The residual effect is a psychoacoustic phenomenon. Human beings can perceive the pitch of a note, even when the fundamental tone is completely missing. If you pull out all registers of a drawbar organ, except for the fundamental—16'—you’ll still perceive the same pitch. The sound becomes thinner, with less bass and less warmth, but the pitch remains the same.
If human beings didn’t hear this way, it would make listening to music on a small transistor radio impossible. The tiny speaker of a small radio can’t accurately play back the fundamental tone of the bass line, as this frequency is far below the range that the speaker can reproduce.
Setting drawbar registrations often involves this psychoacoustic phenomenon. In the lower octaves, mixing the 8' and 5 1/3' sine drawbars creates the illusion of a 16' sound, although the lower frequency is missing.
Old pipe organs also make use of the residual effect, by combining two smaller pipes, thus eliminating the need for long, heavy, and expensive giant pipes. This tradition is continued in modern organs and is the reason for arranging the 5 1/3' under 8': The 5 1/3' tends to create the illusion of a pitch that is one octave lower than 8'.