To solve this problem, we need to understand the fundamental frequencies of sound waves in open and closed pipes.$\\$For an open pipe, the fundamental frequency is given by:$\\ f_{open} = \frac{v}{2L} \\$where $v$ is the speed of sound and $L$ is the length of the pipe.$\\$For a closed pipe, the fundamental frequency is given by:$\\ f_{closed} = \frac{v}{4L} \\$since only odd harmonics are present in a closed pipe.$\\$Now, we need to find the ratio of the fundamental frequency of an open pipe to that of a closed pipe:$\\ \frac{f_{open}}{f_{closed}} = \frac{\frac{v}{2L}}{\frac{v}{4L}} \\$Simplifying the expression:$\\ \frac{f_{open}}{f_{closed}} = \frac{v}{2L} \cdot \frac{4L}{v} \\$Cancel out $v$ and $L: \\ \frac{f_{open}}{f_{closed}} = \frac{4}{2} \\ \frac{f_{open}}{f_{closed}} = 2 \\$Therefore, the ratio of frequencies of the fundamental harmonic produced by an open pipe to that of a closed pipe having the same length is $2 : 1. \\$This corresponds to Option 2.