Sensory Neuroscience: Hearing and speech/Outer & middle ear/middle ear

Function
The function of the middle ear is to get the sound energy which arrives at the ../tympanic membrane/ to the oval window of the cochlea.

Spring-like action
The ossicles do not move like the other joints in your body. That is, there is no flexion or extension. Instead, the ossicles vibrate as a unit, with the tensor tympani and stapedius muscles modulating the movement.

Impedance mismatch problem
Recall that the more different the impedances for two mediums, the less acoustic energy will be transferred into the second medium (and the rest will be reflected). The middle ear faces an impedance mismatch problem since the sound energy is travelling from air into fluid (in the cochlea). According to the equation $$\%\text{amplitude transmission} = 4\frac{Z_1 \cdot Z_2}{[Z_1 + Z_2]^2}$$, the reduction in amplitude due to this impedance mismatch is about 97% of the energy (that's 30dB less). Luckily the middle ear compensates for this mismatch in two ways:
 * 1) The $$A_{\text{tympanic membrane}}:A_{\text{footplate}}$$ ratio is large: $$\frac{\text{pars tensa}}{\text{stapes footplate}} = \frac{59.4mm^2}{3.2mm^2} = 18.6$$
 * 2) The length of the long arm of the malleus is $$1.3\times$$ longer than that of the incus. This produces a lever effect.

$$18.6 \times 1.3 = 24.2$$, which is almost the 30dB amplitude loss the impedance mismatch problem would have created.