Take 15 minutes to prepare this exercise.
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A detailed solution is then proposed to you.
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To study the sound attenuation introduced by a wall, we adopt the following summary model :
In a pipe of cross section , a harmonic incident plane progressive sound wave of angular frequency arrives on a piston of surface , of thickness and of density , free to move around .
Note the speed of sound in air and density of air at rest.
It seeks the form of velocity field :
Justify these expressions and write the corresponding overpressures .
Write the boundary conditions on the non-deformable piston and deduce that :
Deduce the factor of transmittance in power of the wall.
We give :
What should be the minimum thickness of the wall if you want an attenuation of at least decibels for then for ?
The factor of transmittance in power of the wall here :
We wish attenuation (at least). Therefore, .
We obtain at and at .