Waves and how temperature affects their velocity in water

[shmurr]

Is the velocity of water waves created in a container affected by the temperature of water. How?

 

[Bobbywhy]

shmurr,

Temperature is not a variable in calculating water wave speed. The “wave speed” (more precisely, “phase velocity”) of periodic progressive surface waves travel is determined by the acceleration of gravity, wave depth (or upper layer depth), the density of water and the density of air.

Cheers, Bobbywhy

 

[HallsofIvy]

Note that the "density of air", and to a much lesser extent, "density of water", may be affected by temperature.

 

[shmurr]

Ok, so I know that increasing the temperature decreases the density of water. Would water waves behave the same way as sound and travel faster, if by only a small amount, in warmer water?

 

[Bobbywhy]

shmurr,

Surface waves on a fluid such as water do not obey the same laws that govern sound waves in water, so it’s not correct to assume they are affected by the same variables, in this case, temperature.

In this Wiki entry there is no mention of temperature affecting the phase velocity (also called “celerity” or “phase speed”):
http://en.wikipedia.org/wiki/Dispersion_(water_waves )

In this document, where the fluid layer has a uniform mean depth, and the fluid flow is inviscid, incompressible, and irrotational there no mention of temperature affecting the celerity (wave speed):
http://en.wikipedia.org/wiki/Airy_wave_theory

In this document there is no mention of fluid temperature affecting the surface wave speed, either for shallow water waves or deep water waves:
http://www.dogpile.com/info.dogpl.t6.2/search/web?fcoid=417&fcop=topnav&fpid=27&q=speed+of+water+waves&ql

In this document there is no indication that surface wave speed (celerity) is affected by temperature:
http://hyperphysics.phy-astr.gsu.edu/hbase/watwav.html#c3

There is no mention of temperature changing the speed of surface wave speeds in this entry:
http://van.physics.illinois.edu/qa/listing.php?id=2223

Yes, temperature does affect the speed of sound in water.
“The speed of sound in water increases with increasing water temperature, increasing salinity and increasing pressure (depth). The approximate change in the speed of sound with a change in each property is:
Temperature 1°C = 4.0 m/s
Salinity 1PSU = 1.4 m/s
Depth (pressure) 1km = 17 m/s”
http://www.dosits.org/science/soundmovement/speedofsound/

Cheers, Bobbywhy

 

[shmurr]

Thanks for those links, it makes a lot more sense.
Another question on the same topic, how and why do waves in water behave differently than sound waves other than one is longitudinal and the other is transverse.

 

[Bobbywhy]

shmurr,

There is a tradition here on Physics Forums against “spoon feeding” questioners. Will you please first use the Google Search terms “transverse waves longitudinal waves difference between” and then read and study some of those results to discover the answers to your question? After that “self-study” if you have any doubts or specific questions, do come back here and post them. Members here on Physics forums are always ready and willing to assist any true searcher who is interested in advancing her knowledge of science, and, one who has first done her homework!

Cheers, Bobbywhy

 

[olivermsun]

Surface waves on a fluid such as water do not obey the same laws that govern sound waves in water, so it’s not correct to assume they are affected by the same variables, in this case, temperature.

In this Wiki entry there is no mention of temperature affecting the phase velocity (also called “celerity” or “phase speed”):
http://en.wikipedia.org/wiki/Dispersion_(water_waves )

Actually if you look at the phase velocity, $c$, for shallow water waves:

you will notice that there is a dependency on $h$. So if you take the same container of water and heat it so that the water expands, you might imagine that $h$ increases and therefore $c$ does as well.

But, as HallsofIvy alludes to above, that should be a very small increase.

 

[snorkack]

You have changes in the depth of water, density of water... but is the speed of water waves also heavily influenced by the changes in the surface tension of water?

 

[olivermsun]

...is the speed of water waves also heavily influenced by the changes in the surface tension of water?

I suppose there must be an effect as well on the very short-wavelength capillary waves due to the change in [url="http://en.wikipedia.org/wiki/Surface_tension]surface tension[/url] with temperature!

 

[Bobbywhy]

Surface waves on water may be divided into several regimes. The familiar waves on lakes and oceans, with wavelengths ranging from hundreds of meters to a few centimeters, are called gravity waves. As the name implies the dominant restoring force is gravity, which returns the disturbed surface of the water to equilibrium.
http://en.wikipedia.org/wiki/Gravity_wave

According to linear theory for waves forced by gravity, the phase velocity depends on the wavelength and the water depth. For a fixed water depth, long waves (with large wavelength) propagate faster than shorter waves. The phase velocity of an approximately sinusoidal wave is proportional to the square root of the wavelength. These are the waves described in the five examples given in post number five on March tenth that showed no effect of temperature change on phase velocity.

