Early Primitive Elvish
sipi
root. whistle, pipe
þipi Reconstructed
root. whistle, pipe
There are more words but they are from Tolkien's earlier conceptional periods. Tolkien likely changed these words as he evolved the aesthetics and completeness of the languages. You may even find languages that Tolkien later rejected. Do not mix words from different time periods unless you are familiar with the phonetic developments.
Below: Tolkien's Late Period (1950–1973). These are from Tolkien's late conceptual period — his most settled forms of the languages. Prefer these over the earlier ones above when composing new text.
The root ᴱ√SIPI “whistle, pipe” appeared in the Qenya Lexicon of the 1910s with derivatives like ᴱQ. simp(in)a “pipe, flute, flageolet” and ᴱQ. sipi- “pipe” (QL/84). In the contemporaneous Gnomish Lexicon the derived forms were words like G. thibin “flute” and G. thimpa- “to play a flute or whistle”, indicating an actual root form ✱ᴱ√ÞIPI (GL/73). The Gnomish word G. Simfi “Wailers of the Shore” = ᴱQ. Solosimpe does hint at ᴱ√SIPI (GL/67), but I suspect it is a loan word as opposed to native Gnomish G. Thlossibrim (GL/73).
Neo-Eldarin: For purposes of Neo-Eldarin I think it is worth positing a Neo-Root ᴺ√THIP to salvage early “pipe” and “flute” words.