The concept of the fundamental frequency is integral to understanding music. This term refers to the lowest tone or pitch a musical instrument can produce.
In terms of music theory, the fundamental frequency of a musical note is defined as the steady frequency of oscillation of a musical instrument’s sounding body, which creates the sound.
In other words, it is the lowest tone or pitch that a musical instrument can produce when it is in its normal state. The fundamental frequency depends on several factors, including the length and thickness of the instrument and material it is made out of.
Theoretically, any object could produce a fundamental frequency, as everything has some sort of vibration within it. However, not all objects are able to produce sound that is discernible as a note by the human ear. This is because the object may not have enough structural integrity to vibrate at a sufficient level.
Calculate the new fundamental frequency
Once you have the new length of the pipe, you can calculate the new fundamental frequency of the pipe. The new fundamental frequency is found by dividing 1 by the new length of the pipe.
For example, if you cut a one-meter-long pipe in half, the new fundamental frequency of that pipe will be one hertz. One hertz is equal to one cycle per second.
One second is also equivalent to approximately ninety-nine cycles of waves moving through the water in the pipe. This is because there is one complete up and down motion of the water in the pipe per second.
The number of hertz can be determined by finding out how many waves are passing through the water in the organ pipe every second and dividing that number by one thousand. One thousand is just a general average number, it does not necessarily represent exactly one thousand individual waves passing through every second.
Organ pipes are designed to produce several different frequencies at the same time
In the case of the organ pipe, there are three main frequencies that can be produced at the same time. These are called the fundamental frequency, the first harmonic frequency, and the second harmonic frequency.
The fundamental frequency is the lowest tone that can be produced by the pipe. The first harmonic is one octave higher, and the second harmonic is one octave and a half higher.
When all three of these frequencies are heard at once, it creates a more rich and full sound. This is what makes the organ sound like an organ!
Removing any of these frequencies will change the sound of the pipe drastically. If only the fundamental frequency is left, then it will sound like a whistle instead of an organ pipe sound.
The fundamental frequency is the first harmonic produced by the pipe
When the pipe is cut in half, the fundamental frequency of the whole pipe changes, but so does the amplitude. The width of the pipe changes, so does the length of the pipe.
With these changes comes a change in amplitude and frequency. The smaller pipes will produce higher frequencies because of their width and shorter length.
Higher frequencies mean that there are more cycles per second. With narrower pipes, there are more cycles per second as well. This is why when the organ pipe is cut in half, the new fundamental frequency is higher.
When half of the organ pipe is removed, there is less air resistance within the pipe. This allows more energy to escape and decrease its pressure. By cutting the organ pipe in half, it allows for lower pressure at its base, which causes lower frequency sounds to be produced.
The higher harmonics produced by the pipe affect the fundamental frequency as well
In addition to the effect of the length of the pipe, the higher harmonics produced by the pipe affect the fundamental frequency as well.
As we’ve seen, these higher harmonics are produced by dividing the length of the pipe into a certain number of parts and then vibrating them. The more parts there are, the higher the harmonics will be.
Theoretically, there is no limit to how many parts can be divided. Therefore, there is no limit to how high harmonic frequencies can be produced.
In practical terms, however, there is a point at which adding more divisions will no longer significantly increase harmonic frequency. This is due to practical limitations in manufacturing—it is hard to make parts with very fine edges, for example.
When these edges are too fine, they may also have an effect on how sound waves travel through the pipe, which may negate some of the lower harmonics.
Cut the pipe in half and place it next to the original one
A new pipe can be made by cutting the original pipe in half and placing the halves next to each other. This creates a new, shorter pipe with the same diameter.
The length of the new pipe is determined by how far down the original length of pipe is cut. The shorter the new pipe is, the higher-pitched it will be.
By adding more of these pipes together, you can create a set of pipes that go down several octaves. By making the pipes shorter and adding more of them, you make the song lower-pitched.
The ratio between the length and diameter of a pipe directly affects its fundamental frequency. The lower the number is, the lower-pitched it will be. Changing this number will not affect the size of the pipe, but rather what note it plays at.
Find a new location for your organ pipe
Once the fundamental frequency has been identified, it is time to find a new location for your organ pipe.
If you are able to find a new place to live where you can devote time to music, then by all means, do so! Start a band with your friends or go to music school—any of these options will do.
But if you can’t, then start investing in music equipment, books, and other educational materials to learn how to make your own music. There are plenty of ways to do this on a budget, so don’t worry about spending too much.
The most important thing is that you invest in yourself and your passion for music.
Ask yourself why you want to know this in the first place
If you know the fundamental frequency of something, you can understand how it changes if you alter it.
If you know the fundamental frequency of a musical instrument, for example, you can understand how to play songs on that instrument by understanding its notes. You can also understand how to write songs based on the notes of the instrument.
The same goes for any object: If you understand its fundamental frequency, you can understand how it will change if its shape is altered.
By knowing the fundamental frequency of an organ pipe, for example, researchers were able to prove that cutting the pipe in half would not significantly lower its sound. This is because the length and thickness of the pipe offsets any changes in length due to being cut in half.
Research different types of organ pipes and their frequencies
Once you have determined the fundamental frequency of your pipe, you can start experimenting with different types of organ pipes.
If you have access to a wide range of organ pipes, try playing different fundamental frequencies on different pipes to see what sounds good. This way, you can experiment with what sounds best.
You can also try experimenting with the thickness of your pipe as well as the length. These two factors affect the frequency of your pipe, so testing them out will give you new fundamentals.
Another thing to experiment with is cutting your pipe in half. If your pipe is too long, or if it is made of a thick material, then cutting it in half will create a new fundamental frequency.
