Physics

In a pipe closed at one end, only odd harmonics resonate—the fundamental and its odd multiples. The key insight is that successive resonant frequencies differ by exactly one harmonic step, so you can find which odd harmonics correspond to 300 Hz and 500 Hz, then use the relationship between frequency, pipe length, and sound speed. Once you identify the harmonic numbers, the speed of sound follows directly from $v = 2fL/n$.

In a pipe closed at one end, only odd harmonics resonate—the fundamental and its odd multiples. The key insight is that successive resonant frequencies differ by exactly one harmonic step, so you can find which odd harmonics correspond to 300 Hz and 500 Hz, then use the relationship between frequency, pipe length, and sound speed. Once you identify the harmonic numbers, the speed of sound follows directly from $v = 2fL/n$.