Organ Pipe Resonance - How long is the pipe?

In summary: and the wavelength would be the distance between the two antinodes, not the whole length of the pipe.yes! :smile:
  • #1
MystiqThunder
7
0

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 :!)
 
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  • #2
Hi MystiqThunder! Welcome to PF! :smile:
MystiqThunder said:
λ = 1.3122 m

Therefore, the length of the pipe is 1.3 m.

But why would the length be equal to the wavelength? :confused:
 
  • #3
tiny-tim said:
Hi MystiqThunder! Welcome to PF! :smile:


But why would the length be equal to the wavelength? :confused:

I have no idea... I just figured that is the only way to get a length.
 
  • #4
MystiqThunder said:
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?
 
  • #5
tiny-tim said:
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.
 
  • #6
MystiqThunder said:
Well I am assuming the node is on the closed end and on the open end there is an antinode.

yes :smile:

so how long is the wavelength?​
 
  • #7
tiny-tim said:
yes :smile:

so how long is the wavelength?​

Oh I see... so the whole pipe would be half a wave length. Right?
 
  • #8
MystiqThunder said:
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?
 
  • #9
one node and one antinode isn't half a wavelength :redface:
 
  • #10
tiny-tim said:
one node and one antinode isn't half a wavelength :redface:
Oh wait! It is a quarter of a wavelength!
 
  • #11
MystiqThunder said:
Oh wait! It is a quarter of a wavelength!

yes! :smile:

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

What is organ pipe resonance?

Organ pipe resonance is a phenomenon in which a hollow tube or pipe produces a musical tone when air is blown through it.

How does organ pipe resonance work?

Organ pipe resonance works by the movement of air molecules inside the pipe. When air is blown into the pipe, it creates a standing wave that causes the air molecules to vibrate at a specific frequency, producing a musical tone.

What factors affect the length of the pipe?

The length of the pipe affects the frequency and pitch of the musical tone produced. The longer the pipe, the lower the frequency and pitch. Other factors that can affect the length of the pipe include temperature, air pressure, and the material of the pipe.

What is the formula for calculating the length of the pipe?

The formula for calculating the length of the pipe is L = (n * v) / (2 * f), where L is the length of the pipe, n is a whole number representing the number of antinodes, v is the speed of sound, and f is the frequency of the musical tone.

How long is the pipe to produce a specific musical tone?

The length of the pipe to produce a specific musical tone depends on the frequency of the tone and the speed of sound. To produce a tone with a specific frequency, the pipe must be a certain length according to the formula L = (n * v) / (2 * f).

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