higher frequencies. Can I expect that the principles behind these techniques will behave in the same way, even though the medium of transmission is different?
Many of the ideas will be similar, but some assumptions may no longer apply. For instance many signals in EM can be treated as Narrowband (narrow bandwidth with respect to the centre frequency), in Ultrasound you may run into Broadband signals more easily. Another problem you may run into is the speed of propagation varies as a function of frequency.

Exactly what difference you encounter will depend on your experiences with EM and what exactly your are doing in ultrasound.