Direct test of the power function for loudness.

The loudness of a sound was made to grow as a function of time along a variety of paths. Observers judged the degree of apparent deviation from linearity of the various paths of loudness growth. The growth of loudness was judged to be least nonlinear when the sound pressure was made to increase as the 1.67 power of time. It follows, therefore, that loudness must be related to sound pressure by a power function with exponent 0.6 (reciprocal of 1.67). This outcome shows that the exponent of the psychophysical power function may be verified by a procedure that does not require the assumption that numerical estimates are proportional to subjective magnitudes.