The maximum frequency of a static signal that can be captured with a sampling rate of Fn is (Fn/2). This comes from Nyquist’s Sampling Theorem, and is known as the Nyquist frequency.
To avoid digital sampling artifacts, you have to make sure that no frequency above the Nyquist frequency is present in the signal, or you will get aliasing. Typically, you’ll use an analog filter before the digital sampling to remove frequencies above your Nyquist (and a little bit below, because real filters are far from ideal brick-wall filters.)
Also, for dynamic signals (signals that change phase/amplitude/frequency over time,) the error goes towards infinity as the frequency goes towards Nyquist, so you want to stay below Nyquist for your input.
Thus, if your output signal is 330 Hz, and your sampling frequency is 880 Hz, the Nyquist frequency is 440 Hz and thus your signal is at 3/4 of Nyquist, which is a reasonable place to be (slightly aggressive IMO.) For comparison, an oscilloscope with a “100 MHz bandwidth” will typically sample at 1 Gsample/second, and thus have a Nyquist of 500 Mhz. This is so that the “frequency close to Nyquist” problem doesn’t show up on your display.
Hope this helps.