Abstract: For both mechanical wave and optical wave，the half wave loss might happen in the reflected wave at the interface of different media. The half wave loss and energy conservation can be inferred from the solution of wave functions. In this paper，we take the mechanical wave as an example to give the insights of the essential conditions of the half wave loss and its necessary connection with energy conservation from the perspective of unitary transformation.

Key words: unitary transformation, half wave loss, energy conservation