TL;DR

Question about impedance matching in the middle ear

I was wondering if the middle ear's functions can be explained mostly by physics. So the sound waves (in the air) hit the tympanic membrane, which, through the three ear ossicles, is connected to the oval window (on the other side of this, there's fluid). The tympanic membrane has a larger surface area than the oval window, and since P=F/A, decreasing A increases the pressure. Here's my first question:
My textbooks say we're increasing the force (which we are but in a different, unrelated way*), but other sources online say we're increasing the pressure, which one is correct? Like, what is the quantity that I'm supposed to hold constant here?

Also, my textbook says while the force is increased, the amplitude is decreased at the oval window. This is the thing I'm having the most trouble with. It's been a long time since I've taken a physics class so I'm a bit rusty. Is it because, as we make the transition from air to liquid, we lose energy, so we lose amplitude? Or is there some other reason related to hydraulics, or something else?

*There is some force amplification by the 3 ear bones because they act as a lever.

DrBanana said:

My textbooks say we're increasing the force (which we are but in a different, unrelated way*), but other sources online say we're increasing the pressure, which one is correct? Like, what is the quantity that I'm supposed to hold constant here?

Also, my textbook says while the force is increased, the amplitude is decreased at the oval window.

Please cite your specific textbook(s) and online sources so we may also take a look.

renormalize said:

Please cite your specific textbook(s) and online sources so we may also take a look.

Textbooks:
1. Guyton and Hall Textbook of Medical Physiology, 14th edition:
"
“Impedance Matching” by the Ossicular System: The
amplitude of movement of the stapes faceplate with each
sound vibration is only three-fourths as much as the ampli-
tude of the handle of the malleus. Therefore, the ossicular
lever system does not increase the movement distance of
the stapes, as is commonly believed. Instead, the system ac-
tually reduces the distance but increases the force of move-
ment about 1.3 times. In addition, the surface area of the
tympanic membrane is about 55 square millimeters, where-
as the surface area of the stapes averages 3.2 square millim-
eters. This 17-fold difference times the 1.3-fold ratio of the
lever system causes about 22 times as much total force to be
exerted on the fluid of the cochlea as is exerted by the sound
waves against the tympanic membrane. Because fluid has
far greater inertia than air does, increased amounts of force
are necessary to cause vibration in the fluid. Therefore, the
tympanic membrane and ossicular system provide imped-
ance matching between the sound waves in air and the
sound vibrations in the fluid of the cochlea."

Online sources: https://www.scientificamerican.com/article/experts-how-do-the-hammer-anvil-a/

DrBanana said:

TL;DR: Question about impedance matching in the middle ear

The tympanic membrane has a larger surface area than the oval window, and since P=F/A, decreasing A increases the pressure. Here's my first question:
My textbooks say we're increasing the force (which we are but in a different, unrelated way*), but other sources online say we're increasing the pressure, which one is correct? Like, what is the quantity that I'm supposed to hold constant here?

It is assumed that for small hydraulic chambers, the pressure and its variation will remain the same everywhere within the chamber.

Hydraulics considers incompressible volumetric flow. The swept fluid volume, is proportional to the area of the piston-head, multiplied by the length of the stroke. For the same swept volume, a smaller area piston will have a longer stroke. That represents a change in impedance, length/force.

Baluncore said:

It is assumed that for small hydraulic chambers, the pressure and its variation will remain the same everywhere within the chamber.

Hydraulics considers incompressible volumetric flow. The swept fluid volume, is proportional to the area of the piston-head, multiplied by the length of the stroke. For the same swept volume, a smaller area piston will have a longer stroke. That represents a change in impedance, length/force.

The oval window has a smaller area, so it should have a longer stroke, so wouldn't that mean it should have a bigger amplitude?
Also, could you please expand on your last line a bit?

I have found that this channel does a good job of explaining things. I watched this particular video a couple of years ago and it was pretty good.