Fiqh-us-Sunnah Volume 5, Hajj and ‘Umrah, Fiqh 5.041.
Zaid ibn Khalid reported that the Prophet (peace be upon him) said: “Gabriel (peace be upon him) came to me and told me: ‘Command your Companions to raise their voices when saying talbiyah, because it is one of the rituals of Hajj.” This is reported by Ibn Majah, Ahmad, Ibn Khuzaimah and Al-Hakim, who regards it a sound hadith.
Abu Bakr reported that the Prophet (peace be upon him) was asked: “Which Hajj is the best Hajj?” He replied: “One in which voices are raised when saying talbiyah and a sacrifice is offered.” (Reported by Tirmizhi and Ibn Majah) Abu Hazim said: “When the Companions put on ihram their voices would become hoarse even before they reached Makkah.” In the light of these ahadith the majority of scholars prefers that the pilgrims raise their voices when saying talbiyah.
Malik holds that one must not raise one’s voice in saying talbiyah while inside a congregational mosque. One may, however, say it loud enough for oneself or for those around to hear it, except in the Sacred Mosque and the Mosque of Mina. In these two one should raise one’s voice when saying talbiyah. This applies to male pilgrims only.
As for women, they may raise their voices when saying talbiyah so that they themselves or those around them can hear it. To raise their voices above that is disliked for them.
‘Ata said: “Men must raise their voices (when saying talbiyah), but a woman should raise her voice so as to hear it herself, but she should not raise her voice more than that.”