Calculating Organ Pipe Length: Open vs. One End & Beat Frequency Comparison

[dphoos]

Hey all, here is the question:
A friend in another city tells you that she has a pair of organ pipes, one open at both ends, the other open at one end only. In addition, she has determined that the beat frequency caused by the second-lowest frequency of each pipe is equal to the beat frequency caused by the seventh-lowest frequency of each pipe. Her challenge to you is to calculate the length of the organ pipe that is open at both ends, given that the length of the other pipe is 1.10 m. Note that there are two possible answers to this question. List them both, in the order indicated below.
?m (shorter)
?m (longer)

I'm not really even sure where to begin. If someone could just point me in the right direction, that would be great

Thanks

 

[ehild]

Hey all, here is the question:
A friend in another city tells you that she has a pair of organ pipes, one open at both ends, the other open at one end only.

You have to know that there are standing sound waves in an organ pipes. There is a node at the closed end and an antinode at an open end. So the pipe with both ends open contains an integer number of half-wavelenghts ( its length L = n *lambda/2) and the length of the pipe with one end closed is related to the wavelength as L=(2n+1/2)*lambda/4.

In addition, you have to know the relation between wavelength (lambda) , frequency (f) and speed of a wave (V). It is lambda=v/f.

And the beat frequency is the magnitude of the frequency difference.

ehild

 

[wais]

for sharing this question! Calculating the length of an organ pipe can be tricky, but here are some steps you can follow to solve this problem:

1. Understand the concept of beat frequency: Beat frequency is the difference in frequency between two sound waves that are played simultaneously. It is measured in Hertz (Hz) and can be calculated by subtracting the frequency of one wave from the frequency of the other.

2. Identify the two pipes: Your friend has two organ pipes - one is open at both ends and the other is open at one end only. Let's label them as Pipe A (open at both ends) and Pipe B (open at one end).

3. Determine the frequencies of the second-lowest and seventh-lowest notes: The second-lowest frequency of Pipe A will be twice the frequency of the open end (fundamental frequency). Similarly, the second-lowest frequency of Pipe B will be three times the fundamental frequency. The seventh-lowest frequency of both pipes will be six times the fundamental frequency.

4. Set up an equation: Since your friend has determined that the beat frequency caused by the second-lowest frequency of both pipes is the same, we can set up an equation as follows: 2fA - 3fB = 6fA - 6fB. Simplifying this equation, we get fA = 2fB.

5. Calculate the length of Pipe A: We know that the length of Pipe B is 1.10 m. To calculate the length of Pipe A, we can use the formula: L = (n/2) * λ, where L is the length, n is the harmonic number, and λ is the wavelength. Since we know that the fundamental frequency of Pipe B is 1/4 of the fundamental frequency of Pipe A, we can substitute these values in the formula and get: L = (4/2) * λ = 2λ. Therefore, the length of Pipe A can be either 2λ or 4λ.

6. List the two possible answers: As mentioned earlier, the length of Pipe A can be either 2λ or 4λ. Since we do not have enough information to determine the exact value of λ, we can list the two possible answers as follows:

- 2λ = 1.10 m (since the length of Pipe B is 1.10 m, this is the shorter possible answer)
- 4