Do It Better
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For my Do it Better Project I decided to make my Build a Band Project better. I play guitar, so I wanted to understand how harmonics work, not just how sound is created by a vibrating string.
Guitars are a type of string instrument. String instruments produce sound waves by vibration of the string. There are many different ways to create different notes including frets and different strings. The string length, string tension, and string thickness are all factors of the pitch and sound of the note being produced by the guitar. The string length of the string relates to the note because half of the wavelength of the note you are trying to produce. The string tension relates to pitch because if you tighten a string it causes the frequency to go up which causes the pitch to become higher. All of the elements of a guitar for example the string, box, and the air in the sound box vibrate and force nearby air particles into vibrational motion. Therefore a guitar creates sound using forced vibration.
However when you play a guitar you don't always make music just by plucking an open string. Usually you use the frets to make different notes by compressing the string. I decided to explore how physics relates to playing harmonics on a guitar.
First I did some research by watching videos on harmonics and standing wave patterns.
Harmonics relate directly to the standing wave patterns that can be created on a guitar sting. The goal of my project was to investigate which standing wave patterns could be produced on a guitar string by playing harmonics.
Since I completed this project at home during the shelter in place, I could not build a guitar to do the experiment, so I used my own guitar.
A standing wave can be created on a string when it is fixed at two points. This happens on a guitar because the string is fixed at the bridge and the nut which are the two horizontal white lines seen below
When you pluck an open string on a guitar (only fixed at the bridge and the nut), you get the first or fundamental harmonic. That has a standing wave that looks like the first wave in the diagram below. A standing wave is when a wave is reflected and inverted at a fixed point and the waves going both directions add and cancel each other out (constructive and destructive interference) to create a standing wave pattern. This only occurs at certain frequencies of vibration. What these frequencies are is different depending on the length of the string and therefore the wavelength. Frequency is inversely related to wavelength. If you compress a guitar string in the middle of the string, that will create another node or fixed point creating the second harmonic. This is the second wave pattern shown below.
For this experiment, I started by measuring the length of the guitar string: 66 cm. Then I measured to the halfway point of the string at 33 cm. This corresponded to fret 12. I also wanted to create the third and 4th standing wave patterns so I also measured the third way point (22cm which corresponded to fret 7) and the quarter way point (at 16.5 cm which corresponded to fret 5).
I planned to measure the frequency of the note played compressing the string at each of these frets. Doing this decreases the wavelength and should increase the frequency. I used a chromatic tuner that could measure frequency, but it turned out it could only recognize frequencies of the open string which is the first harmonic. (Photo below for open string 1 with stand guitar tuning) So I had to come up with another way of determining the frequency of the other harmonics. I measured the frequency of the first harmonic for strings 1, 2, 3 and 4. Using this information I was able to calculate the frequencies of the 2nd, 3rd, and 4th harmonics. I was then able to test this by comparing the values to a table which shows the frequency for guitar notes. (Tables below)
Data
Content
Energy is transferred in the form of waves and there are models to predict how the energy is transferred.
Velocity=Frequency x Wavelength or v=f𝝺
Frequency: Frequency is the number of occurrences of a repeating event per unit of time
Wavelength: The distance between successive crests of a wave, especially points in a sound wave or electromagnetic wave.
Wave Speed: Wave speed is the distance a wave travels in a given amount of time
Amplitude: The maximum extent of a vibration or oscillation, measured from the position of equilibrium. The maximum difference of an alternating electrical current or potential from the average value.
Standing Waves: a standing wave, also known as a stationary wave, is a wave which oscillates in time but whose peak amplitude profile does not move in space. The peak amplitude of the wave oscillations at any point in space is constant with time, and the oscillations at different points throughout the wave are in phase.
Interference: When two waves meet in such a way that their crests line up together, then it's called constructive interference. The resulting wave has a higher amplitude. In destructive interference, the crest of one wave meets the trough of another, and the result is a lower total amplitude.
Nodes: Nodes are points of no motion in standing waves. An antinode is the location of maximum amplitude of a standing wave.
Harmonics: The set of all possible standing waves are known as the harmonics of a system.
In this experiment, I needed to use knowledge of standing waves, wavelength, and music to determine frequency of the different guitar string harmonics. By decreasing the string length by half by pressing fret 12 for example (second harmonic), wavelength decreased by 50% and frequency doubled. This is because of the inverse relationship between frequency and wavelength.
Reflection
Two things I did well during this project were finding my way around problems and sticking with a certain idea. Two things I want to work on next project are getting even better at problem solving and getting better at teamwork since I didn't have a chance to work with teammates on this project. I also probably need to work on my guitar building skills still.