Equation of a sound wave with viscous damping in ideal gas

AI Thread Summary
The discussion focuses on deriving a non-differential equation for a 1D sound wave in an ideal gas with viscosity, specifically seeking a simple exponential-sinusoidal function to represent damping in harmonic oscillation. Participants note that there may not be a straightforward solution and suggest exploring the viscous Burgers' equation, which is typically associated with fluid flow rather than sound waves. There is a consensus that the Burgers' equation relates to nonlinear waves in acoustics, but it may not directly address the desired wave equation for sound damping. The conversation emphasizes the complexity of modeling sound wave energy loss as it propagates through different layers. Overall, the challenge lies in accurately representing the damping effects on sound waves in a viscous medium.
Tahmeed
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How can we find a equation of a 1D sound wave in a non-differential form in an ideal gas with viscosity? How does the damping work? How does the wave lose energy at each layer as it propagates?

To be clear I am looking for a simple exponential-sinusoidal function for it just in the case of damping in simple harmonic oscillation. If possible it will be great to have an energy analysis too about which layer receives how much of the lost energy.
 
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Maybe you are looking for the solution to the (viscous) Burgers's equation, as stated in this wikipedia article.

I'm afraid that there is no simple solution.
 
Arjan82 said:
Maybe you are looking for the solution to the (viscous) Burgers's equation, as stated in this wikipedia article.

I'm afraid that there is no simple solution.

I don't think that's what I want. This Burger's equation is for fluid flow, it's not something similar to wave equation. I am looking for a wave equation that describes damping of sound wave in an ideal gas
 
Here is something that might give you a couple of ideas to play with.

1of3.png2of3.png3of3.png

From Vibrating Strings by D.R. Bland (1960)

Btw, the Burger’s equation is used for nonlinear waves in acoustics.
 
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