# Homework Help: Harmonics in an Organ Pipe

1. Nov 27, 2007

### BuBbLeS01

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

2. Relevant equations

3. The attempt at a solution
I am not really sure how to calculate these?

2. Nov 27, 2007

### BuBbLeS01

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. Nov 27, 2007

### BuBbLeS01

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. Nov 27, 2007

### BuBbLeS01

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. Nov 27, 2007

### hotcommodity

For a pipe that's open at one end and closed at the other, you'll want to use $$\lambda = 4L$$ for the first harmonic, $$\lambda = 4L / 3$$ for the second harmonic, and $$\lambda = 4L/5$$ for the thrid harmonic, using $$f = v / \lambda$$ for the frequency.

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