Terms and concepts:
• Newton’s Laws of Motion
• Scalar/Vector Quantities
• Sound intensity and pressure
• Energy: potential, kinetic, heat, acoustic
• Law of conservation of energy
The scientific mind works with mathematics, the elegant language that explores beyond three dimensions and time. This is not so different from the spiritual mind, which human ancestors all over the Earth have called the heart. It, too, speaks a language that explores beyond physical dimensions and time.
While mathematics computes, the heart feels. Both math and intuition allow us to travel to worlds the eye cannot see; where time can bend or – in the case of a singularity (black hole) – even stop.
Not all realities are visible, my Haida uncles would say. We cannot see the wind itself. We can only see and hear what it does. But, this does not mean we cannot experience the wind. We can feel the wind directly. This provides our sense of mystery. This is the world of music and intuition.
Despite David Hume’s 18th century empiricism, human beings are more than the sum of five senses. Even though our physical nature has been dealt a hand of just five cards, intuition is an inner prompting that other ways of knowing exist. Something deep within us draws us toward the mysterious; toward the many cards, combinations and permutations we have not seen. Mathematics then provides the ability to predict what some of those might be. At the same time, experimentation provides the means by which we test both mathematics and intuition. Mind and heart therefore can mutually reinforce each other. They bring together the intuitive wisdom of the Aboriginal Elder and the academic discipline of the scientist.
This section deals with the physics of music. Through mathematics and the heart we learn how to sense and work with the music of the Universe; not against it. Scientists know that the disembodied strains of music that reach our ears, drifting invisibly in the air around us, are the result of the same laws of physics that govern our lives and movements in the natural world. In short, music itself is subject to the same forces that keep the Universe in balance and affect our very lives. Therefore, the “how” and “why” of music is in harmony with the laws of physics. These laws enable us to create the sounds that for many thousands of years have inspired musicians and listeners alike.
Physical properties that relate to musical instruments
Consider now, the physics of items that musicians have used to create musical sound. Among them are the skin of the drum, the strings and box of the violin, the long tube of the flute, the pebbles and hide of the rattle as well as the air with which all these parts are in contact. The following are the basic qualities possessed by every physical body: Mass, Weight, Inertia, Elasticity, (occupies a) Medium.
Mass is how much matter an object contains. The most common measurements are the gram (g) and the kilogram (kg).
Weight refers to how much force gravity exerts on an object’s mass, that is, the downward pull that keeps the body connected to the earth’s surface. The mass of an object will always remain constant, but its weight can change if this gravitational pull changes. In outer space, for example, an object keeps its mass, but becomes weightless. Its innate essence remains the same regardless of its interactions with other influences. Both scientific and Aboriginal teachings embrace this principle. The forces that change our true nature are not external. They must come from within.
Inertia is that property of a body that resists changes in its motion. If an object is at rest it will remain at rest, and if in uniform motion along a straight line, it will remain in that motion until an outside force or forces acts upon it.
So, inertia raises two possibilities:
1. If an object is not moving it will stay perfectly still until something makes it move.
2. If an object is moving in a straight line it will keep going forever unless something makes the object change its velocity or direction.
Elasticity is that property of an object that allows an outside force to deform it from its original state without breaking it. It then allows the object to return to its original state once the outside force has been removed. When anything produces a sound, elasticity plays an important role. However, elasticity does not apply to media such as air.
The medium is the material through which vibrations move from one place to another. Medium comes from the Latin word medius, which means “middle.” So, think of a medium as the middle, or go-between, for bringing vibrations from an instrument to your ears. It can be a liquid, such as water; or a gas, such as air. All musical instruments – drums, stringed instruments, flutes and others – produce the vibrations we hear as sound. The music is the sound source and air is the medium, just as for humpback whales the medium is water.
A guitar or violin string vibrates but produces little sound on its own because it does not transmit those vibrations well to the air. The string has too little surface area to move much air. Something must make those sounds louder so we can hear them as music. The guitar body, in contrast, has a lot of surface area. The strings pass over a bridge which presses onto the front face of the instrument. The string’s vibrations are thus transmitted to the guitar’s much larger body, which can make much more air vibrate than a tiny string can do. The vibrating motions of the guitar’s sound box excite vibrations in the medium, which is the air.
That is what produces the musical sounds we hear. Aboriginal musicians and scientists, when working in their respective crafts, respond to music differently. Many Aboriginal crafters probably do not try to analyze why an instrument’s body amplifies the softer sounds of strings, skins or vibrating columns of air. Scientists and physics do that. The Universe likely is big enough to encompass – and to surpass – both ways of knowing.
What science explains, the musician and the hearers experience.
Motion in Musical Instruments
To make music requires motion of either some part of the musical instrument or the air within it. Here we discuss the physical quantities related to this motion. An instrument will remain quiet until vibrations are produced in it, or as a physicist would put it: until it is disturbed from its state of rest or equilibrium. This is related to Newton’s first law of motion:
Every object in a state of uniform motion tends to remain in that state of motion unless something applies an external force.
