A pure tone is a sound wave that has a single frequency, which means it contains energy at only one frequency. It is a sound wave that has a sinusoidal waveform: $ \forall t \in \mathbb{R}, x(t) = \sin(2 \pi \times 440 t) $ $ x: \mathbb{R} \rightarrow [-1,1] $ A pure tone can be generated by a simple oscillator or by a musical instrument that produces a single frequency. For example, a tuning fork produces a nearly pure tone. Musical instruments are often tuned to the frequency of 440 Hz which corresponds to the note A4 in the middle octave of a piano.