Thursday, September 14, 2006

interesting problem (read!)

Working through a set of example candidacy problems. Most are mind numbingly boring, but this one was genuinely fun:

"You are alone in an acoustics laboratory with rather modest equipment. Your job is to measure the temperature of the air. The laboratory equipment you have access to includes: a sharpened pencil, paper, a stopwatch, a large washtub filled with water, several gallons of motor oil, several rubber balloons, a long 5 cm diameter glass tube with open ends, scissors, a 440 Hz tuning fork, a screwdriver, and a measuring tape. All of this may or may not be useful to you. Give a written experimental procedure for measuring the temperature of air, and do an example calculation"

Cool huh? Unlike normal problems, in this one you actually have to be creative and resourceful. Take a whack at it if you want, because I bet that there are tons of ways to do it. I'll post my sol'n later
- Tim

This is all the outside info you need to solve the problem:

c^2 = gamma*r*t
gamma = ratio of specific heats = 1.4 for air
r = 287 joules/kelvin for air
t = tempurature in kelvin
c = sound speed

highschool stuff:
soundspeed = wavelength*frequency

for tubes with open ends:
Resonances are at integer multiples of half-wavelengths

for a tube with an open end and a closed end
Resonances are at 1/4, 3/4, 5/4, etc... wavelengths

and, lastly, resonances are pitches at that the tube will like. I.e. if you hold the tuning fork to a tube that is open on both ends and half a wavelength long, it will sound really loud.

That's all you need to know!

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