# The Fundamental frequency of an open organ pipe

• jen0519
In summary, the fundamental frequency of an open organ pipe corresponds to middle C (261.6 Hz) and the third harmonic of a closed organ pipe has the same frequency. For open pipes, frequency is determined by the harmonic number and speed of sound divided by twice the length of the pipe, while for closed pipes it is determined by the harmonic number and speed of sound divided by four times the length of the 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

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.)

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

## What is the fundamental frequency of an open organ pipe?

The fundamental frequency of an open organ pipe is the lowest frequency at which the pipe can vibrate and produce a standing wave pattern. It is also known as the first harmonic.

## How is the fundamental frequency of an open organ pipe determined?

The fundamental frequency of an open organ pipe is determined by the length of the pipe and the speed of sound in the medium, usually air. It can be calculated using the equation f = v/2L, where f is the frequency, v is the speed of sound, and L is the length of the pipe.

## What factors affect the fundamental frequency of an open organ pipe?

The fundamental frequency of an open organ pipe is affected by the length of the pipe, the speed of sound in the medium, and the boundary conditions. It is also affected by the density and temperature of the medium, as well as any obstructions or openings in the pipe.

## What is the relationship between the fundamental frequency and the harmonics of an open organ pipe?

The fundamental frequency of an open organ pipe is the first harmonic, and the higher harmonics are integer multiples of the fundamental frequency. This means that the second harmonic is twice the frequency of the fundamental, the third harmonic is three times the frequency, and so on.

## How does the fundamental frequency of an open organ pipe relate to the pitch of the sound produced?

The fundamental frequency of an open organ pipe determines the pitch of the sound produced. A higher fundamental frequency will result in a higher pitch sound, while a lower fundamental frequency will result in a lower pitch sound. The harmonics also contribute to the overall tone and timbre of the sound.

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