# Speed of sound: viscosity dependece in liquids and solids

• phixmin
In summary, there is no direct formula that relates the viscosity of liquids and solids to the speed of sound.

#### phixmin

Hello,

Wikipedia gave me prior hints as to how the speed of sound depends on viscosity but after searching on Google scholar and Google, I have yet to find any direct equations/findings that give a direct relationship of the speed of sound to the visocisty of fluids and solids outside of: http://iopscience.iop.org/article/10.1088/0370-1301/66/5/303/pdf

My question: does anyone know how the speed of sound depends on the viscosity of liquids and solids? Are there any known formulas?

phixmin said:
Wikipedia gave me prior hints as to how the speed of sound depends on viscosity...
What article? From what I see, no form of the word "viscosity" appears in the wiki article on the speed of sound:
https://en.m.wikipedia.org/wiki/Speed_of_sound

russ_watters
russ_watters said:
What article? From what I see, no form of the word "viscosity" appears in the wiki article on the speed of sound:
https://en.m.wikipedia.org/wiki/Speed_of_sound
I didn't state that it was from the speed of sound wiki.

Lord Jestocost said:

Yep I already saw this post but it is only for liquids not for solids.

mk9898 said:
Yep I already saw this post but it is only for liquids not for solids.

Huh? Viscosity is a term we use only for fluids, not solids.

Questionable Thought and Lord Jestocost
mk9898 said:
I didn't state that it was from the speed of sound wiki.
No, you didn't. So why don't you help us stop guessing and provide your source!

Further, the fact that it isn't in a relevant article should tell you something.

That linked PF thread is full of some extreme nonsense. Sound speed is not generally considered to have a direct relationship with viscosity.

Hm then what does the speed of sound depend on when the sound moves with longitudinal waves through solids?

Most commonly the bulk modulus (Young's modulus, for a solid) and density. Viscosity isn't even a quantity that makes sense for a solid.

Questionable Thought
mk9898 said:
Hm then what does the speed of sound depend on when the sound moves with longitudinal waves through solids?
This is fully covered in the wiki I linked: elasticity(several ways to describe: "bulk modulus" or "young's modulus" for solids) and density.

You are all totally right with the viscosity...don't know what I was thinking there. Just a mistake Russ ;).

So for liquids boneh3ad, since the other post has things that are nonsense in it, would you or anyone know if there is a direct formula with the viscosity being a part of determining the speed of sound? The comment by Lord J with the paper helps but I'm surprised that the only two papers that I now know of are 50-60 years old.

For solids, is there also a general formula for the speed of sound through solids?

mk9898 said:
You are all totally right with the viscosity...don't know what I was thinking there. Just a mistake Russ ;).

So for liquids boneh3ad, since the other post has things that are nonsense in it, would you or anyone know if there is a direct formula with the viscosity being a part of determining the speed of sound? The comment by Lord J with the paper helps but I'm surprised that the only two papers that I now know of are 50-60 years old.

For solids, is there also a general formula for the speed of sound through solids?
The answer remains: no, viscosity is not a generally accepted factor in the speed of sound in liquids. And the linked wikipedia article still contains all the answers to your questions.

I'm going to lock the thread now since the questions have been fully answered and I don't want it to continue going around in circles. Thanks everyone.

anorlunda and davenn