Perceived Intensity Model of Dual-Frequency Superimposed Vibration: Pythagorean Sum

This paper presents a model for estimating the perceived intensity of a superimposed dual-frequency vibration from the perceived intensities of its two component vibrations. Based on the previous findings in the literature, we hypothesize that the three variables follow the Pythagorean relationship. Two psychophysical experiments were performed for verification with a wide range of single-frequency and superimposed vibrations applied to the fingertip. In Experiment I, we measured the perceived intensities of a large number of single-frequency vibrations and found a psychophysical magnitude function. Experiment II was designed based on the results of Experiment I in order to test the research hypothesis. For the 108 dual-frequency vibrations tested, the Pythagorean model showed 4.0% of average error in estimating the perceived intensity of a dual-frequency vibration from those of its two components. This model is robust and practical, and can be useful for any tactile interaction applications that make use of superimposed vibrations.