If you say that someone or their voice is quivering with an emotion such as rage or excitement, you mean that they are strongly affected by this emotion and show it in their appearance or voice.
1. vibrating slightly and irregularly; as e.g. with fear or cold or like the leaves of an aspen in a breeze;
"a quaking bog""the quaking child asked for more""quivering leaves of a poplar tree""with shaking knees""seemed shaky on her feet""sparkling light from the shivering crystals of the chandelier""trembling hands"