William M. Hartmann - Principles of Musical Acoustics

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Springer Science+Business Media New York 2013

William M. Hartmann Principles of Musical Acoustics Undergraduate Lecture Notes in Physics

1. Sound, Music, and Science

William M. Hartmann 1

(1)

Michigan State University, East Lansing, MI, USA

Keywords

Defend Prefix Acoustics

Sound is all around us. It warns us of danger, enables us to communicate with others, annoys us with its noise, entertains us by radio and iPods, and captivates us in music. It is an important part of the daily lives of hearing people.

We are concerned here with a science of sound, especially musical sound. There is something of a paradox in this concept. Sound itself tends to be personal and it often brings up an emotional response. On the other hand there is science, supposedly rational and objective. Merging these two aspects of human experience is the science and art of acoustics.

Acoustics is foremost a science. As such it is quantitative, attempting to account for the physical world and our perception of it in ways that can be measured with experiments and described with mathematical models. A quantitative science like acoustics operates with a number of ground rules:

• Definitions : We need precise definitions for ideas and for quantities. We often take common words and give them meanings that are more tightly constrained than in everyday speech. For instance, in the next chapter the word period will be given a precise mathematical meaning.
• Simplification : The real world is complicated. Science gains its power by simplification. For instance, everyday materials are complex compounds and mixtures of dozens of chemical elements, but the chemist uses pure chemicals to gain control of his experiment. In the same way, speech and music are complicated signals, but the acoustician uses signals that are no more complicated than necessary for the intended purpose.
• Idealization : The technique of idealization is like simplification in that it is a scientific response to a messy world. Idealization applies to the conceptual models that we use to explain some aspect of the world. An idealized model attempts to capture the essence of something, even though the model may not explain every detail. For instance, there is the concept that planets, like the Earth and Mars, orbit the Sun because of the Suns strong gravitational attraction. That is a powerful model of our solar system. But, it is not a perfect model because the planets attract one another too, and this is not included in the basic heliocentric model of orbital motion. Nevertheless, the model successfully abstracts the most important character of planetary motion from a complicated real-world situation. This model is a useful idealization.

And so we begin with the science of acoustics

An acoustical event consists of three stages as shown in Fig. : First, the sound is generated by a source . Second, the sound is transmitted through a medium. Third, the sound is intercepted and processed by a receiver . These three stages form the basis of acoustical science. We consider them in turn and highlight items that we expect to study in detail.

Fig. 1.1

A sound from a source is transmitted to two receivers, a human listener and a microphone

1.1 The Source

The source of a sound is always a vibration of some kind. For example, it might be the vibration of a drumhead. A drum is a traditional musical instrument , and our approach makes a study of traditional musical instruments by their families: brass instruments, woodwind instruments, string instruments, and percussion instruments.

The human voice is another source of sound, arguably the most important of all. The basic science of the human voice is enormous fun because a few simple principles serve to take us a long way toward understanding what is going on acoustically.

A more modern source of sound is the loudspeaker . It too is a vibrating system, but unlike the other vibrating systems, it is not caused to vibrate directly by human action. The loudspeaker is a transducer that converts electronic signals into acoustical signals. This marriage of electronics and acoustics is called audio ; its technological and cultural significance is so important that it is impossible to imagine modern life without it. It is closely allied with broadcasting by radio and TV. Audio technology has made possible two other kinds of musical instrument. One is the electrified instrument, where the vibrations of a physical object are converted into electronic form. For instance, the vibrations of a guitar string can be converted by a pickup into an electrical signal. The other is an electronic instrument , analog or digital, where the original vibrations are generated electronically.

Vibrations are so basic in the study of acoustics that the first chapters are dedicated to developing the terminology and basic mathematical relations for the study of vibration. These chapters also introduce electronic instrumentation used to study vibrations.

1.2 Transmission

The vibration of the drumhead causes the air around it to vibrate. This vibration propagates as a wave through the air. Accordingly, the study of waves occupies an important place in musical acoustics. The physics of waves is actually a long and deep subject because there is a rich variety of wave phenomena . We shall deal with some of the most fundamental properties. Wave motion is not only a characteristic of sound waves (acoustics), but also characterizes the transmission of light and radio waves. The wave principles that one learns in studying acoustics apply directly to optics (light) and electromagnetic radiation in the form of radio waves. Therefore, by learning about the weird things that can happen to an acoustical wave you immediately understand something about optical mirages and problems with your cell phone.

The transmission of sound from a source to a receiver does not take place entirely by a straight line path. The sound waves are reflected from the walls of a room and by other surfaces in the room. The character of the room puts its indelible stamp on the sound wave as it is finally received. This is the subject of room acoustics . It covers a lot of ground, from the problem of noise in your residence to the design of multi-million-dollar concert halls.

1.3 Receiver

The most important receiver of sound is the human ear and brainthe human auditory system. Sound waves, of the kind that we study in the musical acoustics, are meant to be heard, understood, and appreciated. In the final analysis, the strengths and limitations of the human auditory system determine everything else we do in acoustics. There are two basic divisions of subject matter in the study of human hearing; the first is the anatomy and physiology of the auditory system, the second is the psychoacoustics . The anatomy and physiology describe the tools we have to work with as listeners; the psychoacoustics describes the function of these tools, converting sound waves into perceptions. Important perceptual properties of sound include the loudness of tones, pitch , tone color , and location .

These three stages: source, transmission, and reception, appear in any acoustical experiment or experience, and they can be separately identified. The chapters that follow try to deal with the details of each stage in turn. It all starts with a source, specifically with vibration, which we begin in earnest in .

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