For the project we were asked to build a trio of working instruments that function well, and that can play a scale. We needed to have one percussion instrument, one wind instrument and one string instrument. My group decided to build a standup base, chimes, and the combination of a trumpet/recorder. In the end we had to have three functional instruments that each played a scale, and we needed to talk about the physics behind each instrument. This project seemed easy in the beginning but proved to be harder as we got farther along.
Instrument Descriptions
Physics For Our Bass
Our bass consists of three functional parts: the string, the body, and the base. To produce sound we pluck the string while applying pressure on the base. By using different amounts of force on the base we can alter the tension of the string therefore changing the note. The reason sound emanates from the instrument is because the string is vibrating through the air. As it vibrates, sound waves are created that have a wavelength of roughly two times the length of the string because the string creates half of a standing wave at a time. We can change the length of the vibrating string by holding it against the neck. This lets us have a full scale of notes with only one string. The string itself is small so it does not produce a very loud sound. To amplify the notes, we created a metal body that vibrates as the soundwaves from the string hit it. This causes the metal to vibrate, greatly increasing the volume of our instrument. The length of the string affects the pitch, or note, of our instrument. Our task is to create a musical instrument that is capable of playing a full scale and describe the physics behind it. Our bass was designed with one string to make it easier and less complicated to find and play the notes in the scale. To find the starting note we needed to infer how long the string needed to be. We tested various lengths of strings and researched how long it needed to be to play a note specifically in the second octave. We saw in our research that to play a lower note such as an A2 seen below, it must produce a wavelength of 314 Hz, making a very low note. To achieve this pitch we used a 162 cm long string. The string produces half of a standing wave with each vibration so the string had to be half of the wavelength of the pitch we wanted to make with the bass. Cutting down the string or simply stopping the vibration at certain points on the string changes the length, creating higher notes as you move your finger down. The low notes vibrate slower because the string is longer, creating a larger wavelength and a lower note. Similarly, a shorter string vibrates faster, producing a smaller wavelength and a higher pitch. Using this knowledge we were then able to mark the lengths that we needed to hold the string at to make each note in our scale. The lowest note was A₂, made by letting the string ring open. The highest note was A₃, made by cutting the string in half. Through this data we proved that the length of the string changes the tone of the note. We saw in our testing that the larger the wavelength became, the lower the note became and the shorter the wavelength became, the higher the note became accordingly.
Physics For Our Chimes
Our chimes consist of a row of metal pipes cut to varying lengths. When hit, each one makes a different note on the C phrygian scale from D₅ to D₆. They are held up by string and rubber bands stretching across the frame to suspend them in midair. This let the pipes resonate as opposed to sounding harsh and staccato if they had been resting on a hard surface. That is because the sound is produced by the vibration of the metal. To create the right note, we first figured out the natural frequency, or resonance of the pipe we were using. Then we applied the chime ratio to find each other note The length of the chime directly affects the note produced. We started out by cutting a pipe at 30 cm and finding what note it resonated at. From this point we multiplied or divided by the ratios in the table below. These ratios are all based off of the fact that a chime √2 shorter makes a note exactly one octave higher. As we found, longer chimes create lower pitches while shorter chimes create higher pitches. This is because the air in the longer chimes has to travel further before escaping the tube. Also explaining why hitting chimes at different points give different notes but hitting in the middle gives the correct note. Once we identified the starting note we simply multiplied by the correct numbers in the table below to create our scale.
Physics For Our Trumpcorder
Our trumpcorder produces sound from the vibration of the player’s lips on the mouth piece. The vibrations then travel through the body of the trumpet, a tube. Those vibrations then leave the instrument through the bell. The bell serves to amplify the sound waves traveling out of the instrument. We can change the pitch in two different ways. The first is by changing the shape of the musician’s mouth and tightness of the lips. The second is by covering different holes along the instrument's body. By letting out air through these holes the notes either goes up or down. In our instrument, the more holes we plug, the higher the note becomes. In order to play all the notes of the scale on the trumpcorder correctly we had to drill holes at specific positions. We had a test model that we used to find the scale, because the standard method of finding the positions of the holes did not work for our instrument. Normally you could simply divide by ¼ of the wavelength, but this did not apply to the instrument we made. The frequency of the note being played was not on the scale we were trying to make. Through our tests we found where we wanted the fingerings to be to play the notes. It plays the a C major scale starting at C₄ and goes up to a C₅ We noticed this fact when we were testing holes on our practice model. We heard that the more holes we plugged in the higher pitch the note was. This was given that the same lip position was used for every hole. Also, in our table we saw the wavelength of each wave got smaller for the more holes we plugged in. In the table, the notes we played that were higher are the ones that filled the most hole positions. The evidence shows that the more holes you fill on the trumpet with the same lip tightness the higher the note will become. We found multiple times in our research and saw in the table we made how the wavelengths changed. We noticed that the more holes we plugged the shorter distance the air had to travel creating a higher frequency, or higher pitch note. Finding and understanding the physics of this instrument was tricky. We saw that there was so many factors to why it creates the notes it does. The first factor is tube length and thickness. This factor plays a key role in what octave you want your instrument to play. We chose a 66cm pipe which plays a C₄ and a relatively thin tube. If we had chose a different length pipe we would have been in a completely different octave altogether. The second factor was hole placement. In order for us to play the six notes in the scale that needed to have fingerings, we needed to figure out where the holes needed to be. For our instrument to find the holes, we did not use a formula, because that did not correspond with our design. Instead we chose to have a practice trumpet which we used to find the correct scale and notes. We originally knew that the holes changed how the air traveled, causing a change in wavelength. Having not precise calculations for the placement of the holes affected how we found what each note frequency was, and ultimately what note it plays. This made the tuning process infinitely harder. The third factor is the emberture. The emberture of the player changes how the trumpcorder plays, therefore making the physics very complicated. The wavelength can change depending on how your lips are placed. There are many different lip positions that can play the same note octaves and octaves higher. The more your lips vibrate and the tighter they are, changes the frequency of the note, creating either higher or lower notes.
Physics Concepts
Types of waves: -transverse: movement perpendicular to wave direction, don't require a medium -longitudinal: movement parallel to wave direction, require a medium
Parts of a wave: -crest: high point in a wave -trough: low point in a wave -amplitude: distance from crest to equilibrium -equilibrium: mid line of a wave -wavelength: distance from crest to crest, trough to trough, etc. -frequency: how many waves occur in a second -velocity: speed of a wave
Reflection
This was a very successful project for me and my group. We came up with three instruments that all worked great. It was a hard task but we got it done without any disagreements. We all contributed ideas into building our instruments and we were open minded about what everyone had to say. I think I could have helped my group more by typing more of the presentation. Our group could have improved on our time management. In the beginning we spent so much time on the chimes that we had little time to make the trumpcorder and the upright base. One day we were missing two members of our group and literally nothing got done. We could have used this time to tune the instruments or type of our presentation. Our group did have good work ethic. Everyone contributed, and we made there instruments that worked good, sounded good, and looked good. Everyone worked together well and we all got to learn a lot about sound.