Ah, but the shrinkage / coefficient of thermal expansion of the body material is a red herring, cos playing in a cold room would tend to shrink the whistle, thus making it sharper. It’s the temperature of the air inside that matters, but heat conduction / insulation is what counts. Playing a whistle is more like blowing across a demijohn than blowing a trumpet - air exchange is minimal, so room temperature / body temperature of the instrument makes a big difference.
I’m a lecturer in engineering, and wondered about setting a project on the response to temperature of an orchestra of instruments (whistle included of course). Whereas whistles go flat in cold conditions, what happens to stringed instruments? (Rhetorical question, unless someone wants to hazard a guess!) The thought of locking a student in a cold store and getting them to play a variety of instruments is too good an opportunity to miss!
My guess is they are slightly sharper as the string become more taut. O am assuming it would be the same for any instrument where the physical reverberation of the material is what produces the sound. Xylophones, cowbells, drums . . .
I’d guess wooden stringed instruments tend to go flat when cold. It’s probably not string contraction that’s the main issue. As the wood shrinks in cold, less humid air, the bridge will tend to drop, thus lowering string tension. Also, colder, slower air in the resonant body of e.g. a fiddle or guitar will increase the effective chamber size, resulting in a darker, more bass-heavy sound.
There’s actually a lot of cool science in this. I’m really curious now. I wonder if it’s possible to balance string tautness and body shrinkage or if this is something that expert instrument crafters even think about when shaping the instrument. Of course optimal performance will be room temperature so I guess the practicality of making an all-weather violin is trumped by other design aspects.
Wood whistles definitely need warming up. And they take longer to do so than a metal one too. Usually takes a tune or two to bring them nicely into line. I always recommend that you take your whistle out and leave it on the table for a while to acclimatise to the location before playing it as well.