Physics 1251 HW 10 #8 Part B

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So I was able to get part a pretty easily using the equation f=(n/2L)(T/u)1/2 .  Then for part B it asks in what mode and with what frequency is it vibrating, if a node is observed at distance x (0.31 m in my case) away from one end.  I didn't really know how to approach this problem, or what equation I should be applying. An explanation on how to set up this part would be great. Thanks.

asked Nov 3, 2014 in General

For this question, the distance between this given node and the end can be multiples of $\lambda /2$. So there are a set of modes will fit this configuration. The lowest allowed mode is when this distance equals $\lambda /2$ and you can find how many "loops" there are with this mode -- this gives the mode number (n).
The frequencies need to be also the same number (n) multiples of the fundamental $f_1$.