Physics

For pipes open at both ends, the key insight is that the fundamental frequency depends on both the pipe length and which harmonic is vibrating. The $n$-th harmonic has frequency $f_n = \frac{n v}{2L}$, where $n$ is the harmonic number, $v$ is the speed of sound, and $L$ is the pipe length. Since you know the harmonic numbers and lengths for both pipes, you can set up the frequency ratio directly without needing to know the speed of sound—it will cancel out.

For pipes open at both ends, the key insight is that the fundamental frequency depends on both the pipe length and which harmonic is vibrating. The $n$-th harmonic has frequency $f_n = \frac{n v}{2L}$, where $n$ is the harmonic number, $v$ is the speed of sound, and $L$ is the pipe length. Since you know the harmonic numbers and lengths for both pipes, you can set up the frequency ratio directly without needing to know the speed of sound—it will cancel out.