Answer
a) Open-open tube.
b) $1.32\;\rm m$
Work Step by Step
a) We need to find if the 390 Hz frequency is the fundamental frequency or not. It is the fundamental frequency if the next frequencies are multiple of it.
We can see that 520 Hz is not a multiple of 390 Hz and neither the 650 Hz (we divided both by 390 to see if the result is an integer number or not, and it is not).
But we can see that the difference between the three frequencies is constant since $520-390=650-520=130$.
This means that the fundamental frequency could be 130 Hz.
So,
$$f_m=130m=390$$
So, $m=3$, and hence,
$$f_3=3\times 130=390\;\rm Hz$$
$$f_4=4\times 130=520\;\rm Hz$$
$$f_5=5\times 130=650\;\rm Hz$$
and since $m=1,2,3,..$, it is an open-open tube.
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b) We can find the length of the tube by using the fundamental frequency
$$f_1=\dfrac{v}{2L}$$
Hence,
$$L=\dfrac{v}{2f_1}=\dfrac{343}{2\times 130}$$
$$L=\color{red}{\bf 1.32}\;\rm m$$
