# differences in frequency of open/closed standing waves

Discussion in 'MCAT Study Question Q&A' started by docmayer, Aug 19, 2011.

1. ### docmayer 2+ Year Member

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Hey guys,

I have a quick question regarding standing waves in open and closed pipes. The questions is asking how the frequency of a pipe open at both ends with a 2nd harmonic would change if it was blocked at one end ( so basically a closed pipe). First I determined the wavelength of the open pipe at second harmonic to be 2L/2. Now, to determine it for the closed pipe, how would you go about this? Closed pipes don't have a second harmonic I thought since the # of harmonics is the # of nodes, but it gets reflected back in the pipe so the # nodes (and harmonics) are 1, 3, 5 etc...

Can someone tell me where my thinking is wrong,

Thanks

2. ### cham90 5+ Year Member

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If it makes you feel better, I'm sure your thinking is correct.

Is this a multiple choice question? I would guess that it would change to either 4L/3 or 4L/5, but I'm not too sure which.

(I got the wavelength=4L/n where n=1,3,5.. from http://www.phy.duke.edu/~lee/P53/waves3.pdf)

3. OP

### docmayer 2+ Year Member

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The answer is 4L/3. But I don't understand how that is the second harmonic, since n=#of harmonics in a closed pipe, and since n=3 that would mean 3rd harmonic, not second...sigh...ll jus hope something like this doesn't show up tuesday!

4. ### TheRealAngeleno

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For a closed pipe n = odd #'s ,

So n = 1
n = 3
n = 5

etc.

Sorry op below poster is correct.

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Last edited: Aug 20, 2011
5. ### kehlsh Medic Commando 7+ Year Member

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Nah above posters wrong.

n= harmonic number

one end closed pipe doesn't have even numbered harmonic

6. ### plzNOCarribbean

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if both ends are open or both ends are closed, you use

wavelength = 2L/n and frequency= nV/2L where n= any integer

but if one end is open, you use the other equation where:

wavelength = 4L/n and frequency= nV/4L where n= 1,3,5...etc.

just remember that if the question says one end is open, we switch the 2 in the equation to a 4, and n can only be an odd number. In this case, since 3 comes after 1, this would correspond to the SECOND harmonic, since that is the next integer for n, and the THIRD harmonic would be n=5

7. ### TheRealAngeleno

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kehlsh said that this was incorrect. I thought this was correct as well but could someone clarify this statement?

8. ### BerkReviewTeach Company Rep & Bad Singer Vendor 10+ Year Member

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If both ends of a pipe are closed, I believe you have a sealed container that would be great for holding things like paper clips or rubberbands, but it wouldn't be so great as a sound enhancing pipe.

I think you are referring to a pipe open at both ends or a sting that is fixed at both ends.

The problem in this scenario is that the terms harmonic and overtone are getting confused. As the original question is worded, I don't see an answer to the question. A wave with lambda = 2L/2 = L would not be allowed in a closed pipe, as pointed out in several posts. It would be nice to see the exact wording of the question and the four answer choices that correspond.

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9. ### geeyouknit 2+ Year Member

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I think the OP is saying that the pipe that was open at both ends, has one end blocked. So it's not a closed pipe...
For a pipe that's open at one end and closed at one end with a 2nd harmonic, the wavelength = 4/3*L.

The wavelength for open = L
The wavelength for one side-closed = 3/4*L
Doesn't that mean that wavelength decreases by 25%? So wouldn't we expect frequency to increase by 25%?

Can the OP or anyone confirm or fix my thinking, please? Although I'm sure the fella is enjoying his/her well earned break after taking the MCAT's today.

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