The Fundamental frequency of an open organ pipe

[jen0519]

Homework Statement

The fundamental frequency of an open organ pipe corresponds to the note middle C (f = 261.6 Hz on the chromatic musical scale). The third harmonic (f3) of another organ pipe that is closed at one end has the same frequency. Compare the lengths of these two pipes.

Homework Equations

frequency = harmonic number x (speed of sound in the pipe)/(2)(length of the vibrating air column)
frequency = harmonic number x (speed of sound in the pipe)/(4)(length of the vibrating air column)

The Attempt at a Solution

I'm not sure where to go from here

 

[rl.bhat]

Hi jen0519, welcome to PF.
Your relevant equation for open pipe is correct. But for closed pipe it is wrong.
It should be
Frequency = (2n + 1)(Speed of the sound)/4(length of the vibrating air column.)

 

[Stonebridge]

It's normal to express this as
For the open pipe
Frequency= n(v/2L) where n=1,2,3,etc
For the closed pipe
Frequency=n(v/4L) where n=1,3,5, etc
or
Frequency=(2n-1) (v/4L) where n=1,2,3, etc
L is length of the pipe, v is speed of sound in the pipe