Open ended pipe Harmonics Mastering Physics Question

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TFM

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[SOLVED] Open ended pipe Harmonics Mastering Physics Question

1. The problem statement, all variables and given/known data

Consider a pipe 45.0cm long if the pipe is open at both ends. Use v = 344m/s.
Now pipe is closed at one end.

What is the number of the highest harmonic that may be heard by a person who can hear frequencies from 20 Hz to 20000 Hz?

2. Relevant equations

[tex] f_n = (2n-1)\frac{v}{4L} [/tex]

3. The attempt at a solution

I have an answer that works, but masteringphysics doesn't accept. I first rearranged the equation to give me:

[tex] (2n-1) = \frac{f_n * 4L}{v} [/tex]

then:

[tex] 2n = (\frac{f_n * 4L}{v})+1 [/tex]

and finally:

[tex] n = ((\frac{f_n * 4L}{v})+1)/2 [/tex]

inserting the values gives 52.5 so I inserted 52 as the answer. wrong, I have tried 51-54, all wrong. so I thought tpo go backwards, using:

[tex] (2n-1) = \frac{f_n * 4L}{v} [/tex]

and inserting values, to find the value which is the closest to 20000, buit under it - guess what, the value that came out:

52!

Any ideas

TFM
 

Kurdt

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The harmonics of a pipe closed at one end are all odd. For n = 2 you have the 3rd harmonic. For n=52 what harmonic do you have?
 

TFM

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It will be the 53rd Harmonic. The trouble is, I have put 53 in, and it says its the wrong answer!
 

Kurdt

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It will be the 53rd Harmonic. The trouble is, I have put 53 in, and it says its the wrong answer!
Sorry that third harmonic was a bad example. The harmonics are given by 2n-1. So if n is 52 what is the harmonic. An easier way to have thought about it would to have solved for:

[tex] f_n = \frac{nv}{4L} [/tex]

for n = 1, 3, 5,.....
 

TFM

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Using:

[tex] f_n = \frac{nv}{4L} [/tex]

and using n = 103,

I get a frequency of 19684, which is the first odd number below 20000. would this be the harmonic number?

TFM
 

Kurdt

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I get a frequency of 19684, which is the first odd number below 20000. would this be the harmonic number?

TFM
Yes n is the harmonic number.
 

TFM

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Success!! n = 103.

IOne thing does bother me slightly - where does my orginal answer of 52 fit in?

TFM
 

Kurdt

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2n - 1 is just another way of saying n = 1, 3, 5, .... . So if you stick n = 52 into 2n - 1 you get 103.
 
Last edited:

TFM

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That makes sense.

Thanks,

TFM
 

Kurdt

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That makes sense.

Thanks,

TFM
What I was originally aiming at was for you to put the n = 52 into that equation and get 103 but I used a stupid example which probably mislead you slightly. :smile:
 

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