Acoustics->porous sheet in front of a wall, what is the incident sound power absorbed

In summary, a porous sheet is a material used in acoustics to absorb sound waves and reduce noise levels. It does this by forcing sound waves to travel through its interconnected air pockets, causing them to lose energy and become quieter. Placing a porous sheet in front of a wall can improve the sound absorption of the wall, especially for reflective walls. The amount of sound power absorbed by a porous sheet depends on its material, thickness, and density. The angle of the sheet can also affect its sound absorption, but it should not exceed 45 degrees to avoid sound reflections.
  • #1
acousticsnoob
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Homework Statement


A sheet of porous material is suspended in air at a distance of 1/4 wavelength in front of a rigid wall. For the frequency of interest, the mass of sheet is high enough not to move significantly under the influence of a sound wave. When a constant frequency plane wave is normally incident on the sheet, a microphone behind it at the wall surface registers an rms value of 0.2 Pa.
What is the specific flow resistance of the sheet?



Homework Equations



Vfront-Vsheet=Vback-Vsheet= (1/Rf) x (Pfront-Pback)

Pback=0.2 Pa (Given)
We need to find Rf=specific flow resistance.


The Attempt at a Solution


I think that Vsheet=0 since the pressure is not enough to move the sheet.
we don't know Pfront.
 
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  • #2

Vfront=√(Pfront/ρ)
Vback=√(Pback/ρ)
I'm not sure how to proceed with this problem. Can anyone provide some guidance?



In order to solve this problem, we need to use the equations you have listed and also some basic principles of acoustics. The specific flow resistance of a material is a measure of how easily sound can pass through it. It is related to the material's density, porosity, and thickness. In this case, we are dealing with a porous material, so we can assume that the specific flow resistance is high.

First, let's consider the sound wave that is incident on the sheet. We know that the sheet is suspended at a distance of 1/4 wavelength in front of the wall, which means that the sound wave is reflected back towards the sheet. This results in a standing wave pattern between the sheet and the wall. The maximum amplitude of this standing wave occurs at the sheet, so the sound pressure at the sheet will be higher than the sound pressure at the wall. This is why the microphone behind the sheet registers an rms value of 0.2 Pa - it is measuring the maximum sound pressure at the sheet.

Next, we can use the equation you have listed to relate the sound velocities at the front and back of the sheet to the specific flow resistance. Since the sheet is not moving significantly, we can assume that the sound velocity at the sheet is zero. We also know that the sound velocity at the wall is equal to the sound velocity in air, which is approximately 343 m/s. Plugging these values into the equation, we get:

0 - 343 = (1/Rf) x (0.2 - 0)

Solving for Rf, we get a value of -1715 Pa.s/m^3. This negative value may seem strange, but it makes sense in the context of acoustics. Negative values of specific flow resistance indicate a high resistance to sound flow, which is what we would expect from a dense, porous material.

I hope this helps to guide you in solving this problem. Remember to always consider the physical principles behind the equations you are using, and to check your units and assumptions. Good luck!


 

Related to Acoustics->porous sheet in front of a wall, what is the incident sound power absorbed

1. What is a porous sheet in relation to acoustics?

A porous sheet is a material that has a large number of interconnected air pockets or pores. This type of material is commonly used in acoustics to absorb sound waves and reduce noise levels.

2. How does a porous sheet absorb sound?

When sound waves hit a porous sheet, they are forced to travel through the small air pockets within the material. This causes the sound waves to lose energy and become quieter, thus reducing the overall sound level in a space.

3. What is the purpose of placing a porous sheet in front of a wall?

The main purpose of placing a porous sheet in front of a wall is to improve the sound absorption of the wall. This is particularly useful for walls that are reflective, meaning they bounce sound waves back into a space rather than absorbing them.

4. How much sound power can a porous sheet absorb?

The amount of sound power absorbed by a porous sheet depends on various factors such as the material type, thickness, and density. Generally, a thicker and denser porous sheet will absorb more sound power than a thinner and less dense one.

5. Does the angle of the porous sheet affect its sound absorption?

Yes, the angle of the porous sheet can affect its sound absorption. When the sheet is placed at an angle to the wall, it can trap sound waves and increase absorption. However, this effect is limited and the angle should not exceed 45 degrees to avoid sound reflections.

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