Open ended pipe Harmonics Mastering Physics Question

[TFM]

[SOLVED] Open ended pipe Harmonics Mastering Physics Question

Homework Statement

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?

Homework Equations

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

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

 

[Kurdt]

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]

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

 

[Kurdt]

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:

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

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

 

[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

 

[Kurdt]

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]

Success! n = 103.

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

TFM

 

[Kurdt]

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

 

[TFM]

That makes sense.

Thanks,

TFM

 

[Kurdt]

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.