1) It is permissible to sing during Sefirah. However, one should not sing lively songs that may lead to dancing. (Ruling of HaRav Shlomo Zalmen Auerbach Zatzal). If one is passively listening to music with no intention to bring him/herself to Simcha (e.g. while in a doctor’s waiting room, in a store or in another public place where music is playing) it is permitted to remain there, as it isn’t his/her intention to listen to the music.

If one is exercising and needs music for the rhythm, it is permissible, as it isn’t being done for Simcha. (Psak of Rav Shmuel Felder Shlita, Dayan in Lakewood, NJ and other Poskim)

2) Listening to Cantorial recordings (Chazanus) where the musical accompaniment is only as background, and isn’t part of the music, is permitted.

Likewise, children’s story tapes that have musical background are permitted, even when there are adults present who will hear it. (See Sefer V’Yevarech Dovid Orach Chaim Siman 65)

If music is necessary to calm and/or control small children (e.g. a musical mobile for an infant, or even a music tape in the car on long trips) it is permitted.

However, it should not be played very loud that people outside, who do not know the reason you are playing it, will hear it. (Psak of Rav Shmuel Felder Shlita). Halacha For Today.