Transient and Frequency Response

There are three fundamental questions that need to be answered with respect to the temporal response of a probe and a measurement system which are subjected to a non-zero input. These are :

1. If the input is steady, how long will it take for the probe response to become steady?

2. If the input is steady, is the probe response oscillatory?

3. If the input is periodic, what is the critical frequency beyond which the output has a negligible amplitude?

Question 3 addresses the problem of attenuation of signals as they pass through the probe and the measurement system. Further attenuation of signals can take place in spatially distributed systems due to a non-uniform response of different parts of the probe. For example, in a pitot tube the fluid close to the wall is always at rest while the bulk of the fluid within it will move during a transient. In a hot-wire anemometer, the temperature may not be uniform along its length and in particular, the portion of the wire close to the prongs will be at the prong temperature. Hence it would take finite time to re-establish the temperature profile along the wire. The reciprocal of this time determines the cut-off frequency beyond which the signal amplitude is unacceptably small.