I may remember it wrong, but I believe you need at least double the sampling rate vs the frequency you want to record. And even then it's a very crude representation of the acoustic signal (Basically a one-bit resolution).
As snippyhollow pointed out, you're right with regard to frequency and that is the Nyquist-Shannon sampling theorem. However, it is important to realize that the resolution of the sampled signal is separate from the sampling rate and so the second part of your statement is incorrect. In theory, a signal sampled at its Nyquist-Shannon rate may be perfectly reconstructed to its analog equivalent. In practice, quantization (the number of bits used to represent each digital sample) will cause distortion to occur, but the bit depth or resolution of a sampled signal is only limited by hardware - in other words, there is certainly a limitation but one-bit quantization would not be useful (and thus not used) for recording an ultrasound signal.
You're thinking about the Shannon's theorem. Here it is about knowing what operations the CPU is performing/looping on. This frequency is not related directly to the frequency at which the CPU operates: it's related to the frequency at which the plates of the capacitor oscillates (which is related to the frequency at which the CPU draws power and so operates...).
