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I've got a rather strange question here. I need to find the length of an open tube (silver flute), but I have only been given the frequency of the note that it is playing and the outside temperate (as well as the thermal expansion coefficient for silver).

The only equations I know for frequency are $v = \lambda f$, $f = 1/T$, and $f = \omega/2\pi$. I'm not exactly sure, which equation to use.

I don't think the current temperature will help get this answer, but it looks like I will need it for a later question which gives a new temperature and asks for the new frequency. (I can handle this part with a simple Linear thermal expansion equation).

If anyone can point me in the right direction that would be fantastic, thanks.

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closed as off-topic by John Rennie, Kyle Kanos, user36790, Gert, Sebastian Riese Dec 16 '15 at 16:53

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    $\begingroup$ The speed of sound changes with the temperature. Perhaps the question expects you to take this into account. $\endgroup$ – John Rennie Dec 16 '15 at 10:40
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Since this is homework-and-excercises question, I will not provide full answer, just give hints.

Your equations are correct, but they are not enough if you don't know how to treat the $\lambda$. Standing wave in the tube of the length $L$, opened at both ends has a wavelength of $2L$ (the fundamental mode only). Now you have the missing piece. Why is that so? Cause of the boundary conditions: there is always a node of the acoustic pressure at the open end of a tube. And the distance between the nodes is...

Why the temperature? Cause when you tranfer between the wavelength and the frequency, you will meet the speed of sound which is temperature dependent. See this wikipedia article for more details.

Further discussion. This is only the case valid for basic approximation. It would require that impedance load (see the acoustic impedance for more details) at the end of the tube is perfect zero (which isn't). There are corrections of acoustic length of the tube (regrding the geometrical length). Especially in the case of flutee where the open ends are partially covered with player's lips or tone hole caps.

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I think I was able to find an answer to my own question. I didn't have the equation f = v/2L. Solving for L, L = v/2f. Using the speed of sound in air and the frequency given to me I could solve for the length.

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