Although there are many reasons why music serves as a good context for learning physics, as will be discussed below, many of you may be asking yourselves why do non-scientists need to study physics, at all. On the one hand, we expect a lot from science. We want technology that works flawlessly and simple answers from science especially in medicine or the environment. If we have an illness, we want a specific diagnosis and an effective treatment. We also expect our computers to turn on and run wonderful sophisticated programs. On the other hand, many of us give little thought as to how science produces knowledge and technology. We are inspired and dazzled by close-up images of Mars taken by a small spacecraft millions of miles away, but we really have no idea how this can happen. Even scientists in one field have little understanding of other specialized fields. But more importantly, the general public has little understanding of the conceptual framework that allows thousands of scientists and engineers to work together to generate this image of Mars. A course on science for non-scientists will hopefully bridge this gap.

If the goals of this course are achieved, you will have a much greater appreciation of science. Modern medicine and modern computers are mind bogglingly complex. No one person understands everything about either. Yet, somehow a space station can be constructed high above the Earth or a heart can be transplanted from one human to another. Both rely on a vast amount of knowledge gained over many years by scientists who have probably never spoken directly with each other and most of the time were not even aware of each others work. How can so much information be organized into something as complex as a space station, especially when one individual can only understand a tiny piece of the whole process? This, ultimately, is the best definition of science: science is a system for combining information in a rigorous way that allows us to create useful devices and structures much bigger and greater than anyone one of us could conceive of individually.

Another valid reason to understand something about science is that many arguments or advertisements are presented as scientific even if they have no scientific basis. Some recent examples of this include the dangers of cancer from electric power transmission lines, magnetic therapy and "Vitamin O." While there is no scientific evidence for the dangers or benefits of any of these, they have been presented in the media as having a scientific basis. In the case of vitamin O, it has been claimed that water can be enriched with oxygen and drinking this enriched water can supply extra oxygen to athletes to boost performance. While it is true that water contains oxygen the amount is insignificant compared to the amount that we take in in every breath, but more importantly, the amount of oxygen in water cannot be enhanced. Thus, some understanding of how science works is needed to begin to distinguish between solid science and false claims phrased in a scientific manner.

Finally, in a more general sense, the purpose of a college degree is to teach you skills that will be used later in your life. Among those skills is logical/rational/quantitative thinking. Often people take this ability for granted. When a group of people are betting on the outcome of a sports event, there is usually intense discussion about how the teams are doing, who is on which teams, exactly how will the scores differ and how much is one willing to stake on their analysis. This involves all levels of rational thought. Or, another example is buying a house. One must make many decisions: how much is the house worth, how much can one afford, what is an acceptable mortgage interest rate, etc. However, what is ironic is that as much as people want the ability to make strong arguments and be listened to, they often don’t want to make the effort to develop this ability. Like any skill, logical reasoning can be learned and practiced, as long as we accept that it is not an impossible challenge. Even if we will not become an Einstein, there is still a value to enhancing our scientific skills.

We now return to the main question posed in this Chapter: why use music to learn about physics?

Many aspects of music require an understanding of physics. Musical instruments are constrained by the laws of physics and the development of instruments could not have progressed without the knowledge gained through the study of physics. For example, the modern grand piano is a marvel both of aesthetic beauty and engineering. It simply could not have been built before the eighteenth century because it required the current knowledge of mechanics and state-of-the-art technology. As another example, a sculptor at the University of Connecticut builds ethnic musical instruments for their aesthetic beauty, but he also wants them to sound beautiful. However, to make the latter goal a reality, he ended up having to learn a great deal of physics, otherwise the instruments would simply not have sounded good.

Auditorium acoustics is still an active field of research. As many musicians are quite aware, it is still hard to design a good concert hall.

Lastly, music is greatly influenced by how the ear and the brain actually perceive sound. The ear is a highly complex mechanical device that demonstrates many principles of physics. Understanding hearing perception definitely relies on knowledge gained from physics.

Incidentally, these topics are generally those covered in traditional courses on the Physics of Music course. Although we will discuss them to some extent, music has much more potential for introducing physics than this.

The origins of both music and science go far back in time and have always been closely related, perhaps even back to the Neanderthals! A few years ago, a bone was found in a Neanderthal site. The remarkable observation was that the bone had several small holes cut into it. The holes were all the same size, but the spacing of the holes was not. In fact, after some analysis it was found that the hole spacing was consistent with the spacing in a modern flute or recorder. In other words, the bone may have been a prehistoric flute! So even for the Neanderthals, technology (making precise holes) was used for musical goals. [See www.greenwych.ca/fl-compl.htm for a description of the Neanderthal bone.]

There was a similar connection between music and science/technology for the ancient Greeks. It is no accident that musical instruments and scientific instruments share the same word: for the Greeks they had the same meaning. The Greeks developed the first organ around 300 BC. However, this ‘musical’ instrument was really a demonstration of their understanding of physics principles and was considered to be - a ‘scientific’ instrument.

