The time period of integration refers to a window of time over which an auditory system integrates acoustic energy, and is an important factor studying sound detection. In order for any given sound to be detected, it must have a certain amount of energy that occurs within the time limits of the TPI. If a signal contains enough energy within the TPI, the signal can be “heard”.
The TPI also denotes the temporal resolution of the auditory system. If two separate sounds occur very quickly after one another, such that the time between them is less than the auditory TPI, then the two sounds are perceived as a single sound by the listener. Conversely, when the timing between two sounds is longer than the TPI, the sounds can be perceived as two separate signals.
The integration time constant on the other hand usually refers to the number of cycles of a signal at constant sound pressure level, where any signal longer is not perceived as being louder than the one played at the integration time constant duration (cf Kastelein et al. 2010).