Organ Pipe Resonance - How long is the pipe?

[MystiqThunder]

Homework Statement

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

Homework Equations

v = 332 + 0.59t
v = f λ

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 :!)

 

[tiny-tim]

Hi MystiqThunder! Welcome to PF!

λ = 1.3122 m

Therefore, the length of the pipe is 1.3 m.

But why would the length be equal to the wavelength?

 

[MystiqThunder]

Hi MystiqThunder! Welcome to PF!


But why would the length be equal to the wavelength?

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

 

[tiny-tim]

An open organ pipe has a fundamental frequency - corresponding to the first resonant length -of 262 Hz.

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

so where are the nodes or antinodes at this frequency?

 

[MystiqThunder]

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

so where are the nodes or antinodes at this frequency?

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

 

[tiny-tim]

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

yes

so how long is the wavelength?​

 

[MystiqThunder]

yes

so how long is the wavelength?​

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

 

[haruspex]

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

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?

 

[tiny-tim]

one node and one antinode isn't half a wavelength

 

[MystiqThunder]

one node and one antinode isn't half a wavelength

Oh wait! It is a quarter of a wavelength!

 

[tiny-tim]

Oh wait! It is a quarter of a wavelength!

yes!

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