An organ pipe open at both ends is 1.5 m long. A second organ pipe that is closed at one end and open at the other is 0.75 m long. The speed of sound in the room is 330 m/s. Which of the following sets of frequencies consists of frequencies which can be produced by both pipes?
A) 110 Hz, 220 Hz, 330 Hz
B) 220 Hz, 440 Hz, 660 Hz
C) 110 Hz, 330 Hz, 550 Hz
D) 330 Hz, 440 Hz, 550 Hz
E) 220 Hz, 660 Hz, 1 100 Hz

Question

Quizplus · Accepted Answer

For a pipe open at both ends, the possible frequencies are given by $f_n=nv/2L$, where $n$ is the harmonic number, $v$ is the speed of sound, and $L$ is the length of the pipe. For a pipe closed at one end and open at the other, the possible frequencies are given by $f_n=nv/4L$. 
Using these formulas, we can calculate the possible frequencies for each pipe:
For the open pipe: $f_1=110$ Hz, $f_2=220$ Hz, $f_3=330$ Hz, $f_4=440$ Hz, etc.
For the closed pipe: $f_1=147$ Hz, $f_2=294$ Hz, $f_3=441$ Hz, $f_4=588$ Hz, etc.
From these lists, we can see that the frequencies $110$ Hz, $330$ Hz, and $550$ Hz can be produced by both pipes, so the correct answer is (C).

An Organ Pipe Open at Both Ends Is 1