Is it permissible to pray upon hearing a sound after performing ablution, given the repeated ablution due to the obsessive doubt about nothing having been emitted from the excretory opening?

If a Muslim is certain about having washed a limb during ablution (wudu'), and then experiences doubt (waswasa) concerning it, he should disregard the doubt and act upon his certainty. And whoever doubts the emission of something from himself during prayer or ablution, he remains in a state of purity until he hears a sound or perceives an odor, based on the Prophet's (peace and blessings be upon him) saying: "He should not leave [the prayer] or turn away until he hears a sound or perceives an odor." This applies if the sound originates from the anus. However, if it is only from the stomach and nothing is emitted from the anus, then there is nothing upon him.