Thus, if a musical body is initially at rest, nothing can happen until something disturbs it. Something has to move the musical body to release the sounds it can produce. Music, therefore, is an art of motion: a hand or bow exciting the strings of a violin, a stream of air from the mouth passing through the flute, a musician shaking a rattle or playing a drum.
The following terms measure and define these disturbances.
Displacement happens when a part of the musical instrument initially at rest is moved to a new position. In considering this effect, we must account for both the magnitude (the distance moved) and the direction in which the part moves.
Speed measures how much displacement occurs in a given time. Usually, we express this either by metres per second or kilometres per hour. We calculate speed, which we will call (S), by the quotient of distance (d) traveled and the time (t) the displacement took:
S = d/t
Another way to say this is speed equals distance divided by time.
Velocity is a term we often use synonymously with speed. Although we won’t deal with this here, velocity is more informative than speed alone because it indicates the direction in which the displacement takes place. Technically, speed is a scalar quantity, while velocity is a vector quantity.
Motion and sound in a musical instrument
Newton’s first law of motion works in music because an object in motion keeps going unless an opposite force pushes it back toward the other direction. When someone plucks a guitar string, for example, the opposite force might be the tension in the tightly-stretched string that wants to pull it back to its resting position. This dance between inertia, motion and opposite forces creates vibrations, which we hear as sound. In physics, these actions and how they affect the musical body are as follows:
Force is any external cause that makes a body move or, if it is already moving, changes its speed or direction. Thus, in a object such as a guitar string, a force creates an unbalanced (unequalized) condition when it alters its natural quiescent state.
A guitar string, for example, is under tension. When displaced, the string’s tension always produces a restoring force. Any force, however small, will move an object. But, to produce music the force must be sufficient to set up a large enough vibration to be audible. Lesser masses require lesser force to disturb their state of rest or uniform motion. Greater masses (thicker strings) require greater force to disturb their equilibrium.
Science has fittingly designated one unit of force as a newton (N). Although we won’t need to use the formula here, one newton equals the force required to accelerate one kilogram in a particular direction across one metre per second every second. In other words, in a frictionless world like outer space, the same force would accelerate the body in the same direction faster and faster. Every second the force would keep pushing the object a metre per second faster.
Work is what happens to a body. Work equals force times the body’s displacement in the direction the force is moving it. Unlike force, work is a scalar quantity.
In the 19th century, James Prescott Joule designed a formula to measure work. We have designated his unit as a joule (J).
Joule’s formula for work is simple. To calculate joules of work, (J), multiply the force in newtons (N) times the distance (d) a body moves in metres in the direction the force propels it. The following equation calculates work:
Formula for Work:
J = N times d
In other words, if a constant force moves a body one metre, the work that the force does (in joules) equals the force’s strength (in newtons).
Pressure equals force per unit area. Audible sound, for example, is vibrating air. Technically, sound waves are rapid changes in air pressure – usually hundreds or thousands of times per second. The formula that measures sound pressure is Newtons per square metre (N/m2). Decibels (dB) measure sound intensity level. For readers who are mathematically inclined, decibels are roughly proportional to the common logarithm of the ratio of sound pressure to that at the threshold of hearing.
Energy is the ability to do work. Every physical body has energy. This chapter discusses four types of energy that affect music: Potential, kinetic, heat and acoustic.
A body holds potential energy while at rest. The energy is dormant until something produces work that moves, drops or stretches the body. This releases the body’s energy.
Kinetic energy is what happens when an item moves. For example, if you drop a heavy weight, you are exhibiting kinetic energy (the energy of motion). Also, as the weight falls, the friction between it and the air through which the weight is moving slows it down. This friction transforms some of the weight’s kinetic energy into heat energy. Newton’s third law of motion covers this, including how a musical instrument transforms energy to sound and heat:
For every action, there is an equal and opposite reaction.
The final form, acoustic energy is vibrating air, namely, the sounds we hear as music. The law of conservation of energy says that while energy can change forms, it can neither be created nor destroyed. For example, when a musical instrument vibrates, the air picks the motion up as heat and acoustic energy, which drains away the instrument’s mechanical energy (potential energy plus kinetic energy). Physics mathematically predicts the mechanical energy the instrument loses will precisely equal the sum of the radiated acoustic energy and the dissipated heat loss.
Conclusion: The section has discussed bodies, forces and the laws that govern their interactions. All these are at play when an instrument produces musical sounds.
Again, two great cultures have interpreted the same Universe in their own way. The “Will of the Creator” and the “Laws of Physics” express the same truth. The laws of physics appear to be the same everywhere in a cosmos so huge that light travelling at nearly 300,000 kilometres per second would take billions of years to cross it.
The bottom line is that, in a manner of speaking, music will fill the Universe from the beginning to the end.