See Rama 234:1; M”A 69:4; 234:1; Elya Raba 55:3 [suspects for opinion of M”A initially] and 581:13; Chayeh Adam 30:7; Chesed Lealafim 55:3; Kaf Hachaim 55:5; M”B 55:2; 234:5 [concludes that Achronim rule like M”A ibid]; Kaf Hachaim 55:41; Ketzos Hashulchan 16:2 footnote 6; Ishei Yisrael 15 footnote 100; Custom of Rebbe and Chabad to recite the Mishnayos aloud after Davening; See Hiskashrus 601:19; Siddur Rav Raskin p. 483

Other opinions: Some Poskim rule it is not necessary to recite the Mizmor aloud. [Mateh Efraim 590:38; See also Taz 55:3, brought in M”B ibid]

See regarding listening to music for the sake of mental and emotional health:

Music therapy-May one listen to music during the three weeks [or during Sefirah] for emotional and mental health purposes?

See regarding children listen to music: 

From the Rav’s Desk: May small children listen to music or a music video during Sefirah in order to keep them occupied?

See M”A 560:9 that playing music for the sake of performing a work was never included in the prohibition of playing music after the Churban.

See regarding listening to music for the sake of mental and emotional health:

Music therapy-May one listen to music during the three weeks [or during Sefirah] for emotional and mental health purposes?

From the Rav’s Desk: May small children listen to music or a music video during Sefirah in order to keep them occupied?