To the tl. Its clearly noted in both novel anime that the sound requested & made is in fact puhi.
Comment by M. Knight Myshlongbelong on Honzuki no Gekokujou ~Shisho ni Naru Tame ni wa Shudan wo Erandeiraremasen~ Dai 2-bu 「Hon no Tamenara Miko ni Naru!」 - Chapter 46
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@M. Knight Myshlongbelong Though not every reader might understand how to phonetically read puhi.