The basilar membrane of a model cochlea is 35 mm long…
Contributed by StemPy LabTry it on paper first. A hint, the key idea and the worked solution are here when you need them.
The basilar membrane of a model cochlea is mm long. A tone of frequency in hertz peaks at a distance millimetres from the apex. This is the Greenwood function, a standard model.
- Where does a tone of Hz peak, measured from the apex?
- Where does a tone of Hz peak, measured from the apex?
- How far apart are the two peaks?
Need a reminder? The key ideaShow
Sound goes from the pinna and the canal to the ear drum, then through the malleus, incus and stapes to the oval window. Then it goes through the cochlear fluid to the basilar membrane and the hair cells of the organ of Corti. The auditory nerve takes the impulses to the brain. Pressure is force divided by area, and a gain in decibels is of the pressure ratio.
The worked solution
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Given. Length: mm. Hz and Hz.
Plan. Use the formula twice, then subtract.
Step 1. For 440 Hz. . . mm.
Step 2. For 4000 Hz. . . mm.
Step 3. The distance. mm, using the unrounded values .
Answer: mm; mm; mm.
Check. The higher tone peaks farther from the apex, which means nearer to the base.
Watch out. The distance is from the apex. The distance from the base is .
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