Log relationship between thickness of material and sound absorbed?

In summary, the relationship between the thickness of a material and sound absorption is generally direct; as the thickness of the material increases, its ability to absorb sound also improves. Thicker materials provide more mass and greater surface area, allowing them to dissipate sound energy more effectively. However, the specific frequency of sound and the material's composition also play significant roles in determining overall sound absorption performance.
  • #1
Marcogoodie
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TL;DR Summary
I did an experiement, and found a logarithmic relationship between sound energy absorbed and the amount of mateiral it propagates through. Why is there a logarithmic relationship between the thickness of material and sound absorbed by it?
So I have done an experiment on the amount of sound energy absorbed based on thickness of pvc foam, and found a logarithmic relationship between the two. I've used the frequency-dependent acoustic attenuation power law, which is derived from stokes' law.

Frequency-dependent acoustic attenuation power law:
https://en.wikipedia.org/wiki/Acoustic_attenuation#Power-law frequency-dependent_acoustic_attenuation

My hypothesis is that as sound waves propagate through material, initially, it can bump into more particles and sound waves can be converted into other forms of energy easily, but as the amount of waves decrease when it propagates through thicker material, the chances of it being converted into other forms of energy decrease. Is that correct?

Thanks in advance!
 
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  • #2
The energy loss, per unit length, is proportional to the energy propagating.
So the energy is reducing exponentially as it propagates.
What is the inverse of exponentiation?
 
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FAQ: Log relationship between thickness of material and sound absorbed?

What is the log relationship between thickness of material and sound absorption?

The log relationship indicates that as the thickness of a material increases, the sound absorption increases at a logarithmic rate. This means that doubling the thickness does not necessarily double the sound absorption; instead, the increase becomes less significant as the thickness grows, reflecting diminishing returns in sound absorption efficiency.

How does material type affect the log relationship in sound absorption?

Different materials have varying properties that affect sound absorption, such as density, porosity, and internal structure. While the log relationship generally holds, the specific sound absorption coefficients will vary by material, meaning that some materials may absorb sound more effectively than others at the same thickness.

Can the log relationship be applied to all types of sound frequencies?

No, the log relationship may not apply uniformly across all sound frequencies. Generally, lower frequencies require thicker materials for effective absorption, while higher frequencies can be absorbed more efficiently with thinner materials. Thus, the effectiveness of thickness in sound absorption can vary significantly depending on the frequency of the sound.

What measurements are typically used to quantify sound absorption?

Sound absorption is typically quantified using the sound absorption coefficient, which is measured in a controlled environment using standardized tests. This coefficient indicates the percentage of sound energy absorbed by a material compared to the total sound energy incident on it. The relationship between thickness and the sound absorption coefficient can be analyzed to understand the log relationship better.

How can this log relationship be practically applied in acoustic design?

In acoustic design, understanding the log relationship allows engineers and architects to make informed decisions about material selection and thickness for soundproofing or noise control. By knowing how much sound absorption can be achieved with a given thickness, designers can optimize material use and ensure effective sound management in spaces such as recording studios, theaters, and offices.

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