Factors affecting the loudness of modulated sounds

Loudness matches were obtained between unmodulated carriers and carriers that were amplitude modulated either periodically (rates between 2 and 32 Hz, modulation sinusoidal either on a linear amplitude scale or on a dB scale; the latter is called dB modulation) or with the envelope of the speech of a single talker. The carrier was a 4-kHz sinusoid, white noise, or speech-shaped noise. Both normally hearing subjects and subjects with cochlear hearing loss were tested. Results were expressed as the root-mean-square (rms) level of the modulated carrier minus the level of the unmodulated carrier at the point of equal loudness. If this difference is positive, this indicates that the modulated carrier has a higher rms level at the point of equal loudness. For normally hearing subjects, the results show: (1) For a 4000-Hz sinusoidal carrier, the difference was slightly positive (averaging about 0.7 dB). There was no significant effect of modulation rate or level over the range 20-80 dB SL. (2) For a speech-shaped noise or white noise carrier, the difference was close to zero, although for large modulation depths it tended to be negative. There was no clear effect of level (over the range 35-75 dB SPL) or modulation rate. For the hearing-impaired subjects, the differences were small, but tended to be slightly negative for both the 4000-Hz carrier and the noise carriers, when the modulation rate was above 2 Hz. Again, there was no clear effect of overall level. However, for dB modulation, the differences became more negative with increasing modulation depth. For modulation rates in the range 4-32 Hz, the results could be fitted reasonably well using the assumption that the loudness of modulated sounds is based on the rms value of the time-varying intensity of the response of the basilar membrane (taking into account the compression that occurs in the normal cochlea). The implications of the results for the fitting of multi-band compression hearing aids and for the design of loudness meters are discussed.