# Homework Help: PVC Open Pipe Organ Help

1. Nov 27, 2011

### itsbert

PVC Open Pipe Organ...Help!!

1. The problem statement, all variables and given/known data

Urgent
As part of an assignment, I need to create an open pipe organ that plays two different octaves. I don't know anything about octaves or music, but Google defines octave as :
A series of eight notes occupying the interval between two notes, one having twice or half the frequency of vibration of the other.
So, I need two different sets of eight notes, with each higher note double the frequency of the previous. I am constructing this with 2" PVC pipe from a local home improvement store.

I plan on cutting the PVC into different segments to create each frequency. I'll hit the top of each PVC with a drumstick to create the sound (vibrations) needed to produce each frequency.

So, octaves should I try to hit with the 2" PVC? I can also buy a different diameter PVC if necessary. I researched this and found the formula, but I still am a bit confused (again, I don't know anything about music).

Does the plan sound right (hitting the top of each pipe segment with a drumstick?

2. Relevant equations

Harmonic series of an open pipe organ
Frequency = Harmonic number * (speed of sound in pipe)/2(length of vibrating air column)

3. The attempt at a solution
How would I determine which harmonic number to use? My textbook didn't explain this well. Also, the speed of sound would be approximately 345m/s (we're on Earth)

Which frequency would I attempt to achieve for each note? Also, how does the diameter of my pipe affect this? --> I don't see a place in the formula for you to change the diameter of each open pipe.

Last edited: Nov 27, 2011
2. Nov 27, 2011

### physicsvalk

Re: PVC Open Pipe Organ...Help!!

Do you know how a flute works? You can cover different holes with your fingers and produce notes. If you cover a certain combination, then you can receive a frequency that is twice the frequency of the fundamental. Try using a concept similar to this (since it works so well, haha) to your instrument. You'll have to do some intricate math to find out what lengths and frequencies work best.

Also note that the speed of sound you listed (345 m/s) heavily depends on air density and temperature. Try to give yourself some buffer space (like placing a number of small holes along a line parallel to the pipe) so you can find the right frequency.

3. Nov 27, 2011

### itsbert

Re: PVC Open Pipe Organ...Help!!

I'm newbie when it comes to music, so forgive me if I ask some introductory questions.

Wouldn't the frequency created depend on the width of the pipe? How would this come into play?

And, which two octaves should I attempt to hit with 2" PVC? Should I buy a different diamater PVC for a different octave?

About the flute suggestion: I could try this, but I need to be able to play a melody/song.. and it might get confusing if I did this as to what holes to cover/keep open at specific times...you know what I mean?

I don't mind cutting extra PVC as long as I can accurately determine the length to cut it at, to create each octaves. Using this, I believe I need 16 pieces. 8/octave. Higher octaves (less pipe used) seem to be the most cost-effective and least time-consuming way to complete the project.

If this helps: The pipe organ will be played in a temp. of 69*F, altitude of 1060 ft (what Wiki says is the altitude in my city), in the Midwest

4. Nov 27, 2011

### physicsvalk

Re: PVC Open Pipe Organ...Help!!

This source should answer some of your questions: Standing Waves - The Physics Hypertextbook

I'm not an expert in sound, and we know that most physicists are infamous for over-simplifying problems. I am not 100% confident that frequencies depend on the thickness of a pipe, but most physics problems ignore this and I, having practiced them for many years, do not believe that the thickness of a pipe affects the frequencies it can play.

So, I don't think the thickness of the PVC pipe matters. What matters is how long it is. Most lightweight wind instruments are between 1-2 ft in length. This is what affects your frequency, and wavelength.

Your wavelength depends on the length of your pipe (see the link above for a more detailed explanation). The frequency depends on the note. The speed the wave propagates depends on the speed of sound. In short,
$$v = fλ$$
Where v = speed of sound, f = frequency, λ = wavelength.

The flute suggestion was just a note, you can try to use that to determine how far from the edges you should place the hole. I suggested multiple holes so you can test each one.

5. Nov 27, 2011

### PeterO

Re: PVC Open Pipe Organ...Help!!

A drum stick is not to be recommended - you are trying to excite the air in the pipe. A flat piece of rubber which completely covers the end of the pipe is best.
We have simple rubber summer shoes that we call thongs, but many cultures call "flip-flops" and I am sure there are other names. They make perfect strikers.

When you strike the end of the pipe, you will hear the fundamental - also called the first harmonic or harmonic #1.

http://en.wikipedia.org/wiki/Thongophone

You no doubt have a formula relating the length of the pipe to the frequency you want.
The length of the pipe in the formula means effective length, so you need to take account of end correction. This will mean the physical length of the pipe will be slightly shorter than the formula predicts.

If you make your organ with two pieces of pipe which fit snugly over each other - so one with an outside diameter of 50cm while the other has an inside diameter of 50 cm, you would be able to make an adjustable length pipe that can be adjusted slightly to achieve the actual frequency you want.

Note that if you had one set of open pipes, and another set of pipes closed at one end [stopped pipes] exactly the same length - those stopped pipes would sound at half the frequency of the open pipes - that means an octave lower.