Is it obligatory for women to cover their head when they hear the Ādhān and while reading the Qur’ān?.
Women are required by the Qur’ān to keep their head covered when other people are present except if they are mahram relatives:
[O Prophet!] tell believing men to restrain their eyes and guard their private parts. That is purer for them. And Allah is well aware of what you do. And tell the believing women to restrain their eyes and to guard their private parts and to display of their finery only that which is apparent by drawing their coverings over their chests. They should not reveal their finery to anyone save their husbands or their fathers or their husbands' fathers or their sons or their husbands' sons or their brothers or their brothers' sons or their sisters' sons or other women of acquaintance or their slaves or male servants lacking in physical needs or children who have no awareness of the hidden aspects of women. [In order not to reveal their finery except which is apparent], they should [also] not stamp their feet in order to draw attention to their hidden ornaments. Believers turn to Allah in repentance that you may prosper. (24:27-31)
The word Khimār in Arabic is used for a shawl that covers the head.
If a woman is alone or there are just ladies around her or she is reading the Qur’ān or hearing the Adhān, then this is not necessary.