Open ended pipe Harmonics Mastering Physics Question

In summary, the conversation is discussing the calculation of the highest harmonic that can be heard by a person with a hearing range of 20 Hz to 20000 Hz in a pipe that is 45.0cm long and closed at one end. After some trial and error, it is determined that the 52nd harmonic is the closest to 20000 Hz, but the correct answer is actually the 53rd harmonic. This is because the harmonics are given by 2n-1, and inserting n=52 into this equation gives a frequency of 19684, which is the first odd number below 20000. The correct harmonic number is therefore 103. The original answer of 52 was obtained by rearranging
  • #1
TFM
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[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



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

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
 
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  • #2
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
It will be the 53rd Harmonic. The trouble is, I have put 53 in, and it says its the wrong answer!
 
  • #4
TFM said:
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,...
 
  • #5
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
 
  • #6
TFM said:
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.
 
  • #7
Success! n = 103.

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

TFM
 
  • #8
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:
  • #9
That makes sense.

Thanks,

TFM
 
  • #10
TFM said:
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:
 

Related to Open ended pipe Harmonics Mastering Physics Question

1. What is an open ended pipe?

An open ended pipe is a type of musical instrument that produces sound by vibrating air molecules inside the pipe. It is called "open ended" because one end of the pipe is open while the other end is closed.

2. How does an open ended pipe produce different pitches?

An open ended pipe produces different pitches by changing the length of the pipe or the amount of air flowing through it. By altering these factors, the speed of the air molecules inside the pipe changes, resulting in different frequencies and thus different pitches.

3. What are harmonics in an open ended pipe?

Harmonics in an open ended pipe are the different frequencies produced by the pipe when air is blown through it. These frequencies are whole number multiples of the fundamental frequency, which is the lowest frequency that the pipe can produce.

4. How are harmonics related to the length of an open ended pipe?

The length of an open ended pipe determines the wavelengths of the different harmonics it can produce. The fundamental frequency has a wavelength that is twice the length of the pipe, while the second harmonic has a wavelength equal to the length of the pipe, and so on.

5. Can harmonics be manipulated in an open ended pipe?

Yes, harmonics in an open ended pipe can be manipulated by changing the length of the pipe or the amount of air flowing through it. This allows musicians to produce different pitches and create melodies and chords on the instrument.

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