# Getting the length of an open tube with only a frequency and temperature given? [closed]

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.

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

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• The speed of sound changes with the temperature. Perhaps the question expects you to take this into account. – John Rennie Dec 16 '15 at 10:40

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...