What affects the speed of sound - does viscosity?

Main Question or Discussion Point

What factors affect the speed of sound besides the temperature? Does viscosity affect the speed of sound?

Thanks

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Bobbywhy
Gold Member

http://en.wikipedia.org/wiki/Speed_of_sound

There you will find a fairly well-written explanation of the factors affecting the speed of sound in air.

Viscosity is normally not considered to be a characteristic of gasses like air. Usually it is applied to liquids. Therefore, you would need to research "speed of sound in water" for example.

yes. I cant find viscosity anywhere. that is the parameter I was wondering. I was just wondering if there was any less obvious parameters...

Yes, many things can effect the speed of sound, temperature, humidity ect..
As BobbyWhy stated, viscosity isn't really thought of, but yes it drastically effects the speed of sound. Temperature of the medium also has an effect . Sound permeates through hot water slower then it does through cold water because the molecules in hot water are agitated more so than their counterparts in cooler water, thus causing a small (small!) amount of resistance. Hope this helps!

Bobbywhy
Gold Member

What factors affect the speed of sound besides the temperature? Does viscosity affect the speed of sound?

Thanks
lavster, Yes, viscosity does affect the speed of sound in fluids. Here are some websites that may illuminate the mechanism:

Just to be sure we all use accepted terms, I post these two Wikipedia excerpts:
“Viscosity is a measure of the resistance of a fluid which is being deformed by either shear stress or tensile stress. In everyday terms (and for fluids only), viscosity is "thickness" or "internal friction". Thus, water is "thin", having a lower viscosity, while honey is "thick", having a higher viscosity. Put simply, the less viscous the fluid is, the greater its ease of movement (fluidity).[1]
Kinematic viscosity
In many situations, we are concerned with the ratio of the inertial force to the viscous force (i.e. the Reynolds number, ), the former characterized by the fluid density ρ. This ratio is characterized by the kinematic viscosity (Greek letter nu, ν), defined as follows:

The SI unit of ν is m2/s. The SI unit of ρ is kg/m3.
The cgs physical unit for kinematic viscosity is the stokes (St), named after George Gabriel Stokes. It is sometimes expressed in terms of centistokes (cSt). In U.S. usage, stoke is sometimes used as the singular form.
1 St = 1 cm2•s−1 = 10−4 m2•s−1.
1 cSt = 1 mm2•s−1 = 10−6m2•s−1.
Water at 20 °C has a kinematic viscosity of about 1 cSt.

The kinematic viscosity is sometimes referred to as diffusivity of momentum, because it is analogous to diffusivity of heat and diffusivity of mass. It is therefore used in dimensionless numbers which compare the ratio of the diffusivities.”
http://en.wikipedia.org/wiki/Viscosity#Kinematic_viscosity

"Volume viscosity (also called bulk viscosity or second viscosity) becomes important only for such effects where fluid compressibility is essential. Examples would include shock waves and sound propagation."
http://en.wikipedia.org/wiki/Volume_viscosity

“The speed of sound in air and other gases, liquids, and solids is predictable from their density and elastic properties of the media (bulk modulus).
The bulk modulus of a solid influences the speed of sound and other mechanical waves in the material.”
http://hyperphysics.phy-astr.gsu.edu/hbase/sound/souspe2.html

Just as is shown by the above, the speed of sound in fluids (gasses and liquids) is dependent on density and bulk modulus (Hooke's Law). The bulk modulus of a substance measures the substance's resistance to uniform compression.

Now, this appears in Encyclopedia Britannica:
“...(in the direction of the wave) is a combination of a uniform compression and a shearing stress (a force that causes one plane of a substance to glide past an adjacent plane). Hence, both bulk and shear viscosity also govern the propagation of sound in a liquid.”
http://www.britannica.com/EBchecked/topic/124117/coefficient-of-viscosity

In order to read that article one needs to join and pay. This is frustrating to say the least. I hesitate to pay just to learn some basic science.

This article clearly states that viscosity does affect the sound velocity in liquids:
S Parthasarathy and N N Bakhshi 1953 Proc. Phys. Soc. B 66 368 doi:10.1088/0370-1301/66/5/303
“Relation between Velocity of Sound and Viscosity in Liquids”
Abstract:
A new relationship, viz. v1/3/ρ = A + B/η1/2, between sound velocity v, viscosity η and density ρ of a liquid, has been obtained. It is observed that A is a constant (=13.56) for all the homologous series considered, whereas B is different for different series. A plot of v1/3/ρ against 1/η1/2 gives a set of straight lines diverging from the same point on the y-axis (0, 13.56)."
http://iopscience.iop.org/0370-1301/66/5/303

