There is increasing interest in the use of the LEArnable Front-end (LEAF) in a variety of speech processing systems. However, there is a dearth of analyses of what is actually learnt and the relative importance of training the different components of the front-end. In this paper, we investigate this question on keyword spotting, speech-based emotion recognition and language identification tasks and find that the filters for spectral decomposition and the low pass filter used to estimate spectral energy variations exhibit no learning and the per-channel energy normalisation (PCEN) is the key component that is learnt. Following this, we explore the potential of adapting only the PCEN layer with a small amount of noisy data to enable it to learn appropriate dynamic range compression that better suits the noise conditions. This in turn enables a system trained on clean speech to work more accurately on noisy test data as demonstrated by the experimental results reported in this paper.