Fathom, sound, plumb all mean to measure the depth (as of a body of water) typically with a weighted line.
Fathom implies a measuring in fathoms (units of six feet).
Sound typically suggests the use of a sounding line in measuring, but it may come close to probe (see under ENTER 1 ) when it deals with the investigation of a body of water to ascertain not only its depth but the character of its bottom or floor.
Plumb implies the use of a plumb line, a wire or cord to which is attached a plummet that keeps the line in a vertical position as it falls. These differences are seldom apparent, because such measurements are usually taken by similar means, but in extended usage they take on importance and usually determine the specific implications of the words.
Fathom implies an attempt to get through or beneath the obscuring layers of something mysterious or incomprehensible so as to reveal or comprehend its true nature.
Sound implies particularly the use of such indirect methods as cautious questioning or examination to elicit information as to someone’s views or feelings, as to the real state of affairs in a particular case, or as to the worth, status, or possibility of something.
Plumb suggests the ascertaining of something hidden usually by minute and critical examination. Sometimes, however it comes pretty close to fathom <who can plumb what the future holds in store?>