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I honestly can't come up with anything that makes sense, because obviously, energy cannot be created nor destroyed.

I think the question is pretty self-explanatory, so there isn't much to say here.

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After amplification (more sound wave!) by outer hair cells in your ear, the sound wave ends up moving the flimsy bits of inner hair cells, a sensory input of your inner ear, expending some energy in the process. The rest of the energy in the sound waves also gets converted into something else, namely heat as it interacts with various parts of your ear.

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The ear picks up only a tiny fraction of the energy in a sound wave, but does so very effectively because of the acoustic arching mechanisms in the inner ear. The sound energy (pressure) is converted into motion of cells, and thence into heat. The amount of heat is miniscule: the sound level in a "quiet" room might be around 40 dB which corresponds to an energy level of $10^{-8} J/m^2$ of which only a tiny fraction ends up in the ear. The limit of hearing is even lower.

So the short answer is "heat". Or entropy, if you prefer.

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The sound waves die down.

Obviously, the sound waves, which cause a hearing sensation in our ears, cause physical movement of the eardrum and the like.

but I honestly can't come up with anything that makes sense, because obviously, energy cannot be created nor destroyed.

Don't worry, energy is NOT being destroyed here, it is just being transferred from the sound wave to the ear, and that is exactly why you have a hearing perception. It will continue to transfer its own energy until its energy is zero.

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Obviously, the sound waves, which cause a hearing sensation in our ears, cause physical movement of the eardrum and the like. A ‘wavy movement’ is observed on the basilar membrane, with a short wavelength, with which in combination with the accompanying vibration frequency by means of the equation [propagation velocity = frequency × wavelength] an extreme low propagation velocity result for mechanical vibrations in the cochlea.

Based on the fact that the propagation velocity for mechanical vibrations and waves – and hence also for acoustical vibrations – is a physics quality that is bound to the medium [solid, liquid or gas] in which that propagation is taking place, this means that there cannot exist an active transmission line inside the cochlear duct, and that there cannot propagate a traveling wave inside the cochlear duct with extreme small wavelength that transports vibration energy. Neither forwards nor backwards.

Because of that, the propagation velocity of the mechanical vibration is the – by the medium involved and bounded – decisive quantity for the relation that will exist between the frequency and the wavelength in the follow-up. And not vice-versa.

What will remain inside the cochlear partition is the hydrodynamic stimulus introduction in the cochlea in the form of the sound energy signal (the perilymph velocity distribution and the perilymph pressure distribution), a noticeable pressure in front of the basilar membrane, activating the motion of that basilar membrane by the non-stationary Bernoulli effect.

Calculation of the perilymph velocity and the evoked pressure in the cochlear partition can be observed as the numerical confirmation for the analytical solution for the non-stationary Bernoulli equation.

The latter is based on the following conditions: the scala tympani and the scala vestibuli can be regarded as a tube filled with perilymph; an incompressible fluid of low viscosity. This fluid flows back and forth periodically, along a short trajectory that is aligned with the core direction of the tube.

The Reynolds number in the fluid is far below the threshold for turbulent flow conditions; hence the flow will be laminar. When we depart from the generally valid Navier-Stokes equation for hydrodynamic behavior, it follows that the above mentioned restrictive conditions allow us, without further restriction, to reduce the complexity of the Navier-Stokes equation to the non-stationary Bernoulli equation.

Without creating any additional errors the spiraled cochlear partition can be unrolled and the hydrodynamic problem to be solved can be observed as a one-dimensional flow, hence free of rotation. That means it can be seen as a periodic potential flow in which the fluid velocity is the gradient of a so-called velocity-potential. The fluid velocity distribution will be a solution of Laplace’s equation for the velocity-potential. And the solution of the non-stationary Bernoulli equation in this case results in the typical Bernoulli relation between the pressure change in the fluid and the fluid velocity.

And if all this analytical model for perilymph movement in the cochlear duct, where the non-stationary Bernoulli effect results as the solution, will be correct then it leads to the uniform conclusion that inside the cochlea the sound pressure signal, evoked in the outer ear channel, will be transferred into the sound energy stimulus. And that this stimulus is responsible for the activation of the basilar membrane and for the signal to the brain.

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protected by Qmechanic Mar 28 '15 at 21:50

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