The fundamental frequency for a pipe open at both ends is given by $f_{\text{open}} = \frac{v}{2L}$. The fundamental frequency for a pipe closed at one end is given by $f_{\text{closed}} = \frac{v}{4L}$. Taking the ratio of the two frequencies for the same length $L$: $\frac{f_{\text{open}}}{f_{\text{closed}}} = \frac{\frac{v}{2L}}{\frac{v}{4L}} = \frac{4L}{2L} = \frac{2}{1}$. Therefore, the ratio is $2:1$.