Question

i) Imagine that sound is incident directly on the fluid(electrolyte in the inner ear. Calculate the percentage of the sound energy that is reflected and the percentage that is transmitted into the fluid. ii) how is the human ear structured to overcome this impedance mismatch problem?

Answer 1

99.9% sound is reflected due to high impedance of fluid in the cochlea (0.1% sound is only passed = - 30 dB sound loss from air - fluid impedance mismatch) Middle ear bones overcome the loss of sound by increasing sound pressure (+34dB)=> Impedance matching

Here we have three middle bones again. The arm of the malleus is attached to the eardrum, and the footplate of the stapes is attached to the oval window of the cochlea (inner ear). What they are doing is they transmit vibrations of the eardrum into the cochlea. But here we have a problem. Because the impedance of air and impedance of liquid is really different.Impedance in the liquid is much bigger than that of air.

We can think of an example. Let's say we are in a swimming pool. And we are under water in a swimming pool. And then we cannot hear well the speech of outside even though the voice is loud. Try it later at the gym. That is because the impedance of liquid is so high, most of sound is reflected when the sound hits the water. And 99.9%, most of sound is lost. In other words, only 0.1% of power is passed.

That sound loss gives us -30dB sound level loss just because of impedance mismatch between air and liquid. But fortunately our middle ear bones overcome that sound loss. The process is called impedance matching because they are matching, making up that loss.

Three mechanisms for impedance matching

1. Area ratio of the ear drum to the stapes footplate (20:1) => 20 log (20/1) = +26dB SPL * Basic concept: p = f/a
2. Lever action of the ossicles (1.3:1) => 20 log(1.3/1) = +2 dB SPL
3. Buckling of ear drum ( x 2 pressure increase => 20 log(2/1) = +6dB SPL

What they are doing is they are amplifying sound level to overcome mismatched impedance. It can work due to their physical structure.

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