Harmonics in an Organ Pipe

In summary, the correct frequencies for the lowest three harmonics produced by an organ pipe that is 1.70 m long and open at one end and closed at the other are 50 Hz, 150 Hz, and 250 Hz, using the equation F = m * (v/4L) where m = 1, 3, and 5 respectively. The speed of sound is 340 m/s.
  • #1
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Homework Statement


An organ pipe is 1.70 m long and it is open at one end and closed at the other end. What are the frequencies of the lowest three harmonics produced by this pipe? The speed of sound is 340 m/s. Only one answer is correct.
200 Hz, 400 Hz, 600 Hz
200 Hz, 300 Hz, 400 Hz
200 Hz, 600 Hz, 1000 Hz
50 Hz, 100 Hz, 200 Hz
100 Hz, 200 Hz, 300 Hz
50 Hz, 150 Hz, 250 Hz
100 Hz, 300 Hz, 500 Hz
50 Hz, 100 Hz, 150 Hz


Homework Equations





The Attempt at a Solution


I am not really sure how to calculate these?
 
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  • #2
Do I use...
F = (V/2L) = 100 Hz
F = (V/2L) * 2 = 200 Hz
F = (V/2L) * 3 = 300 Hz
So my answer would be...
100 Hz, 200 Hz, 300 Hz
 
  • #3
No Wait if it's open-closed it would be...
F = (V/2L) = 100 Hz
F = (V/2L) * 3 = 300 Hz
F = (V/2L) * 5 = 500 Hz
So my answer would be...
100 Hz, 300 Hz, 500 Hz
 
  • #4
Oh no wait...lol...thats not the right equation is it? It should be...
F = m * (v/4L), m = 1, 3 5
so I get...
50 Hz, 150 Hz, 250 Hz
is that right?
 
  • #5
For a pipe that's open at one end and closed at the other, you'll want to use [tex] \lambda = 4L[/tex] for the first harmonic, [tex] \lambda = 4L / 3[/tex] for the second harmonic, and [tex] \lambda = 4L/5 [/tex] for the thrid harmonic, using [tex] f = v / \lambda [/tex] for the frequency.
 

1. What are harmonics in an organ pipe?

Harmonics in an organ pipe refer to the multiple frequencies that can be produced by a single pipe when air is blown through it. These frequencies are determined by the length and shape of the pipe.

2. How are harmonics produced in an organ pipe?

Harmonics are produced in an organ pipe when air is blown through it, causing the air molecules to vibrate and create a sound. The length and shape of the pipe determine which harmonics are produced.

3. Can you explain the concept of overtones in relation to harmonics in an organ pipe?

Overtones refer to the higher frequency harmonics that are produced in an organ pipe. They are generated in addition to the fundamental frequency and give the sound its unique timbre or quality.

4. How do changes in the length of an organ pipe affect its harmonics?

Changing the length of an organ pipe will alter the frequencies of the harmonics produced. Shortening the pipe will increase the frequency, while lengthening it will decrease the frequency.

5. Are there any practical applications of understanding harmonics in an organ pipe?

Yes, understanding harmonics in an organ pipe is important for tuning and designing musical instruments. It is also used in fields such as acoustics and physics to study the properties of sound waves.

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