The Nyquist Frequency

Sampling is used to convert from a continuous analog signal to a discrete digital signal. Intuitively, if the sample rate is too small, then the digital signal will not be a good representation of the analog signal. If a sound wave is oscillating at 10,000 Hz, then sampling at 5,000 Hz would be insufficient since the samples would completely miss half the cycles of the analog signal. With a sample rate of 5,000 Hz, it is impossible to record frequencies greater than or equal to 5,000 Hz. Those frequencies will be distorted and appear as noise in the audio recording.