Physics
Physics
Problem
A pipe X has both ends open and a pipe Y has one open and one closed end. The second harmonic in X has the same frequency as the first harmonic in Y. Calculate the ratio of the length of pipe X to that of pipe Y.Intuitive explanation
The key is recognizing that open and closed pipes have different harmonic patterns: open pipes resonate at all integer multiples of the fundamental, while closed pipes only at odd multiples. Since the second harmonic of X matches the first harmonic of Y, you need to set their frequencies equal using for open pipes and for closed pipes, then solve for the length ratio.
Intuitive explanation
The key is recognizing that open and closed pipes have different harmonic patterns: open pipes resonate at all integer multiples of the fundamental, while closed pipes only at odd multiples. Since the second harmonic of X matches the first harmonic of Y, you need to set their frequencies equal using for open pipes and for closed pipes, then solve for the length ratio.