The response of a linear system to multiple inputs is just the sum of the individual responses.
N different frequency inputs will produce a response given by the same N frequencies (with the possibility of total cancellation of same-frequency components).
Two simple harmonic waveforms of the same frequency will add to produce a single harmonic waveform of the same frequency. The resulting amplitude and phase will depend on the individual amplitudes and phases of the two waveforms.
When two pure tones of slightly different frequency are superposed, our ears perceive audible beats at a rate given by the difference of the two frequencies.
Beats are heard as a pulsation in the loudness of a tone at the ``average'' frequency
When the difference frequency exceeds about 15 Hz, the beat sensation disappears and a characteristic roughness of sound appears.
As the difference frequency is increased further, a point is reached at which the ``fused'' tone at the average frequency gives way to two tones, though still with roughness. At this point, the resonance regions on the basilar membrane are sufficiently separated to produce two distinct pitch signals, but these regions still overlap to produce roughness.
Finally, when the difference frequency exceeds the critical bandwidth, the roughness disappears completely.