According to Rav Shlomo Zalman Auerbach a person should not use an alarm clock with melodies, and certainly not recorded music to wake up to in the morning (Halichos Shlomo Tefila 13:18). The footnote brings that this is based on the Shulchan Aruch (OC 560) that prohibits musical instruments and song because of the Churban. Even though the Rema permits listening to music and says that the issur only applies to Kings and those accustomed to going to sleep and waking up to music, in this case one should be machmir.
In general Rav Shlomo Zalman was machmir on listening to music and tapes, and advised against them except for by Simchos. Even at simchos he cautioned regarding songs with psukim that have no direct relationship to the simcha, since the gemara (Sanhedrin 101a) says that the psukim complain to Hashem that we turn them into songs.
Important Note: We bring this tshuvah as a starting point for discussion and not to convey any halacha. We try to convey the Tshuva to the best of our ability. We admit that our understanding may not be accurate. One should learn the tshuva to verify the accuracy of our interpretation. Please understand that this Tshuva may not be the final word on this topic. One should consult a Rav before drawing any conclusions.