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02 April 2004
E-Bulletin Backscatter
Home sweet home?
Forrest,
Your comment in the E-Bulletin article about Mars being "foreboding and inhospitable" is interesting [26 March 2004]. Shortly after the rovers landed I became interested in figuring out just how inhospitable Mars was. A lot of time and at a lot of places it is way too cold even for the comfort of the electronics on the rover. But from what I can figure out from the comments about the rovers during the day, it is not too bad. I looked into the atmospheric pressure also. It is equal to about 30,000 feet here on Earth.
Given that, I suspect a person
could survive around the rovers during the day with not much more than
a oxygen mask like high flying planes have.
Jim Hannon
www.fmtcs.com/web/jmhannon
Forrest Mims replies: Many good web sites discuss surface conditions on Mars. Because Mars has only a minuscule ozone later, solar ultraviolet at the surface extends well into the UV-C region, which is extremely dangerous to exposed organisms. The temperature at Mars is described by James E. Tillman in "Mars: Temperature overview": "The temperatures on the two Viking landers, measured at 1.5 meters above the surface, range from + 1° F, ( -17.2° C) to -178° F (-107° C). However, the temperature of the surface at the winter polar caps drop to -225° F, (-143° C) while the warmest soil occasionally reaches +81° F (27° C) as estimated from Viking Orbiter Infrared Thermal Mapper." See www-k12.atmos.washington.edu/k12/resources/mars_data-information/temperature_overview.html.
Coffee mug music reply
In a previous Backscatter item (26 March 2004), Bob Hall asked about an unusual phenomenon he noticed. Jim Hannon and SAS President Shawn Carlson have replied. Bob's letter and the replies are given below. Editor.
Dear Forrest,
While stirring my morning coffee, I notice that the spoon tapping on the side of the ceramic mug produces a tone that increases in frequency with each tap.
What causes this phenomenon and how can it be harnessed. Does it relate directly to the temperature of the ceramic? Do the frequency changes stop when the ceramic reaches the temperature of the coffee inside? Does the type and thickness of the ceramic affect the frequency response?
Curiously,
Bob Hall
Jim Hannon replies:
Forrest,
There is a bit of discussion
of effect described in the coffee mug music on the SAS forum. Also
SAS member Kevin Kilty has written on the subject. See http://www.kilty.com/coffee.htm.
It is most often called
the "hot chocolate effect," and a web search will turn up some more information.
Jim Hannon
Shawn Carlson replies:
So far as I know, this effect was first described by my friend and
colleague Frank Crawford. Frank was a professor of physics at UC
Berkeley, and a very colorful character. Sometime I should tell
everyone the story of how he got shot down over occupied Europe during
World War II and spent the next few months evading the Nazis to rejoin
his unit in England. His adventures (especially his encounters with
lovely French lasses in the underground, which he bragged about incessantly)
could have made for a best-selling biography. (I'm very sorry to
say that Frank died last year.)
Nothing escaped Frank's interest. He was especially fascinated by
the physics of everyday phenomena. When I worked with him at UC
Berkeley (we shared the same office), he told me that some decades ago,
while romancing a flaxen haired beauty, he decided to make two cups of
fine hot chocolate, and noticed the very effect you described. After
a literature search failed to turn up an explanation of the phenomena,
(presumably sometime after his date was over) he decided to discover it
and publish a paper about his observations. Today, it's called the
Hot Chocolate Effect in Frank's honor.
In brief, according to Frank, the effect has to do with the speed of sound.
The tone you heard, Bob, arises because your spoon caused sound waves
to bounce back and forth between the bottom of your cup and the surface.
These waves cause the surface to undulate up and down, acting like the
surface of a speaker, and generate the tone you hear. The faster
sound travels in the liquid, the more frequently these waves strike the
surface and the higher the frequency of the tone. So the first question
is, what determines the speed of sound?
The speed of sound depends of two parameters: the stiffness of the
medium, and its density. Very stiff materials transmit sound rapidly.
But sound travels more slowly in dense materials, because, given the same
force, heavier things are harder to accelerate than lighter things.
It turns out that the speed of sound is proportional to the square root
of the stiffness (Young's modulus) of the medium divided by its density.
This is why the speed of sound in air (a material with a small stiffness
and low density) and the speed of sound in steel (a material that is very
stiff and very dense) aren't really that different. (For a physicist,
if two quantities are within a fact often of each other, we often think
of them as essentially the same.) The ratio of two small numbers can be
close to the ratio of two large numbers, and when you throw in the square
root, it's easier still to get numbers that aren't too far apart.
Like steel, water also has high stiffness and high density relative to
air. But if the water has small air bubbles in it, then the mass
hasn't changed very much, but the stiffness changes dramatically. Any
small volume is about as difficult to accelerate as it was before, but
the air bubbles make the fluid quite squishy. So the speed of sound
goes from being the square root of a large number over a large number,
to the square root of a small number over a large number. As a result,
the speed of sound drops like a stone and is in fact much smaller in such
a medium that it is in either pure water or pure air. That's why
you hear the tone drop when you stir your coffee. The tone then
slowly rises as the bubbles rise to the surface and break. As this
happens, the medium looks less and less like a mixture of air and water,
and more and more like pure water.
The only remaining question is how do the air bubbles get there?
It is a fact that water contains dissolved gases (that's how fish breath,
after all) and that cold water can hold more gas than hot water.
When you take water cold from the tap, it's saturated with air.
However, when you heat it so rapidly that the gas doesn't have time to
come out of solution, it becomes supersaturated. (This is easiest
to do in a microwave oven, where the uniform heating reduces the mixing
due to convection currents that always show up when water is heated from
the bottom, say on a stove.) Supersaturated fluids exist in what
we call a"metastable state." That means, when you stir in your cream,
the gas explodes out of solution into many tiny bubbles.
So try the following experiment. Compare the strength of this effect
when using water that has been heated in a microwave to what you observe using water that has been thoroughly boiled on a stove. (Boiling removes the dissolved gases.) Or compare the strength of the
effect to water that was kept for a long time at a relatively high temperature,
say be a mug filled with water on heating plate set on low, to a mug of
water that was kept overnight in your refrigerator. How many times can
regenerate the effect by re-stirring the same cup of coffee with the originally
hot or cold cups?
I've never had cause to question Frank's explanation. However, I
invite everyone to experiment with it on your own and form your own conclusions.
Perhaps you'll find an error in Frank's explanations, and bring us closer
to the complete understanding.
Shawn Carlson
