"애태우는" - 애타다: = 애가 타다. 애(old word for "guts") + 타다(burn) => worry, agonize, anguish(vi). - 애태우다: causative form of 애타다. worry (someone) extremely; anguish; torment (vt). * 애태우다 is used for doing it to oneself as well as to others. ex) - 가뭄에 농민들은 애탄다[애가 탄다]: The farmers are anguishing because of the drought. - 가뭄에 농민들은 애태운다[애를 태운다]: (same - drought makes them suffer in their guts) - 가뭄이 농민들을 애태웠다: The drought anguished the farmers. (애탔다 can't work here) - 가뭄이 농민들의 애를 태웠다: (same - 애태웠다 is fully spelled out) So 애태우는 소리 is a sound of anguish, an anguished lament, or just moaning utterance,.. And 그 가수는 춤이 애태웠습니다 is "That singer's dancing was heart wrenching" (slightly odd?). Here's an example from an old song (안개 - "Mist" by 정훈희, covered by 보아, el al). 생각하면 무엇하나 지나간 추억 그래도 애타게 그리는 마음 (which is roughly) => What use to dwell on past memories now => Yet my heart desperately clings back