What is meant by resonance frequency in WBT and how is it calculated?

When we refer to the admittance of the outer and middle ear system (i.e. its ability to convey sound energy) then we can consider the spring elements that compress and expand (like a spring) including some soft tissues and the air in the ear canal and middle ear.  We can also consider the components of the outer and middle ear that move without compressing much, primarily the ossicular bones. 

For different probe tone frequencies (or frequency components of the click stimuli used in WBT) the middle ear will be either spring dominated (sometimes called stiffness dominated) or mass dominated. 

Mass resists high frequency oscillations and stiffness more easily accepts high frequency oscillations (and vice versa), meaning admittance of the middle ear to acoustic energy is mostly opposed by spring (stiffness) elements with low frequency probe tones (stiffness dominated), while admittance of the middle ear is mostly opposed by the mass elements with high frequency probe tones (mass dominated).


The (lowest) frequency at which the spring and mass elements of the outer and middle ear structures contribute equally to the admittance is the resonant frequency.


The resonant frequency will move upwards or downwards according to outer and middle ear pathologies that affect the mass and stiffness differently. An increase in stiffness increases the resonant frequency whereas an increase in mass decreases the resonant frequency. 


Therefore, one major advantage of WBT is easy identification and analysis of the resonant frequency, for example via the absorbance display.

There are several ways in which resonant frequency can be calculated. In admittance terminology (Y,B and G components of the tympanogram), the method used in the Titan relates to analysis of susceptance (B) at peak pressure (i.e. pressure where absorbance is highest). The B component tympanogram should be zero mmhos when the stiffness elements (which produce positive mmhos) and mass (negative mmhos) are equal. Hence the lowest frequency at which B is zero mmohs (at peak pressure) is the resonant frequency.

For a review of these concepts, please see Shanks (1984)

Another major advantage of WBT is that the admittance tympanogram at resonant frequency is easily obtained. With single-frequency tympanometry it would be a time consuming process to obtain this. 

n.b. the resonant frequency tympanogram is clinically relevant because the resonant frequency tympanogram should be sensitive to middle ear disorders affecting both mass and stiffness.


References and caveats
Shanks, J.E. (1984) Tympanometry. Ear and Hearing, 5 (5), pages 268-280

November 2016
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