Page 73 - Master Handbook of Acoustics

connected by an articulated connecting rod having a lever arm ranging from 1.3:1 to 3.1:1, yielding a
total mechanical force increase of between 35 and 80 times. The acoustical impedance ratio between
air and water being on the order of 4,000:1, the pressure ratio required to match two media would be
, or about 63.2. This falls within the 35 to 80 range obtained from the mechanics of the middle

ear illustrated in Fig. 4-4B. It is interesting that the ossicles in infants are fully formed and do not
grow significantly larger over time; any change in size would only decrease the efficiency of the
energy transfer.
The problem of matching sound in air to sound in the fluid of the inner ear is solved by the

mechanics of the middle ear. The evidence that the impedance matching plus the resonance
amplification of Fig. 4-3 really work is that a diaphragm motion comparable to molecular dimensions
gives a threshold perception.
A schematic of the ear is shown in Fig. 4-5. The conical eardrum at the inner end of the auditory

canal forms one side of the air-filled middle ear. The middle ear is vented to the upper throat behind
the nasal cavity by the Eustachian tube. The eardrum operates as an “acoustical suspension” system,
acting against the compliance of the trapped air in the middle ear. The Eustachian tube is suitably
small and constricted so as not to destroy this compliance. The round window separates the air-filled
middle ear from the practically incompressible fluid of the inner ear.

FIGURE 4-5 Idealized sketch of the human ear showing the uncoiled fluid-filled cochlea. Sound
entering the ear canal causes the eardrum to vibrate. This vibration is transmitted to the cochlea
through the mechanical linkage of the middle ear. The sound is analyzed through standing waves set
up on the basilar membrane.