Try it on paper first. A hint, the key idea and the worked solution are here when you need them.
An organ pipe closed at one end is long. Its third harmonic has the same frequency as the second harmonic of a pipe open at both ends. Sound travels at . Find the length of the open pipe and the common frequency.
In a pipe, a closed end is a displacement node and an open end a displacement antinode. Closed at one end: , odd harmonics only. Open at both ends: , every harmonic.
Have you tried it?
Work it out on paper first. It is fine to get stuck or make a mistake: that is how we learn. When you are ready, go through the solution one step at a time, and check each step against your own.
Step 1. Equal frequencies. .
Step 2. Length. We want , so .
Step 3. Frequency. .
Answer: and .
Check. The closed pipe's fundamental is , and three times that is .
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