"Longitudinal rheology. Bulk Viscosity and Longitudinal Viscosity
Propagation of a longitudinal stress wave through a visco-elastic media creates dissipation of mechanical energy, similarly to a shear stress wave. The rate of dissipation depends on two parameters: bulk viscosity and longitudinal viscosity. For Newtonian liquid it is bulk viscosity that is analog to the dynamic viscosity for the shear stress. For non-Newtonian liquid it is longitudinal viscosity, analog to the shear viscosity for the shear rheology.
Measurement of ultrasound attenuation is the only known way of characterizing these parameters for both Newtonian and non-Newtonian liquids. Our Acoustic sensor allows very precise measurement of the ultrasound attenuation. It is important to perform this measurement at different frequencies. Frequency dependences allow resolving between bulk viscosity and longitudinal viscosity.
Dukhin, A.S. and Goetz, P.J. " Bulk viscosity and compressibility measurement using acoustic spectroscopy," The Journal of Chemical Physics, Vol.130, Issue 12, (2009)"
http://www.dispersion.com/bulk-viscosity.html

Sound Speed and Kinematic Viscosity Table

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AlephZero
Homework Helper

yes. I cant find viscosity anywhere.
You can't change the viscosity of a fluid indepedently of other parameters, the same way you can change parameters like temperature, pressure, or denisty (for compressible fluids). The way viscosity varies with say temperature is wildly different for different fluiids. That fact doesn't suggest it is going to be a very useful predictor of sound velocity.

For any practical purposes that I know of, the formula in terms of bulk modulus and density is adequate, and that formula can be easily derived using Newtonian mechanics without the need for any more assumptions about the fluid behaviour.

In post #5, the quote from Parthasarathy and Bakhshi only "clearly states that viscosity does affect the sound velocity in liquids" in the sense that they have produced a formula that replaces one parameter (bulk modulus) by another one (viscosity), and they state their formula only holds for homologous series of compounds (though the abstract doesn't way what particular homologous series they measured). Since their formula contains two constants that apparently depend on the particular series, this looks more like an exercise in curve fitting than fundamental physics IMO. There is nothing surprising in the fact that for a homologous series of compounds (i.e. a seriies of compouds with similar chemical structures, for example methane, ethane, pentane, hexane, etc), there are "simple" relations between different physical parameters. Presumably somebody was interested in this in 1953, but the abstract quoted doesn't seem to give any motiation for doing the work.

The quote from Dukhin, and Goetz says nothing about sound velocity, only about using energy dissipation as a way to measure viscosity.

Bobbywhy
Gold Member

AlephZero,
Thank you for your clarifications and explanations. Although I posted all those things about viscosity, I was never sure of their meaning.

During many years of sonar work I never heard of anyone using the viscosity of seawater to predict the sound speed.

Cheers,
Bobbywhy

Physicist50
Gold Member

What effects the speed of sound other than temperature and viscosity, is the thickness of the medium it's traveling through. For example, sound travels approximately 4.3 times faster through water than air. The second factor that affects a sound wave's speed is pitch. Apparently, the higher the pitch, the faster the speed of sound. Pitch is determined by how bunched up the waves are, and therefore, the more bunched up they are, they must be traveling much faster to complete the track of waves.

What effects the speed of sound other than temperature and viscosity, is the thickness of the medium it's traveling through. For example, sound travels approximately 4.3 times faster through water than air. The second factor that affects a sound wave's speed is pitch. Apparently, the higher the pitch, the faster the speed of sound. Pitch is determined by how bunched up the waves are, and therefore, the more bunched up they are, they must be traveling much faster to complete the track of waves.
I am not sure what you mean by "thickness" but your post is quite confusing and misleading.

The speed of sound depends on the density of the medium and its elastic properties.
The dependence on density is inverse, increased density results in decreased speed, for the same elasticity.

The speed may depend on frequency (see dispersion) but is not due to "bunched waves" whatever that means. In most common media (water and air included) the dispersion is quite negligible.

Ive just noticed all these posts - thank you! (sorry for the delay!)

Physicist50
Gold Member
I am not sure what you mean by "thickness" but your post is quite confusing and misleading.

The speed of sound depends on the density of the medium and its elastic properties.

The dependence on density is inverse, increased density results in decreased speed, for the same elasticity.

The speed may depend on frequency (see dispersion) but is not due to "bunched waves" whatever that means. In most common media (water and air included) the dispersion is quite negligible.

Sorry, you're right, I was absolutely exhausted when I wrote my previous post, by thickness I meant density, thanks nasu. And as for bunched up waves, well, forget that, I was referring to diagrams and the way the sound waves are pictured as tighter together the higher the pitch. Good question lavster!

Chestermiller
Mentor
Viscosity is normally not considered to be a characteristic of gasses like air.
This is not correct. Try calculating the pressure drop of air flowing through a capillary or through a porous medium without using its viscosity.

Bobbywhy
Gold Member
This is not correct. Try calculating the pressure drop of air flowing through a capillary or through a porous medium without using its viscosity.
You are quite correct! I'd not considered that scenario. Thank you for your attention to detail!

Bobbywhy