Page 71 - The Master Handbook Of Acoustics

46 CHAPTER THREE

Ossicles

A

Eardrum Oval window
Eardrum B

80 Sq mm
1.3–3.1 to 1

1 3 Sq mm
oval window

FIGURE 3-4
(A) The ossicles (hammer, anvil, and stirrup) of the middle ear, which transmit mechan-
ical vibrations of the eardrum to the oval window of the cochlea. (B) A mechanical ana-
log of the impedance-matching function of the middle ear. The difference in area
between the eardrum and the oval window, coupled with the step-down mechanical link-
age, match the motion of the air-actuated eardrum to the fluid-loaded oval window.

ratio leverage ranging from 1.3:1 to 3.1:1. That is, the eardrum motion is
reduced by this amount at the oval window of the inner ear.
This is only part of this fascinating mechanical-impedance-match-
ing device. The area of the eardrum is about 80 sq mm, and the area of
the oval window is only 3 sq mm. Hence, a given force on the eardrum
is reduced in the ratio of 80/3, or about 27-fold.
In Fig. 3-4B, the action of the middle ear is likened to two pistons
with area ratios of 27:1 connected by an articulated connecting rod
having a lever arm ranging from 1.3:1 to 3.1:1, making a total mechan-
ical force increase of between 35 and 80 times. The acoustical imped-
ance ratio between air and water being on the order of 4,000:1, the
pressure ratio required to match two media would be 4,000 , or about
63.2, and we note that this falls within the 35 to 80 range obtained
from the mechanics of the middle ear illustrated in Fig. 3-4B.