Pipe Open or closed from a Standing Wave Equation Here is the full question:

The part in the brackets are the answers. I am still terribly confused.
Lets say we are given an equation for a standing wave in a pipe:
$$y(x,t) = A\sin\left(\frac{3\pi x}{L}\right)\sin(\omega t).$$
Is this enough information to know whether it is an open-open or open-closed pipe system? Obviously at $x = 0$, we have a node, so at a minimum there is one closed end. $k = \frac{2\pi}{\lambda} = \frac{3\pi}{L} \rightarrow \lambda = \frac{2}{3}L$.
I know that a one-sided open system $\lambda_n = \frac{2L}{n}$ which would work if $n = 3$. Hence it is an open-closed system? I am super confused about what $L$ is here. Is this the length of the tube?
 A: The question in isolation is not well posed for a single answer; in fact, there are an infinite number of "correct" answers that could be given.  Further information could be provided (or assumed by the questioner) that would lead to a particular solution.

Analysis
First, I will assume that $y$ denotes the particle displacement within the tube (and not the pressure).  Then, as you comment, we may say that the tube is closed at $x=0$.  However, the length may be any value of $x$ such that $\sin(3\pi x/L)=0$ if the tube is closed at the far end, or any value of $x$ such that $\cos(3\pi x/L)=0$ (anti-node) if the tube is open at the far end.  Why don't we calculate all of these distances, just for fun!
Closed Far End
We are looking for
$$
  \sin\left( \frac{3\pi x}{L} \right) = 0 \hspace{15mm}\Rightarrow\hspace{15mm} \frac{3\pi x}{L} = n\pi,
$$
where $n$ is any integer.  Thus, we may conclude that the tube may be any of the following lengths:
$$
  \left\{ \frac{nL}{3}: n\in\mathbb{Z} \right\}.
$$
We are only interested in positive values of the length, and so the lowest possible length of a closed-closed tube would be $n=1$, and so the tube length is $L/3$.
Open Far End
In this case we are looking for
$$
  \cos\left( \frac{3\pi x}{L} \right) = 0 \hspace{15mm}\Rightarrow\hspace{15mm} \frac{3\pi x}{L} = \frac{2n-1}{2}\pi,
$$
where $n$ is again any integer.  Thus, we may conclude that the tube may be any of the following lengths:
$$
  \left\{ \frac{2n-1}{6}L: n\in\mathbb{Z} \right\}.
$$
Again, we are only interested in positive lengths, and so the smallest tube would be one where $n=1$, which yields a tube length of $L/6$.  The answer they provided is the case where $n=3$.
One set of information they could have provided to force a specific answer is how many nodes and anti-nodes are present in the tube (3 and 3 in the case given by the answer).  I am sure there are other options as well.
