Does the ability of an observer to hear a sound wave depends solely upon the intensity of the sound wave?
Audibility depends on the intensity but also very strongly on the frequency. There are some curves called the Fletcher-Munson audibility curves showing this. The maximum audibility is at something like 3 kHz. But the curves differ depending on intensity, so that at low listening levels the low and high frequencies fall off even more. That is why music lacks bass and treble if played quietly.I would say intensity is the largest factor, as long as the frequency is within hearing range.