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Save the tough questions for Rick. Even I can answer that one!

To whatever infinitesimal degree the instrument expands in length, it is insignificant when compared to change in pitch as the air temperature inside the horn increases.

According to Backus' "The Acoustical Foundations of Music", the pitch rises 3 cents for each degree Celsius the air temperature rises. The smaller the instrument the greater the change would be, but even in a tuba I suspect there would be a change of 7 - 8 degrees C in a cool (not cold) room. That's ~20-25 cents! Doing the math in my head (dangerous!!) I figure that'd be comparable to shortening a BBb tuba by about 2.25". I don't think the same (well, actually LESS) temperature change is going to grow the length of the tuba QUITE that much!
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Joe Baker, who WILL leave it up to Rick to calculate just how much longer a BBb tuba will get when warmed 7 degrees C.

I'm no Rick Denney, but I would just ask you to think about what's vibrating, and how it's density varies with temperature .

Sorry to be cryptic, but some things can be reasoned out if you cast aside erroneous premises, e.g. the length of the tuba varies significantly from cold to warm.

(I read the answer sometime within the past year, but I can't put my finger on a reference for you right now. Think about it--you'll figure it out.)

Jerry "waiting for Rick to give the authoritative answer " Wilkins

Hey, at least you gave some details about WHY the pitch rises when it heats up. In reading over my hasty response, I didn't even do that!

Maybe I should have let Rick take it after all.
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Joe Baker, who observes that sometimes it's not just knowin' it, it's knowin' how to say it.

Hmmm... just where is Rick Denney I thought sound travelled faster through denser (colder) air.

Nope. Speed of sound is the positive sqrt(k*R*T), where

k=adiabatic index (constant for a given gas)
R=Universal Gas Constant (constant, obviously, for a given gas)
T=Temperature in degrees Kelvin

So the speed of sound in any GAS increases proportionaly to the square root of the Temperature in Kelvin.

If I remember correctly, the explanation for this is that as the temperature increases, the molecules move more quickly, therefore the likelihood of them colliding increases, therefore the wave will propogate more quickly.

What you probably remember is that sound travels more quickly in solids than in liquids, and more quickly in liquids than in gasses. This is true for a similar reason: the molecules are in successively closer proximity as we move from gas through liquid to solid, allowing each molecule to transfer the energy to the next molecule more quickly.
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Joe Baker, who is much more lucid in the afternoon than in the evening AFTER band rehearsal.

Joe Baker wrote:Nope. Speed of sound is the positive sqrt(k*R*T), where

k=adiabatic index (constant for a given gas)
R=Universal Gas Constant (constant, obviously, for a given gas)
T=Temperature in degrees Kelvin

Right. But isn't cold air denser?

What a discussion! In the words of Bill Cosby, "Why is there air?"

Duh! I'm just a tuba player and I know the anwer to that one. As Cos said, "to blow up volleyballs."

Please notice how I have so positively contributed my vast scientific(and engineer-type) knowledge to the discussion. Sometimes I overwhelm myself. Whew! I'm tired now.

TubaTinker wrote:

Joe Baker wrote:Nope. Speed of sound is the positive sqrt(k*R*T), where

k=adiabatic index (constant for a given gas)
R=Universal Gas Constant (constant, obviously, for a given gas)
T=Temperature in degrees Kelvin

Right. But isn't cold air denser?

Confined in a balloon, yes. Roaming freely through the atmosphere (or your horn), no.

In a balloon, the increased temperature (see Boyle's law) causes an increase in pressure compared to the air outside the balloon, so it expands the balloon's volume. Greater volume, same mass => lower density. But in the tuba, the pressure has means of escape, so it is the same pressure as the air outside the tuba. So the tuba doesn't expand, and the air inside is pretty much the same density as the air outside (if anything, it's denser, since it is MUCH more humid).
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Joe Baker, who is heading to his son's band contest in 4 minutes!

Joe Baker wrote:In a balloon, the increased temperature (see Boyle's law) causes an increase in pressure compared to the air outside the balloon, so it expands the balloon's volume. Greater volume, same mass => lower density. But in the tuba, the pressure has means of escape, so it is the same pressure as the air outside the tuba. So the tuba doesn't expand, and the air inside is pretty much the same density as the air outside (if anything, it's denser, since it is MUCH more humid).

