Additionally, the way we hear and process musical sounds requires a complex biological system. The study of sound goes back thousands of years to ancient cultures-Chinese, Japanese, and Egyptian, to name a few-that invented instruments in order to create music 1. Around BC, Pythagorous of Samos invented the monochord using a soundboard and a single string draped across a stationary bridge and a movable bridge 2. By manipulating the location of the movable bridge, he discovered that when the string length was halved, the pitch produced was an octave higher.
He later concluded that small whole number ratios were the foundation for consonant sounds in strings as well as in volumes of air in pipes and water in vases. The frequency ratios for a major scale are as shown in Table 1. Table 1: Frequency ratios are from the first note in the scale to the nth scale degree.
Aristotle also studied strings and their vibrations about years later. He also established that a medium was required for sound to travel.
In , English trumpeter John Shore invented the tuning fork, a resonator that produces a single, pure tone when struck. In the s, Christian Doppler studied sounds emitted from a moving source and concluded that waves compress when the source moves toward the listener and expand when the source moves away 4. This law states that tones are composed of different combinations of simple tones of different frequencies 1. The list of modern contributors goes on. Vibrations are small oscillation disturbances of the particles in a given body, such as water or a string. Regular vibrations have a defined period, the amount of time it takes to complete a cycle, while irregular vibrations do not, like those created by snare drums or a giant wave crashing on the ocean shore 5.
Figure 1: Tuning fork vibration: three snapshots within a second.
When struck, a tuning fork vibrates at a single, particular frequency. The constant movement of the prongs back and forth causes repeated sound impulses, which are really disturbances in the air 6. The prongs hit the air, and the air continues to hit neighboring air molecules. At one instant, some molecules are close while others are further apart, a phenomenon known as condensation and rarefaction of air see Figure 1.
The more common, sinusoidal depiction of a given wave comes from an oscilloscope, an apparatus that senses the pressure from a wave and translates it into an electric signal. Instruments produce a fundamental tone, the most audible tone, as well as many additional frequencies above the pitch , known as overtones. The fundamental and the additional overtones form the series of harmonics that give a sound or pitch a certain quality.
In other words, each note sounds the way it does because the wave is a complex combination of frequencies.
7: Solids and Liquids
Musical instruments create sounds through the physical communication of a primary vibrator, resonant vibrator, and a sound effuser 7. These components provide the initial vibrations, amplify the vibrations, and allow the vibrations to escape. String instruments like the viola or cello amplify the sounds made by bowing or plucking the strings. The strings are held tightly around the pegs at one end and the tailpiece at the other end. When the string vibrates, the vibrations propagate down to the bridge, which carries them to the soundboard that spans the inside of the wooden body 8.
The soundboard amplifies the vibration, and the sound waves emerge through the two f-shaped holes. Together, they state that the frequency is inversely proportional to the length, proportional to the square root of the tension, and inversely proportional to the square root of the mass per unit length, as shown in Figure 2 1. As the string is pulled more tautly on a violin by turning the peg towards the scroll, the pitch increases, and as the musician presses on the string, the length of the string decreases and the frequency increases.
Cellos and basses have longer strings than violins and violas, which is why these larger instruments can play in a lower pitch register. While string instruments typically have four or six strings, the piano has two or three per note. An enormous amount of combined tension, up to 30 tons in a concert grand piano, compensates for the great length of the strings. Since the fundamental frequencies of the piano range from 27 Hz for the lowest A to Hz for highest C, it would be farcical to make the A1 lowest note strings times longer than the C8 highest note strings 8.
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Instead, both the tension and the length vary for each note. The piano is especially unique with its equal temperance. This allows pieces to sound pleasing in any key. The vibration of air in woodwind instruments to produce sounds comes in two categories: the edge tones of direct vibrations between the musician and the instrument, as in the flute and piccolo, and the vibration of a reed indirectly causing a sound, as in the clarinet and oboe 4.
In both cases, the player supplies the energy to cause a vibration. The molecules are set into random motion when the player blows a note, moving the sound forward within the column. Molecules in a column of air, just as in a string, have a frequency of free vibration and can be excited by matching frequencies. Similar to string instruments, the standing waves produced have a fundamental tone and many overtones.
The pitch produced by many wind and brass instruments depends on the embouchure, or shape of the mouth and tongue when creating a note, as well as the keys pressed, both of which alter the size of the column through which the air travels. Brass instruments are set up much differently. The trombone has a slide to change the size of the air column and the further out the slide, the lower the note. Trumpets have three valves: the first lowers the frequency by a whole tone, the second lowers the frequency by a half tone, and the third raises the frequency by a whole tone 4.
Again, the embouchure allows a trumpeter to create a wide range of notes. Lastly, the human voice relies heavily on vibrating air. The vocal anatomy has three key parts: the lungs for power, the vocal cords to vibrate, and the vocal tract to resonate the sounds. To produce different notes, a singer varies the tension in his or her vocal cords.
Many instruments bring together different sounds to produce rich music in an ensemble.
Vibrations Surround Us: The Science of Music
All of these waves travel through the space in which they are played, and the acoustical energy of the waves decrease with the square of the distance from their sources. For music created indoors, sound waves either reach a listener directly or after reflecting off of other surfaces and losing some energy to the surface; the nature of the surface affects how much energy is reflected and how much is absorbed.
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Vibrations Surround Us: The Science of Music – Dartmouth Undergraduate Journal of Science
Cited by. Back to tab navigation Download options Please wait Article type: Paper. DOI: Download Citation: Phys. Ciobotarescu, N. Hurduc and V. Teboul, Phys.
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