The Nyquist sampling theorom states that, in digitally reproducing an analog signal, the digital sampling rate must be at least twice the highest frequency (f) of the components making up the analog signal.  The Nyquist frequency is then 2f, so the sampling frequency must be at least 2f = 1/Dt where Dt is the time interval between signal samples.  As the sampling frequency drops below the Nyquist frequency, the digital signal begins to show frequency components that differ from the original, an effect known as aliasing. 

This simulation generates a sine wave with user-defined frequency (f) and amplitude, along with a background of Gaussian white noise.  The user sets the sampling rate for the digital signal, and both the analog and digital signals are displayed.  Aliasing can be seen as the sampling frequency drops below the Nyquist frequency (2f).  Also, it can be seen that features of the analog signal are lost when the sampling frequency drops below ~20f. 

(Reference: Skoog, Holler, and Crouch Principles of Instrumental Analysis, 6th Ed Thomson Brooks/Cole 2007)