When it's cold...

[jeopardymaster]

A while back I was asked by a nonbrass person: "When it's cold, string players go sharp and brass players go flat. How can that be?" What I told the questioner was this -- because in the case of stringed instruments, the strings themselves do the vibrating and when they get cold, they shrink, getting tighter and going sharp. But in the case of brass instruments, the vibration is provided by the lips of the player rather than the horn itself. And when the brass tube gets cold, it doesn't really get demonstrably shorter, but becomes less resonant and fails to be as responsive to the vibrations being pushed through it. The sound is deader and is perceived as flat.

I think I might have gotten away with this one, but I know my answer was at least half wrong. Anyone care to elucidate?

[UDELBR]

The colder the air, the slower the speed of sound ( C_air = 331.3 + (0.66 x T) m/s, where T is the temperature in °C ), making brass instruments tune flat in cold air.

[Ben]

Uncle Beer is correct, the speed of sound is slower at lower temperature (see above equation).


Since the speed of sound is slower relative to a warm tuba, the the standing wave resides in the tuba longer, and the horn goes flat because the tuba appears longer to the standing wave.

[Full Metal Ratchet]

The resonance formula(s) puts the speed of sound in the numerator. The only thing that affects the speed of sound in air (roughly an ideal gas) is temperature. Density and pressure are related, and any change in one is canceled by the other, thus only temperature affects the speed of sound in air. So, the frequency ends up being proportional to temperature since the speed of sound is in the numerator.

When generally considering transmission mediums, density, stiffness, and compressibility all play a role. Within a single ideal gas, only temperature really matters... to a point.

[Dan Schultz]

I've always known that it's the temperature of the air column (and not the horn itself) that causes the pitch to rise and fall.

But... a new 'twist' to this finally dawned on me today (an 'aha' moment) while playing my trusty red. white, and blue Selmer fiberglass souzie at a memorial service this morning.....

The temperature was about 70 degrees this morning and the horn was about 20 cents flat with the main shoved all the way in. Within a quicker than normal 'warm up' period, the horn was already a little sharp so I pulled out about 1/2". The horn stabilized very quickly.

Here's what I think.... Maybe you guys can confirm or deny the logic... Fiberglass is an insulator and brass is a good conductor of heat. It takes longer to warm up a brass horn because the body tends to sap heat from the air inside until the brass gains a little temperature. Meanwhile... the fiberglass body tends to have less effect on the air column within due to it's insulative properties.

Goodgigs.... maybe you can chime in on this with the work you've done with the plastic tubas. Do they tend to warm up quickly? and cool down slower that brass?

[Full Metal Ratchet]

Sounds like a valid theory to me.