I am currently trying to explain the reasons for my sound transmission loss for my material selection and design. I am using polymers of different depths and currently in my model I'm considering acoustic impadence(reflection and loss(absorption) to understand transmission. First of all please let me know if there is any other effect that I need to consider. Secondly I have only access to loss factor of materials but "Stokes's law of sound attenuation" works with "dynamic viscosity coefficient". I'd appreciate if someone can tell me how can I relate the loss factor of material($\tan(\delta))$ to attenuation of sound.
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You mentioned that you have the loss factor $ \text{tan}(\delta) $ for your material, but Stokes’s law requires the dynamic viscosity. The loss factor is closely tied to how much energy a material loses as heat due to internal friction when it deforms. This is important because it helps us understand how sound waves lose energy as they pass through a material.
The loss factor $ \text{tan}(\delta) $ measures the ratio of the energy lost to the energy stored during each cycle of deformation — essentially, it's a measure of the material's damping ability. In viscoelastic materials, the dynamic viscosity $ \eta $ that appears in Stokes’s law describes how effectively the material can dissipate sound energy through internal friction.
The attenuation coefficient $ \alpha $, which quantifies how much sound is absorbed by the material, is proportional to both the loss factor $ \text{tan}(\delta) $ and the frequency $ f $ of the sound wave: $$ \alpha \propto \text{tan}(\delta) \cdot f. $$ This shows that higher damping (or a higher loss factor) leads to more sound attenuation.
If you also have access to the material's storage modulus $ E' $ and loss modulus $ E'' $, you can connect them to the loss factor by the relationship: $$ \text{tan}(\delta) = \frac{E''}{E'}. $$ From this, you can estimate the attenuation coefficient $ \alpha $ as: $$ \alpha \approx \frac{\omega \, \text{tan}(\delta)}{c}, $$ where $ \omega $ is the angular frequency of the sound and $ c $ is the speed of sound in the material.
If you don’t have direct information on the dynamic viscosity, you might still be able to estimate it by looking at the relationships between the material's modulus, density, and damping properties, based on how the material behaves at different frequencies.
If you need any clarfication please ask
