An apparatus for use in a wellbore is provided that in one embodiment may include at least one transmitter configured to generate acoustic signals in the wellbore, at least one receiver configured to receive acoustic signals from a formation surrounding the wellbore in response to the transmitted acoustic signal and also configured to provide electrical signals representative of the received acoustic signals, a circuit configured to apply a time-variable gain to the electrical signals to amplify the electrical signals, and a processor configured to process the amplified electrical signals and provide a property of interest.