I am new to StackExchange, and I have a question about a school project I'm working on involving constructing an instrument. I am building a xylophone-glockenspiel-mash kind of thing, but I wanted to save some money on materials and I need to know: If I have the right material, and I know the current length and the current pitch in Hz when struck, can I calculate the length it needs to be to reach a specific note (in this case, F4)? The current length is 3ft or 91.4cm, and currently it hits 218.2Hz when struck. I have found nothing in my searches on the internet so far, although this may be because I don't know the proper terminology to search for. Thank you for reading, and thanks in advance for helping.
This question is more suited to physics stackexchange but anyway..
This shows you to calculate frequency of vibrating bars, rods and tubes:
This is a paper on building a copper tube Xylophone:
If you have any further questions check out physics SE
Eq. 4.39 of H. Olsen, Music Physics and Engineering 1967 gives the equation for the fundamental frequency of a free bar. For this problem, where you have the same material and the same cross-sectional shape, the frequency is proportional to 1/(length squared)
I think that rote numbers will not work. Wood is not a material of homogenous resilience, and xylophone bars are hollowed out for best resonance (and as part of tuning). So you need to figure in some waste material for experiments.