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
.
the length of the tuba varies significantly from cold to warm.
I thought sound travelled faster through denser (colder) air.
