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 th

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.