>
confusing wavelength with frequency
And maybe the resonator with the transmission path?
Your unhappy customer calls, and holds the phone to the marimba. By experience, we know the pitch will be "right". But what is the speed of sound on a phone wire? Dang near the speed of light, thousands of times faster than speed of sound in air. What is the wavelength? Typically miles. However if speed of sound in the transmission line (and its length) are constant, the pitch is unaffected.
(Ah, and then there's cellphones, which use a store-and-forward network, bursting at speed of light then being held for random times at every node. However pitch-shift is undesirable so the system preserves pitch, even dropping bits when they do not arrive in good time.)
What is the speed of sound in your resonator? The speed of sound in WOOD. Which is several times faster than in air. Find a long wood beam, bridge, building, over 40 feet long. Have a friend hammer one end while you put an ear on the other end. You will see the hit, then hear it in the wood, then hear it through air. (It may be awful hard to find a wood structure big enough and tight enough to carry sound far enough to hear the difference in speed.)
Or what is the size of your air-pipe acoustic resonator compared to the size of your wood-chunk primary resonator? Even ignoring open/closed-end corrections, the pipe is a lot longer than the wood.
The wood is the prime resonator. Certainly you can play wood chunks without air resonators. And if the air resonator is mis-adjusted, the loudness is hurt far more than the pitch.
So first-glance, this is not relevant:
http://www.fonema.se/soundspeed/soundspeed.html
However at the end it addresses "Reed pipes". The reed is tuned and is the prime pitch. A naked reed is a harmonica, organ builders dress it up with a pipe. The graph shows a 3 semitone-off pipe shift the reed 1 semitone. Certainly a close-coupled pipe will bend the prime resonator. However the reed is very light and tightly sealed to the tube. A marimba bar is much heavier than a reed, much heavier than the air in the pipe, and there's a large gap between bar and pipe. Much looser coupling. Probably few-cents, not semi-tone errors.
I don't see free info on wood stiffness versus temp. "Generally" wood strength and stiffness go together.... it's all about the lignin. I'm not sure this can be generalized to temperature, but WTH.
Encyclopedia of Materials: Science and Technology ISBN:0-08-0431526 pp. 9732-9736
30 deg C change of temp gives 20% change of strength.
Understanding wood:..., Hoadley, Taunton Press, 2000, pg 95:
"...air-dry wood changes in strength by an average of 2% to 5% for every 10 deg F change of temperature." In deg C this is 2%-5% per 5.5 deg C. IOW 30 deg C gives 10.8%-27% change of strength.
There is also change of length with temperature. My gut says this is too small to worry about at bedtime.
Mass unchanged, stiffness increases (say) 20% in 30 deg C, or 1.2 times stiffer. Square-root stiffness times mass. Frequency should change to 1.095, or about 160 (87-216) cents, in 30 deg C. Being sloppy, 3 to 7 cents per degree C, 2 to 4 cents per deg F, pitch up when temp is down.
> tuned ...72-75 degrees
> about 50
> padauk +11 cents
> cherry +20 cent
23 deg F colder gives 11 or 20 cent sharp. That's 0.47 to 0.85 cents per degree F. Much less than over-extrapolated from strength trends. Not length-change: the bars are shorter when cold, which makes them more-sharp not less-sharp. God only knows (we could speculate) why tree-stuff stiffness does not rise in cold as fast as strength.