In (Old) Sindarin medial [s] became [x] before semi-vowels y, w [j, w]. There is pair of a very clear examples of this sound change in Definitive Linguistic Notes (DLN) from 1959:

• ✶lisyā > liχı̯ā > leχı̯ > leich > S. laich “sweet” (PE17/148).
• ✶teswā > teχwā > teχw̯ > S. tewch “(?chip)” (PE17/148).

The (archaic) aspirate mutated form a chwath (from *as-wath) also implies this sound changes (PE17/41). As these examples indicate, this was an early change, occurring even before long final vowels were shortened, and probably in parallel to the initial developments whereby initial [s] unvoiced following consonants.

Tolkien described similar developments in notes on the Common Eldarin Article (CEA) from 1969 (PE23/138):

Medially and initially in S. sy > ꜧ (voiceless spirantal y); and this eventually was retracted to χ (back spirant identical in sound with the product of CE kh). sw > voiceless spirantal ƕ (hw, wh), which later became χw (tr[anscribed] chw).

In this 1969 note Tolkien transcribed these sounds using the characters ꜧ (heng) and ƕ (hwair) rather than χı̯ and χw̯ as he did in 1959. It seems likely Tolkien adopted ꜧ and ƕ from contemporary phonetic descriptions like those of the Dania Transcription of the 1920s, probably representing voiceless palatal(ized) or labial(ized) spirants or approximants like [xʲ]/[ç] or [xʷ]/[ʍ]. For simplicity I represent these as [xʲ] and [xʷ] to indicate both their frictional character and their palatal/labial character.

In CEA Tolkien went on to describe how ꜧ and ƕ vocalized to produce a variety of diphthongs; see that entry for details.

Conceptual Development: There seems to be at least one example of a similar change in Noldorin:

• ᴹ√PIS > N. peich “juice, syrup” vs. ᴹQ. pirya < *pisyā (Ety/PIS).

David Salo gave a different explanation of this word in Gateway to Sindarin, positing that [h] became [x] after [i] (GS/§4.101), but the Sindarin evidence given above was not available when Salo did his research.

See OS. medial [sj], [sw] became [xʲ], [xʷ] for discussion.