Problem

This problem investigates stopped pipes and open pipes. Stop pipes are closed on one end and open on the other end. Open pipes are open on both ends. For the following problem, assume that the speed of sound through air is 340 m/s.

Pipes.jpg

Part 1: A stopped organ pipe has a fundamental frequency of 220 Hz. How long is this pipe?

Part 2: The second overtone of the stopped organ pipe has the same wavelength of the third harmonic of an open pipe. How long is the open pipe?

Solution

Part 1

The formula for the fundamental frequency, or first harmonic, of a stopped pipe is

.

Thus

.

Part 2

The second overtone .

For an open pipe

.
.
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