Waves with intermediate wavelengths are known as gravity-capillary waves. In these waves gravity and surface tension play comparable roles. The phase velocity of a gravity–capillary wave on a fluid interface is influenced by the effects of gravity, surface tension, density, and by fluid inertia. Since surface tension and density are affected by temperature, the phase velocity begins to become slightly affected by changes in temperature.
http://en.wikipedia.org/wiki/Wind_wave#Types_of_wind_waves

Waves with wavelengths of a few millimeters and less are known as capillary waves. In this regime the dominant restoring force is the surface tension, which tends to minimize the surface area by smoothing out any wrinkles while gravity plays only a minor role. For very short wavelengths – two millimeters in case of the interface between air and water – gravity effects are negligible.
http://en.wikipedia.org/wiki/Wind_wave#Types_of_wind_waves

The phase velocity of capillary waves of infinitesimal amplitude depends on the wavelength and surface tension. Phase velocity increases when the wavelength becomes shorter. The dispersion data is temperature dependent because both surface tension and density are functions of temperature.
http://en.wikipedia.org/wiki/Airy_wave_theory
http://en.wikipedia.org/wiki/Surface_tension#Influence_of_temperature

“The Bond number is a measure of the importance of surface tension forces compared to body forces. A high Bond number indicates that the system is relatively unaffected by surface tension effects; a low number (typically less than one is the requirement) indicates that surface tension dominates. Intermediate numbers indicate a non-trivial balance between the two effects.”
http://en.wikipedia.org/wiki/Bond_number

“Steep gravity waves on the water surface with wavelengths less than 0.5 m can generate short gravity-capillary waves near their crests, which then propagate along the steep forward wave slopes. Since they do not propagate with their own phase velocity but with the (higher) phase velocity of the generating (parent) wave, they are called bound or parasitic waves. Their generation is linked to the fact that large-amplitude gravity waves have non-sinusoidal profiles and thus contain higher order harmonics. These harmonics are bound waves which, in general, do not obey the dispersion relation for free gravity-capillary waves. They propagate with the phase velocity of the 0th-order (parent) wave and since the phase velocity of these parent gravity waves is higher than the minimum phase velocity of water waves, some high-order harmonics may satisfy the dispersion relation for gravity capillary waves. The higher order harmonics are identical to free surface waves traveling at their intrinsic phase and group velocity, and they form a wave packet moving along the steep gravity wave profile.”
http://www.ifm.zmaw.de/research/rem...e-lab/bound-and-free-gravity-capillary-waves/

Here are a few general references:
http://en.wikipedia.org/wiki/Water_(data_page )
http://www.student.math.uwaterloo.ca/~amat361/Fluid%20Mechanics/topics/gravity_waves.htm
http://www.seafriends.org.nz/oceano/waves.htm
“Capillary Waves Understood by an Elementary Method” Kern E. Kenyon, J. of Oceanography, Vol. 54, pp 343 to 346, 1998

Lastly, here is an excellent article. The introductory section explains much of the above information succinctly. Also there are many remarkable images from Google Earth for those interested in the physics of water waves.

“Teaching Waves with Google Earth”
Author: Fabrizio Logiurato
(Submitted on 24 Dec 2011)

Abstract: Google Earth is a huge source of interesting illustrations of various natural phenomena. It can represent a valuable tool for science education, not only for teaching geography and geology, but also physics. Here we suggest that Google Earth can be used for introducing in an attractive way the physics of waves.
http://arxiv.org/abs/1201.0001v1

Cheers, Bobbywhy

 

[olivermsun]

According to linear theory for waves forced by gravity, the phase velocity depends on the wavelength and the water depth. For a fixed water depth, long waves (with large wavelength) propagate faster than shorter waves.

The linear dispersion relation is usually understood for its behavior in two limits: In the limit of long waves (shallow water waves), the phase speed is affected only by depth, so that all waves propagate at the same speed. For the opposite limit (deep water waves), the wavelength matters but not the depth, and the waves become dispersive.

The phase velocity of an approximately sinusoidal wave is proportional to the square root of the wavelength. These are the waves described in the five examples given in post number five on March tenth that showed no effect of temperature change on phase velocity.

In the case that depth matters (shallow water waves), then one might suppose that the temperature affects the phase speed through the (surely microscopic) change in depth, as suggested in posts three and eight.