Investigations of temporal loudness summation of tone pulses have been performed. The investigations comprised equal loudness determinations between pairs of tone pulses with a duration ratio of 1:2, and threshold determinations of the same tone pulses. Pulse durations ranged from 5 to 640 ms. The frequencies were 500, 1000, and 4000 Hz. All pulses were shaped by means of 1/3 octave filters. For 25 normal hearing observers the investigations were performed at the observer's threshold, and at 35 and 55 dB SPL. Fitting of the experimental data to a single exponential function yields a time constant (tau) of about 200 ms near and at the threshold, whereas tau is about 100 ms at levels well above threshold. Discrepancies exist, nevertheless, between this single-time-constant model and the experimental data obtained for the pulses of shortest duration. To account for this, a model is proposed comprising a combination of two exponential functions. This yields a short time constant of 5 to 10 ms combined with the longer time constant mentioned above.
Acoustical Society of America. Journal, 1981, Vol 69, Issue 6, p. 1786-1790