An open-open organ pipe is 73.5 cm long. An open-closed pipe has a fundamental frequency equal to the third harmonic of the open-open pipe. How long is the open closed pipe?

The length of the  open closed pipe is 12.25 cm

Explanation:

In open - open organ pipe, third harmonic has Antinode to Node, Node to Node, Node to Node and Node to Antinode.

The length of the open-open organ pipe is equal to the sum of wavelength in Antinode to Node, Node to Node, Node to Node and Node to Antinode.

L = A→N + N→N + N→N + N→A

In open-closed pipe, Fundamental frequency has Antinode to Node.

Thus, length of the open-closed organ pipe is equal to the wavelength in Antinode to Node.

L = A→N

From the information in the question, fundamental frequency of open-closed pipe is to the third harmonic of the open-open pipe.

F₀ = F

Therefore, the length of the  open closed pipe is 12.25 cm

Length of the open closed pipe is 196cm

Explanation:

the fundamental frequency of an open-closed

f1 = v /4L

f1 = v/4x(73.5)

and the third harmonics of an open-open pipe f2 = 2v/3L

since from the above statement in the question makes the Fundamental frequency of an open-closed pipe equal the frequency of third harmonics of an open open pipe

Hence,

f1 = f2

v/294 = 2v/3L

L = (294 x 2)/3 = 196cm

The length of the close opened pipe is 196cm

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