cash (n.)youdaoicibaDictYouDict[cash 词源字典]
1590s, "money box;" also "money in hand, coin," from Middle French caisse "money box" (16c.), from Provençal caissa or Italian cassa, from Latin capsa "box" (see case (n.2)); originally the money box, but the secondary sense of the money in it became sole meaning 18c. Cash crop is attested from 1831; cash flow from 1954; the mechanical cash register from 1878.

Like many financial terms in English (bankrupt, etc.), ultimately from Italian. Not related to (but influencing the form of) the colonial British cash "Indian monetary system, Chinese coin, etc.," which is from Tamil kasu, Sanskrit karsha, Sinhalese kasi.[cash etymology, cash origin, 英语词源]
register (n.1)youdaoicibaDictYouDict
late 14c., from Old French registre (13c.) and directly from Medieval Latin registrum, alteration of Late Latin regesta "list, matters recorded," noun use of Latin regesta, neuter plural of regestus, past participle of regerere "to record; retort," literally "to carry back, bring back" from re- "back" (see re-) + gerere "carry, bear" (see gest).

Also borrowed in Dutch, German, Swedish, Danish. Some senses influenced by association with Latin regere "to rule." Meaning in printing, "exact alignment of presswork" is from 1680s. Musical sense is from 1811, "compass or range of a voice or instrument," hence "series of tones of the same quality" (produced by a voice or instrument). Sense "device by which data is automatically recorded" is 1830, from the verb; hence Cash register (1875).
ring (v.1)youdaoicibaDictYouDict
"sound a bell," Old English hringan "sound, give a certain resonant sound when struck; announce by bells," from Proto-Germanic *khrengan (cognates: Old Norse hringja, Swedish ringa, Middle Dutch ringen), probably of imitative origin. Related: Rang; rung. Originally a weak verb, strong inflection began in early Middle English by influence of sing, etc. To ring down a theatrical curtain is from 1772, from the custom of signaling for it by ringing a bell. To ring up a purchase on a cash register is by 1937, from the bell that sounded. Specialized sense "give a resonant sound when struck as an indication of genuineness or purity," with transferred use (as in to ring hollow) is from 1610s.
ka-chingyoudaoicibaDictYouDict
"Used to represent the sound of a cash register, especially with reference to making money", Imitative; compare with ching.
chingyoudaoicibaDictYouDict
"An abrupt high-pitched ringing sound, typically one made by a cash register", Imitative.