# Open ended pipe Harmonics Mastering Physics Question

1. Mar 3, 2008

### TFM

[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

$$f_n = (2n-1)\frac{v}{4L}$$

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:

$$(2n-1) = \frac{f_n * 4L}{v}$$

then:

$$2n = (\frac{f_n * 4L}{v})+1$$

and finally:

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

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:

$$(2n-1) = \frac{f_n * 4L}{v}$$

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

2. Mar 3, 2008

### Kurdt

Staff Emeritus
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?

3. Mar 3, 2008

### TFM

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

4. Mar 3, 2008

### Kurdt

Staff Emeritus
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:

$$f_n = \frac{nv}{4L}$$

for n = 1, 3, 5,.....

5. Mar 3, 2008

### TFM

Using:

$$f_n = \frac{nv}{4L}$$

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

6. Mar 3, 2008

### Kurdt

Staff Emeritus
Yes n is the harmonic number.

7. Mar 3, 2008

### TFM

Success!! n = 103.

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

TFM

8. Mar 3, 2008

### Kurdt

Staff Emeritus
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: Mar 3, 2008
9. Mar 3, 2008

### TFM

That makes sense.

Thanks,

TFM

10. Mar 3, 2008

### Kurdt

Staff Emeritus
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.