where P1 + –P2 + and P2–P1 represent the dissipated powers of W+ and
W, respectively. Because W+ flows across L1 and L2 successively, P1 +
is larger than P2 + owing to energy dissipation during propagation.
Similarly, P2 is larger than P1. Since W is the reflection wave of
W+, P2 + is larger than P2. Thus, Ep exceeds zero, which indicates that
Eq. (3) is effective in calculating the dissipated energy when a traveling
wave and a standing wave are generated simultaneously. In
the experiments for Q-factor measurement described later, as
high-amplitude vibrations are generated on long polymer-based
bars, the active vibration power and dissipated power are measureable.
Note that it is difficult to estimate Q factors of materials with
extremely low mechanical loss, such as sapphire [14], for which P1 +
equals P1 – approximately, and P becomes too small to be detected.
In an alternating current circuit, the active power (or real
power) P is calculated from the zero-to-peak voltage u and current
i [12]: