Alternatively, in the αλ representation commonly used here:

Here Q = f/Δf is the quality factor. In the case of an ideal resonator, a particularly simple relationship holds:

At this point it becomes clear that determining αλ for a real resonator is considerably more complicated, because the idealized assumptions no longer apply. A range of resonator types—spherical, focusing and planar resonators—must be used for specific regions of the absorption spectrum.

So far, the quartz transducers between which the sound wave is reflected have been treated as acoustically rigid, with reflection coefficients rₑ = rₛ = 1. This is not true in practice and has a substantial influence on the resonator transfer characteristics. The associated problems can be summarized as instrumental losses. Assuming that the causes of attenuation combine linearly, the total quality factor obeys:

With Q = f/Δf, it follows that:

Using Eq. (4.10), one finally obtains:

The following effects must be classified as instrumental losses, Qₐₚₚₐᵣₐₜᵢᵥₑ:

Original mathematical notation is preserved in the extracted image assets.