This analogy between music and science is also valid in other ways. Both music and physics have many layers and great depth, but this is not always appreciated. Often, when we look at some endeavor unfamiliar to us, it may, on the one hand, appear impossible that we could ever become good at it. On the other hand, it is easy for us to think that it must come "naturally" to the people who do it. But this is not right! Playing an instrument well requires an incredible amount of work and dedication and can take years to master. As professional musician matures they go through many stages, such as:

• Learning to play the notes
• Learning to phrase
• Playing a whole piece
• Performing an entire program
• Playing in an ensemble
• Understanding music in the context of European culture

However, the important point is that we don’t need to go all this way to get some enjoyment or satisfaction out of learning to play an instrument. Just trying to learn an instrument gives us a much greater appreciation for those who do master their instruments. The same thing is true for the sciences. At first, physics may seem impossibly difficult to you, while, at the same time you may think it must be easy for physicists. This leads to a false appreciation of physics and science. And deeper appreciation can only come through attempting to learn some physics. Moreover, although you may never become a professional physics, you may still find that you enjoy gaining a better sense of how we make sense of the world and develop new technologies. Like music or any of the arts, it can be rewarding to learn a little bit about physics.

I try to study something new all of the time. For awhile it may be tennis, or martial arts or ballroom dancing. I may never become very good at any of these, but it changes how I experience the world. I am much more impressed with the players when I watch a tennis match, now that I have actually tried to learn the same shots. After taking dancing lesson, I am more aware of my posture and how I walk and all of the muscles that go into moving and dancing. However, there is a danger here: ignorance is bliss. Before we have tried something new, we have no idea how hard it can be. After a little experience, we can get the feeling that this is not so difficult, after all. We are really making progress when it hits us how difficult the task we are trying to lean really is! This is not the point to give up! I hope to get you to this point in this course.

It is usually generally accepted that a full understanding of the production and perception of music was driven by developments in physics. What is not so well acknowledged is that at many critical times, music actually propelled the development of physics! As discussed above, it appears that the Neanderthals created a flute out of bone. However, it may have been their desire to create and control sound that led them to develop techniques (technology) to drill precise holes. Pythagoras showed that it was worth developing mathematical analysis, because with it he could explain the musical scale. An analysis of the vibration of strings on a violin lead to a mathematician, Fourier, to develop one of the most powerful analytic techniques in science, now called Fourier Analysis. Galileo Galilei's revolutionary views of the natural world were probably influenced by his father's, Vincenzo Galilei, revolutionary ideas of musical harmony. Finally, many of the founders of Quantum Mechanics started out studying the physics of music and this fact may well have helped them accept the revolutionary ideas that went into the development of Quantum Mechanics. The acceptance of Quantum Mechanics may have been made easier by the field of psycho-acoustics, which studies how our brain processes and interprets sound, highlighting the subtle interplay between reality and our perception of reality. Quantum Mechanics focuses directly on the possibility that measuring (or perceiving) a system may actually influence the system, itself.

Physics of music is really the physics of waves. We will concentrate on sound waves, but all waves behave in a similar way. Wave theory is probably the most important concept in physics and especially modern physics, much more so than projectile motion and classical mechanics.

If you went to college in ancient Greece you would have take just four subjects: Geometry, Astronomy, Arithmetic and Music. There is much talk these days about our schools needing to offer a technical education to help graduates survive in a world dependent on high technology. This is nothing new: the ancient Greeks choose the state-of-the-art (at the time) sciences as the basis of their education. Interestingly, however, they included music up there with their technical fields of study.

Much of physics is unintuitive from everyday experience. Studying physics forces you to look at the world in a different way. This is beneficial, but can be rather difficult. Music is a good starting point because most of us have some intuition about music and that gives us some direct insight into difficult concepts in physics, such as ‘Fourier Analysis’. All of the concepts that we will study will have a direct connection to ideas that you are familiar with.

Over the years, physics has gotten a bad reputation. Many of you probably thought you would never take a physics course. Unfortunately, there are some good reasons for this. Someone counted the number of new words in an introductory physics course and it was more than the number of new words in a foreign language course! But, the problem is actually even worse! In a foreign language course, the meaning of a new word is usually pretty clear, you just need to learn the word in the new language. In physics, the words are new, but they also have unfamiliar meanings. For example, the word adiabatic could well be a word from a foreign language, which you need to learn how to pronounce and spell. But in physics, you also need to learn the whole concept behind the word adiabatic. In the case of adiabatic, it is probably clear to you that this word represents a new concept. However, in physics, familiar words, like work, are given a new precise definition and you must forget your previous understanding of the word. This redefinition of familiar words can often cause greater problems than the introduction of unfamiliar words.

Despite the difficulties of teaching physics, traditional physics courses have been very passive with the professor doing all the talking and the students just sitting and probably not paying much attention. It is very hard to learn this way, and it is NOT how physicists learn physics. What is required is much more interaction. We will often work in groups and we will try to make use of interaction capabilities on the Internet.

On final note before we begin the next Chapter: YOU DON'T NEED TO KNOW MUSIC TO DO WELL IN THIS COURSE! I am not relying on a technical knowledge of music that a music major might have, only your general awareness and experience of music.