# Homework Help: Organ Pipe Resonance - How long is the pipe?

1. Jan 25, 2014

### MystiqThunder

1. The problem statement, all variables and given/known data
An open organ pipe has a fundamental frequency - corresponding to the first resonant length -of 262 Hz. The room temperature is 20.0°C. What is the length of the pipe. [The answer is 0.66m]

Given: 262 Hz and 20°C

2. Relevant equations
v = 332 + 0.59t
v = f λ

3. The attempt at a solution
v = 332 + 0.59t
= 332 + 0.59(20°C)
= 343.8 m/s

v = f λ
343.8 m/s = 262 Hz X λ
λ = 1.3122 m

Therefore, the length of the pipe is 1.3 m.

I realize I may be well off. Thanks for your assistance in advance :!!)

2. Jan 25, 2014

### tiny-tim

Hi MystiqThunder! Welcome to PF!
But why would the length be equal to the wavelength?

3. Jan 25, 2014

### MystiqThunder

I have no idea... I just figured that is the only way to get a length.

4. Jan 25, 2014

### tiny-tim

so the pipe has an open end and a closed end …

so where are the nodes or antinodes at this frequency?

5. Jan 25, 2014

### MystiqThunder

Well I am assuming the node is on the closed end and on the open end there is an antinode.

6. Jan 25, 2014

### tiny-tim

yes

so how long is the wavelength?​

7. Jan 25, 2014

### MystiqThunder

Oh I see... so the whole pipe would be half a wave length. Right?

8. Jan 25, 2014

### haruspex

Not quite. Think of one whole wavelength of a sine wave, but only paying attention to the magnitude at each point. It starts at 0, increases to a maximum, returns to zero, increases to a maximum again, and finally back to zero. What fraction of that does the magnitude of vibration at different distances along the pipe look like?

9. Jan 25, 2014

### tiny-tim

one node and one antinode isn't half a wavelength

10. Jan 25, 2014

### MystiqThunder

Oh wait! It is a quarter of a wavelength!

11. Jan 25, 2014

### tiny-tim

yes!!

hmm … sorry … looking at the answer, i think the question must mean the organ pipe is open at both ends​