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Unformatted text preview: Physics 1240 Hall Chapter 8 Notes 1 Focus questions and learning goals Chapter 8 focus questions: 1. Why do different instruments sound different even when they are playing the same note? 2. How is a sound spectrum physically & mathematically described? Chapter 8 learning goals. After studying this chapter, you should be able to: 1. Understand the connection between harmonic number, pitch, and octave, so you can describe what notes you are hearing when a string makes many tones at the same time. 2. Relate a sound waveform and the spectrum of frequencies that make it up. If you are given a spectrum, describe how the resulting sound is perceived, and what the impact of various changes like adding or subtracting various harmonics would have on the waveform. Which alterations to a spectrum change the period? the pitch? the loudness? 3. Explain how you might build other waveforms (like square waves) up from different harmonics, and describe qualitatively why and how a square wave sounds different from a sine wave with the same period. 4. Define sine wave, and relate back to chapter 1 and 2. Define and distinguish sine, square, pulse, and triangular waves. 2 Timbre and harmonics We just learned that if you wiggle a string, only certain special frequencies, the harmonics , will resonate. All other frequencies tend to die away almost instantly. So if you pluck a string, you will hear the fundamental frequency f 1 , and the higher harmonics (2 f 1 , 3 f 1 , 4 f 1 , 5 f 1 , and so on) all at the same time, all superposed. If you look back to Chapter 2 (section 2.2, on waveforms), there were pictures of complex waves that had some basic (fundamental) frequency, but didnt look like a simple sine wave. Heres one of the most remarkable things about waves (discovered by a mathematician named Fourier): If you superpose a bunch of waves ( all harmonics of a given fundamental frequency f 1 ) you can generate any possible waveform that repeats itself at frequency f 1 . In other words, all those complex waveforms shown back in Chapter 2.2. of the text can be thought of as arising from some particular simple sum of harmonics of the basic frequency f 1 . A given string will produce a particular characteristic sum of harmonics (e.g., the higher harmonics might die away quickly in amplitude), and that will yield a characteristic sound, or timbre associated with the string. You perceive the fundamental frequency f 1 as the pitch , and all the higher harmonics add in just to change the shape of that tone from the whiny, annoying pure sine wave to a richer, fuller tone. The point is, if a string plays A440, you hear a pitch of 440 Hz, but the character of the sound depends on how many (and which, and how strong) harmonics you add 1 Physics 1240 Chapter 8 notes in. If you dont add in any, you hear a very electronic sound. If you add in higher harmonics in just the right way, you can produce an A that sounds like a violin, or a saxophone, or....just aboutjust the right way, you can produce an A that sounds like a violin, or a saxophone, or....
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- Spring '08