# Determining if pipe is open or closed from given frequencies

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1. Nov 30, 2014

### AAAA

1. The problem statement, all variables and given/known data
A pipe resonates at successive frequencies of 540 Hz, 450 Hz, and 350Hz. Is this an open or a closed pipe?

2. Relevant equations
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3. The attempt at a solution
My assumption is that because the harmonics of an open pipe are odd number multiples of the fundamental frequency (1f, 3f, 5f), and ∵ the difference between the frequencies is the fundamental frequency (I think?). The fundamental frequency is ∴ around 100 (?). And ∵ the frequencies go up by ~100 each time, it's an open pipe, as it's harmonics are even number multiples (1f, 2f, 4f, 6f).

I don't think my assumptions are correct. Any help is appreciated, thanks.

EDIT: Is it possible to determine the fundamental frequency from the given frequencies? I'm beginning to think that the fundamental frequency is the difference between those frequencies, divided by two. Because to get from on harmonic to the next, we multiply by two to get from one freq to the next, with the exception of the even number multiples(1f→2f).

2. Nov 30, 2014

### AAAA

Is it even possible to determine if it's open or closed based on the given information? I imagine it would be easier if they told you which harmonics those are, so the fundamental frequency could be determined, and from that information determine whether pipe is closed or open.

3. Nov 30, 2014

### haruspex

Yes, because the number of wavelengths goes 1/4, 3/4, 5/4...
I assume you meant to write 'closed pipe' here. Anyway, that list is wrong. Consider the numbers of wavelengths.
Right, so what do you get for the fundamental frequency? What multiples of that are the given frequencies?
Yes, because you are told these are successive harmonics.

4. Nov 30, 2014

### AAAA

Well, 450-350= 100
100/2 = 50

50*7 = 350
50*9 = 450
50*11 = 550 ≈ 540

∵ I used odd number multiples to get that value, it must be a open pipe with a closed end (a fixed and free end system), it can't be an open pipe (with two free ends) because then the successive frequencies would be 50 apart, no?

And a pipe with two free ends is 1f, 2f, 3f, 4f... Right? Which is the same as a pipe with two fixed ends?

5. Nov 30, 2014

### haruspex

That all looks right.

6. Nov 30, 2014

### AAAA

Thanks! I had neglected to do the math for the frequencies and just looked it up online, I guess I interpreted it wrong. I just did the math for the frequencies, and now it all make sense, thanks again!