Wave Mechanics in Musical and Structural Systems

The Violin: History and Acoustic Principles

Stringed instruments of some sort have existed for millennia. There is evidence that the ancient Egyptians knew how to achieve a range of pitches using strings of varying lengths on the same instrument. For the most part, stringed instruments were plucked until the development of the bow by Islamic and Byzantine cultures in the 11th century. The violin in its modern form did not develop until the 16th century.

As with all bowed string instruments, sound on the violin is created by dragging tightened, rosined horsehair across strings of metal or gut. This rubbing of the strings creates vibrations and torsion, which in turn create sound waves in the form of pitch and timbre. Pitch is determined by three things: the thickness of the string, the tension in the string created by turning the tuning pegs, and the length of the string determined by the player placing his fingers on the fingerboard. Timbre is created by harmonic waves superimposed over the fundamental note.

The sound waves are amplified in the body of the violin, which acts as a resonant box. The energy of the vibrating strings is transmitted to the body of the violin through the bridge, a thin wedge of wood across which the strings are strung. On the inside of the violin beneath the bridge is the soundpost, which connects the front plate of the violin body to the back plate. This couples the vibrations from both sides of the body to provide amplification of the energy waves. The energy from the vibrating strings, transmitted to the body through the bridge and soundpost, creates sound waves in the air inside of the violin, which is directed through the f-holes toward the listener.

The Kettledrum: Construction and Sound Production

The kettledrum, or timpano, is one of the oldest percussion instruments in the Western tradition. It is probably Middle Eastern in origin and most likely came to Europe during the Crusades of the 12th and 13th centuries. It played a central role in the royal and religious music of the Baroque period and in the orchestral works of the Romantic era.

The kettledrum is constructed of a round membrane, known as the head, stretched over a deep, sealed enclosure. Tension in the head can be changed by a foot pedal connected to lugs that tighten or loosen the membrane. The pitch of the drum can be changed by the tension of the membrane, and the timbre can be changed by where on the head the player strikes.

A Hybrid Instrument Design

The wave mechanics of a kettledrum are somewhat complex. Sound is created by the interaction between vibrations in the air outside the body, or bowl, of the drum and the air trapped inside. When the player strikes the head with the mallet, the air mass outside the drum dampens the vibrations of the membrane itself, making for a muted fundamental note. However, the waves in the internal space bounce off the round sides of the bowl, amplifying and increasing the vibrations and creating a series of harmonics. The sound emanating from the drum is a combination of the weak fundamental note created by the vibrating membrane and the stronger series of harmonics created by the bowl and the vibrating air inside it.

A hybrid instrument can combine elements of stringed and percussion instruments. It features a drum with a hollow, bowl-shaped body set upon a pin like a cello, with a fingerboard extending up, also like a cello. The bowl is made of copper or some other easily bendable metal capable of resonating, with a steel rim to keep the shape of the bowl intact against the tension of the strings. Across the rim is stretched a very thin membrane of calfskin. On both the top and the bottom of the rim are wooden bars about two inches wide and one inch high, across which are stretched five strings of varying thickness made of gut or metal. The strings extend up over the length of the fingerboard and are wound on pegs that can tighten or loosen them. The instrument is held upright like a double bass, and the strings are played by a bow of rosined horsehair. The player controls pitch by choosing which thickness of string to play and placing his fingers on the fingerboard to change the length of the string.

The sound of the instrument is created by two sets of vibrations. The first is the very weak set of sound waves created by the vibrating strings themselves when the friction of the rosined horsehair pulls against the tension of the strings. This vibration, however, is not enough to produce a rich timbre. This is the reason for the drum-shaped body. The energy of the string vibrations travels through the wooden bars and sets in motion the second set of vibrations in the body of the instrument. The thin membrane translates the vibrations of the strings traveling through the wood into vibrations in the air inside the body of the bowl. As they bounce back and forth within the bowl-shaped body, the frequencies of the vibrations resonate with one another and the sound waves become amplified, much like in the kettledrum. The result is a series of harmonics superimposed over the fundamental notes played by the vibrating strings, creating a rich, resonant timbre.

The Doppler Effect and Cosmological Discovery

The Doppler Effect is when light or sound waves change as they come close to or move away from an observer. In sound, the effect is heard as a change in pitch. As the sound gets closer, the pitch becomes higher, and as it moves away, the pitch becomes lower. This effect is caused by the movement of the object making the sound: as the object moves closer to the observer, it pushes the sound waves in front of it. This increases the frequency with which the listener hears the sound, and therefore the sound presents as a higher pitch. As the object moves away, the sound waves spread out, creating a lower frequency and a lower pitch.

The same thing happens with light, but instead of hearing a different pitch, the observer sees a different color from the higher or lower frequency of the light as it moves toward or away from him. Light with a high frequency appears on the blue end of the spectrum, while light with a slow frequency appears on the red end of the spectrum. Astronomers can use the Doppler Effect of light to make conclusions about in what direction and how fast stars are traveling. When observing stars, astronomers can see either "blueshift" or "redshift." Blueshift means that the light waves have a higher frequency, so the stars are moving toward Earth. Redshift means the light waves are moving at a slower frequency, so the stars must be moving away from Earth.

The Doppler Effect revealed profound implications for the nature of the universe. In 1923, Edwin Hubble discovered that, with the exception of stars within the Milky Way, all of the stars in the universe show the redshift of light waves. This means that all of the stars in the universe must be moving away from Earth. If all of the stars are moving away, the universe itself must be expanding. It was this discovery of the Doppler Effect in starlight that led to the Big Bang Theory.