Open Organ and Closed Organ lengths?

Question

An open organ pipe has a fundamental frequency of 440 Hz. A closed organ pipe has a fundamental frequency that is second harmonic of the open organ pipe. What are the lengths of the two pipes?

Answer 1

Let's call the 440 Hz wavelength λ1; λ1 = c/440. Assume c = 330 m/s, then λ1 = 0.75 m.

The open pipe length Lo = its fundamental wavelength/2 = λ1/2 = 0.375 m.

The wavelength λ2 of the second harmonic of the open pipe = λ1/2 = 0.375 m.

The closed pipe length Lc = its fundamental wavelength/4 = λ2/4 = 0.09375 m.