How do you describe the frequency of waves perceived by the observer from the moment the source appears to the moment it disappears ?

the frequency increases and decreases.

Explanation: According to doppler effect, the frequency of waves tends to increase as the source approaches and decrease as the source disappears.

The Doppler effect occurs when a source of waves and/or observer move relative to each other, resulting in the  observer measuring a different frequency of the waves than the frequency that the source is emitting.