If the frequency of the input wave is abruptly changed, there will be some transient response of the filter which is decay of the signal with previous frequency and at the same time a growth of the signal with trailing frequency. The signal can be modeled as a step wise terminated signal with the previous frequency and step wise starting signal with the new frequency. So the filter will output a signal with the initial frequency then at the abrupt change of the frequency there will a transient period after which the filter settles down to the new frequency.
One can use the signal model brought here and a CAD tool to determine specific transients for certain filter designs.
In some cases, there will be a voltage surge, especially across inductor, in the transient period which could be regarded as a harmful thing to electronic components.