On the loudness of low-frequency sounds with fluctuating amplitudes

Some environmental sounds have strong amplitude fluctuations that may affect their perceived loudness and annoyance. This study assessed the effect of beat rate (f_b) and center frequency (f_c) on the loudness of low-frequency beating tones. The loudness of two-tone complexes (TTCs) with f_c = 40, 63, 80, and 1000 Hz was matched with that of unmodulated tones (UTs). Frequency differences between the TTC components, corresponding to f_b = 1, 2, 5, and 12 Hz, were used. To compensate for the steep decline in hearing sensitivity below 100 Hz, prior to the loudness match, subjects adjusted the relative levels (ΔL) of the TTC components to give maximum beat perception. Twenty-four normal-hearing subjects were tested. The values of ΔL giving best beats were well predicted from the transfer function of the middle ear and the estimated shapes of the auditory filters, assuming that the auditory filter whose output dominated the beat percept was centered somewhat above f_c. At the same root-mean-square level and independent of f_c, TTCs were perceived as louder than UTs for f_b ≤ 2 Hz, had roughly equal loudness to UTs for f_b = 5 Hz, and were less loud than UTs for f_b = 12 Hz.