An organ pipe of length $L$ is open at both ends. Another organ pipe of the same length is closed at one end. If they produce the same fundamental frequency, what must be true about their lengths in general?

Principle: the fundamental frequencies are $f_{\text{open}}=\dfrac{v}{2L_o}$ and $f_{\text{closed}}=\dfrac{v}{4L_c}$. Set them equal for the same fundamental frequency: 1. $\dfrac{v}{2L_o}=\dfrac{v}{4L_c}$ 2. Cancel $v$: $\dfrac{1}{2L_o}=\dfrac{1}{4L_c}$ 3. So $4L_c=2L_o$, hence $L_o=2L_c$. Therefore the open pipe must be twice as long as the closed pipe. Option A is tempting because both are organ pipes, but their boundary conditions differ. Option B reverses the relation. Option D ignores the standard resonance formulas.