The tympanic membrane is the connective tissue between the external and middle auditory canal. It protects, and transport soundwaves, to the inner ear.
Human
In Human anatomy the tympanic membrane is also known as the eardrum.
Ferengi
In Ferengi anatomy the tympanic membrane is believed to perform the same function as it human counterpart. When it gets infected and left untreated for more then three weeks, Ferengi can die from it. A massive infection of the tympanic membrane is a chronic condition among Ferengi.
The infection itself is painful for a Ferengi and can cause dizziness. It can even cause a Ferengi to faint when treatment is postponed to long. Although some Ferengi have household remedies to treat the infection themselves, Rom tried one off Ishka's (his mother), but it did not work, medical attention is needed to cure it completely.
For Ferengi, the tympanic membrane can also be stimulated with the help of a feather. This is known as a Tympanic Tickle. When performed by an amateur the feather can get stuck and medical attention is needed to remove it. Antibiotic is needed to prevent infection of the membrane.