Oh, well, not quite.

Hotter air has fewer molecules in a given space. If the tuba was sealed, it would be pressurized by heat, like your ballon except that it doesn't stretch noticeably in response. But the bell is open, so the molecules spill out. The density is still lower inside, because of fewer molecules in the same space. Or, the density would be lower except that we are blowing in a new supply of molecules, and the air is slightly pressurized by the resistance of the movement of that air through the instrument. The heat-generated flow of air out of an instrument that is heating up will sit on top of that flow. But hotter air is less dense, even when it is humid.

That's why airplanes require more runway on hot days, and particular hot, humid days--the air is less dense. It's also why race cars go faster on cold days--they get more molecules of air into the engine (assuming they match it with fuel).

But in the response to the original question, the answer is the same as for most acoustical tuba questions where people commonly confuse cause and effect: The metal doesn't matter compared to the air within it. The metal expands, but so does the air. The longer tube is more than offset by the lighter air. The speed of sound is higher in hotter, lighter air, and that's why the pitch goes up. That's also why the pitch of your voice goes up if you inhale helium, which is much lighter than air, even though you still have the same vocal chords.

When the tuba sits in the sun, the air within it heats up dramatically to a much higher temperature than what we exhale. When the tuba sits in the trunk of the car on a cold day, the air inside it becomes very cold. As we play, the heated or cooled is replaced by what we exhale. And that movement of air takes heat with it from the brass. So, both tend to stablize after a while.

Rick "who was BUSY!" Denney

One curious phenomenon is that atmostpheric pressure does not appear to affect the speed of sound under ordinary conditions. (i.e., the speed of sound is the same at 20C whether you're in Death Valley or on top of Pike's Peak):

http://www.sengpielaudio.com/SpeedOfSoundPressure.pdf

OTOH, the molecular weight of a gas has a very great effect on sound propogation speed. Try filling a tuba with CO2 or helium and enjoy the fun!

Rick Denney wrote: Oh, well, not quite.

Hotter air has fewer molecules in a given space. ...

Of course, that is correct. I realized I had misspoken (hey, it was 25 years ago, and I never USE any of this stuff... ) in the car on the way to the boy's band contest (straight 'I's, btw, a very impressive job -- and astonishingly good on the sight-reading). I vaguely remember this discussion about the concept of a "perfect gas", in which the speed of sound would be dependent on ONLY temperature, and not at all on pressure or density; and that air is an "almost perfect gas". Yes, of course warmer air "pushes the molecules farther apart", leaving a lower density (I still think the water vapor present would jack up the density somewhat; but I have no data to prove it). It just doesn't matter very much, compared to the effect of temperature.

Now, Rick, exactly how MUCH, as a percentage, does .750 ID brass tubing (70/30 cartridge brass), .005 thick, expand in length as it warms by 10 degrees C?:lol:
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Joe Baker, whose acoustical physics is W-A-A-A-Y rusty!!

I knew Rick would answer.He never lets us down!

Doc wrote:...All you damned engineers... Why couldn't you have just stuck to driving trains?

Doc

You know, I would just LOVE to drive a train!! If it weren't such hot, noisy work, and if I didn't have to work for the railroad to do it....it mighta happened.

MA

MaryAnn wrote:

Doc wrote:...All you damned engineers... Why couldn't you have just stuck to driving trains?

Doc

You know, I would just LOVE to drive a train!! If it weren't such hot, noisy work, and if I didn't have to work for the railroad to do it....it mighta happened.

MA

Honking the horn might be fun

Joe Baker wrote:Now, Rick, exactly how MUCH, as a percentage, does .750 ID brass tubing (70/30 cartridge brass), .005 thick, expand in length as it warms by 10 degrees C?:lol:

0.019%, of course.

(The Celsius coefficient of thermal expansion of brass is 0.000019.)

The diameter, thickness, and alloy (within reason) make no difference.

Rick "did you think I wouldn't know?" Denney

Rick Denney wrote:"did you think I wouldn't know?"

I was certain you'd know where to look, anyway!
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Joe Baker, who doesn't know MANY things!