Does passing wind audibly necessitate performing ablution, or is it treated the same as passing wind silently?

There is no difference between the emission of wind with or without sound. Whenever a Muslim is certain that wind has been emitted from him, his ablution (wudu') is invalidated. However, if it is merely a doubt, the ablution is not invalidated, based on the saying of the Prophet, peace and blessings be upon him: "He should not leave (his prayer) until he hears a sound or perceives a smell."

If a woman is certain that wind has been emitted from her, and its emission is continuous, then if she finds a time when she can purify herself and pray without anything coming out, she must wait for it. Otherwise, her ruling is the same as that of a woman with irregular bleeding (mustahadah). She should perform ablution for each prayer after its time has begun and pray with this ablution the obligatory prayer and whatever voluntary prayers she wishes. What comes out of her does not harm her unless she intentionally commits an act that invalidates ablution. The ablution is invalidated by the departure of the prayer's time according to many scholars.