|Physics of the
Ear and Hearing
The sense of hearing involves: -
The mechanical system that stimulates the hair cells in the cochlea.
The sensors that produce the action potentials in the auditory nerves.
The auditory cortex, the part of the brain that interprets the signals from the auditory nerves.
Deafness or hearing loss results if any of these parts malfunctions.
The ear is a cleverly designed converter of very weak mechanical waves in air into electrical pulses in the auditory nerve.
The ear is divided into three areas: -
The outer ear consists of the ear canal, which terminates at the eardrum (tympanic membrane).
The middle ear includes the three small bones (ossicles) and an opening to the mouth (Eustachian tube).
The inner ear consists of the fluid-filled, spiral-shaped cochlea containing the organ of Corti. Hair cells in the organ of Corti convert vibrations of sound waves hitting the eardrum into coded nerve pulses that inform the brain of these sound waves.
Figuer1: Anatomy of human ear
The outer ear
The outer ear does not refer, as you might think, to the visible part of the ear, which in medical jargon is called the external auricle or pinna. The outer ear is the external auditory canal, which terminates at the eardrum. The outer structure, or auricle, is the least important part of the hearing system; it aids only slightly in funneling sound waves into the canal and can be completely removed with no noticeable loss in hearing, although its removal will not help anyone's appearance. The external auditory canal, besides being a storage place for ear wax, serves to increase the ear's sensitivity in the region of 3000 to 4000 Hz. The canal is about 2.5cm long and the diameter of a pencil.
Figuer2: The outer ear
The eardrum, or tympanic membrane, is about 0.1mm thick (paper thin) and has an area of about 60mm2. It couples the vibrations in the air to the small bones in the middle ear. Because of the off-center attachment of the malleus, the eardrum does not vibrate symmetrically like a drumhead.
Figuer3: this figure illustration the eardrum vs Oval window area
However, it is clear that the actual movement of the eardrum is exceedingly small since it must be less than the movement of the air molecules in the sound wave. This movement at the threshold of hearing at 3000Hz is about 10-9cm. At the threshold of hearing at the lowest frequencies that we can hear (~20Hz), the motion of the eardrum may be as large as 10-5cm.It is possible for sound pressures above 160dB to rupture the eardrum. A ruptured eardrum normally heals just as other living tissue does.
The middle ear
The dominant features of the middle ear are the three small bones (ossicles). These bones are full adult size before birth. (The fetus can hear while it is still in the womb).
The ossicles play an important role in matching the impedance of the sound waves at the eardrum to the liquid-filled chambers of the inner ear. The ossicles are named after the objects they resemble: the malleus (hammer), the incus (anvil), and the stapes (stirrup). They are arranged so that they efficiently transmit vibrations from the eardrum to the inner ear. They transmit poorly vibrations in the skull-even the large vibrations from the vocal cords. You hear your own voice primarily by transmission of sound through the air. Try plugging both your ears and listen to the reduction in your sound volume.
Figuer4: A-The ossicles of the middle ear are the malleus (hammer), the incus (anvil), and the stapes (stirrup). B-The ossicles transmit vibrations from the eardrum to the inner ear.
The ossicles amplify the pressure of the sound waves at the entrance to the inner ear. The lever action of the ossicles is such that the motion of the plate of the stapes at the oval window of the inner ear is about 0.7 that of the malleus at the eardrum. Thus the lever action amplifies the force by a factor of about 1.3. A much larger gain in pressure is obtained by the piston action.