The Gemara in Masechet Pesachim (56) discusses the practice of reciting the passage "Baruch Shem Kevod Malchuto Le'olam Va'ed" after reciting the verse of "Shema Yisrael." The Gemara tells that Yaakov Avinu assembled his sons before his death and wished to reveal to them when the Mashiach will come to the world, when suddenly the Shechina (divine presence) left him. Yaakov suspected that this perhaps occurred because one of his sons was unworthy, and so all his sons declared in unison, "Shema Yisrael, Hashem Elokenu Hashem Echad" ("Hear, O Israel Hashem our God, Hashem is one!"), announcing to Yaakov that they were all believers in the one G-d. Yaakov was overjoyed to hear his sons' collective declaration, and he praised G-d by exclaiming, "Baruch Shem Kevod Malchuto Le'olam Va'ed" ("Blessed is the Name of the Glory of His Kingship, forever!"). In the Book of Devarim, however, when Moshe declared the verse of "Shema Yisrael," he did not then proclaim "Baruch Shem." We thus face the dilemma of whether we should follow Yaakov's example, and recite "Baruch Shem" after "Shema Yisrael," or the precedent set by Moshe, to recite "Shema Yisrael" without adding "Baruch Shem." For this reason, the Gemara writes, we recite "Baruch Shem" in a low tone after reciting the verse of "Shema Yisrael." We do this as a compromise, of sorts, between the respective practices of Yaakov and Moshe. Out of respect for Yaakov, we follow his example by reciting "Baruch Shem"; in deference to Moshe, however, who did not follow "Shema Yisrael" with "Baruch Shem," we make a point of reciting "Baruch Shem" silently. (The one exception is Yom Kippur, when we declare "Baruch Shem" in a loud tone; we explained the reason for this practice in an earlier edition of Daily Halacha.)
The Ben Ish Chai (Rabbi Yosef Chayim of Baghdad, 1835-1909) raised the question of whether one must recite the passage of "Baruch Shem Kevod Malchuto" silently in the context of the Ana Be'ko'ach prayer. Each morning we recite the paragraph of Ana Be'ko'ach, a liturgical poem composed by the Tanna Rabbi Nechunya Ben Ha'kana, which concludes with "Baruch Shem Kevod Malchuto Le'olam Va'ed." Must this declaration be recited silently in this context, too? In his work of responsa entitled "Torah Li'shma," the Ben Ish Chai observes that from the Gemara it appears that only in the context of Shema must one ensure to recite "Baruch Shem" silently, whereas in other frameworks it may be recited audibly. Elsewhere, however, in his work Od Yosef Chai, the Ben Ish Chai rules that even during Ana Be'ko'ach one should make a point of reciting "Baruch Shem" silently, as we do in the context of Shema. But on other occasions, such as if one comes across this sentence over the course of his studies, he need not recite "Baruch Shem" silently.
In summary, then, both in Shema and in the Ana Be'ko'ach prayer, one should recite the sentence of "Baruch Shem Kavod Malchuto" silently. If one recites this declaration on other occasions, he may recite it audibly.
