# How far does eardrum move?

Sound waves move human eardrum back and forth, like the peak to peak excursion of speaker driver, how much is it though? Ofcourse this movement depends on sound pressure, frequency and even location on eardrum, the edge moves less than center just like rubber surround around driver diaphragm.

I am interested in center of eardrum, the part of it that moves the furthest. The SPL is 100db at the eardrum and I would like to know how far it moves at 20 Hz and 20 KHz. I know this is hard question without specific answer becose every person have different eardrum but I believe there must be some rough average, some decent estimation about how much is it.

Is it micrometers? Is it nanometers? Or does it exceed 1 milimeter?

Tympanic displacement measurement (TMD) is a well studied field using hi-tech tools (i.e. stroboscopic holography), and complex units:
Vm = volume displacement in nl nanoLiters.
μm/pa (UDTF) = Linear tympanic membrane displacement is known as the umbo displacement transfer function.

The graph on the left gives you a value of 0.8-0.6 = 0.2 microns:

The graph above can be seen as resonances in an images sequence of stroboscopic holograms of tympanum (cool name to call your band) https://i.stack.imgur.com/fD6E9.jpg

According to this graph a 94dB sound wave gives you 0.1 micron displacement and a 100dB sine wave gives you 2pa, 0.2 microns. https://i.stack.imgur.com/O7nQL.jpg

The first research document on google gave me a volume displacement from -120 to -700 nl.

1000 nano Liter = 1mm3

So the TMD volume displacement when very loud can be 1-2mm3, and eardrum rupture probably occurs from 10 to 100 mm3.

There are even muscles in the ear that can modify the way that you hear, i.e. the stapedius muscle which protects against low fequencies, and perhaps which can focus your eardrum elasticity modulus to let hear different frequencies, perhaps conciously? fascinating, I don't know.

See also pages describing elastic measurement of the eardrum, energy transfer by the tympanum by the cone, through these two google search phrasings: "eardrum response measurement" and "tympanic membrane displacement measurement"

Here is research comparing the eardrum to microphone design which is written easily.

• This was best answer I ever got here on Stackexchange, the whole thing you wrote is treasure saturated with the juiciest most valuable information. I never knew this TMD field exist nor did I ever heard about stroboscopic holography, I will study these things passionately, big thanks com.prehensible. – wav scientist Dec 22 '18 at 12:47
• Cheers man, it's a very cool topic can do some YT videos from this kind of research. I design synthesizers so I am a fan of waves, sometimes on the DSP forums here. – aliential Dec 22 '18 at 19:45
• I want to ask just one very important extra question, is that 0.2 micron at 100db with or without the ear gain? I ask becose the ear canal and outer ear can boost frequency around 3 KHz by up to 20db, thats 10x the pressure. Was that 100db measured at the ear drum or somewhere else before the ear gain happened? Wasnt it some dead body test where they cut out the middle ear and the outer ear was gone? – wav scientist Dec 31 '18 at 16:30
• Yes for the dB graph: a uniform unit sound pressure was applied to the outer side of the tympanic membrane. springerplus.springeropen.com/articles/10.1186/2193-1801-2-527 – aliential Jan 4 '19 at 10:48