Equation of a sound wave with viscous damping in ideal gas

[Tahmeed]

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.

 

[Arjan82]

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.

 

[Tahmeed]

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

 

[Frabjous]

Here is something that might give you a couple of ideas to play with.



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

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