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Unformatted text preview: Physics 1240 Hall Chapter 12 Notes 1 Focus questions and learning goals Chapter 12 focus questions: 1. How does a wind instrument work? 2. How is the sound affected by the physical characteristics of the pipe and the way it is played? Chapter 12 learning goals. After studying this chapter, you should be able to: 1. Predict what frequencies a wind instrument can produce, and how they are related to one another. 2. Describe what properties of the pipe can be used to change the pitch (and which don’t matter). 3. Understand the connection between harmonic number, pitch, and octave—so you can describe what notes you are hearing when a pipe makes many tones at the same time. 4. Look at a snapshot of standing wave air pressure in a pipe and describe the characteristics, including wavelength and pitch. 5. Explain how the end conditions determine the allowed frequencies of a closed or open pipe. 6. Describe how the air is moving inside a singing pipe, and where the pressure is high. 7. Predict what happens to the music if you put holes in various places along a pipe. 2 Open pipes When we studied strings, we saw that the fact that a string has no vibrations at the two ends leads to very important consequences, basically everything we’ve talked about for the last several weeks! (The nodes at the ends mean that only special wavelengths “fit”, these are the harmonics!) Think back to Chapter 10, when we drew pictures of all the har- monics on a string. The fundamental, n = 1, was the simplest (longest wavelength) wave we could draw which went to zero at the two ends. The boundary (forcing zero motion at the two ends) is what deter- mines the allowed wavelengths, which in turn determines the sounds we hear! Now let’s turn to wind instruments. The story is similar but it is a bit more complicated. That’s partly because the vibration inside a wind instrument is not so easy to visualize as the vibration of the string. When I draw my string picture (above) you can picture the actual metal string vibrating in the pattern shown. It’s a transverse wave of the string atoms. But in a wind instrument, we have longitudinal pressure oscillations in the air. It’s the pressure that varies sinuosoidally (wave-like) as you move along the tube. Now, it’s true, you could 1 Physics 1240 Chapter 12 notes think about the longitudinal displacement of air molecules, again a wave-like pattern in there, but we’ve mostly tried to think about sound as a pressure wave, so that’s the language we’ll often stick with. Let me imagine a tube which is open at both ends. It could be a flute (just an empty cylinder, basically), if you want something concrete to visualize. You apply some pressure variations (by blowing), and it sets up pressure waves which travel down the inside of the tube, bounce off the ends, interfere with themselves, and set up a standing wave. To be very precise, I’m talking about over pressure waves here (the air starts off at atmospheric pressure, and then you get some...
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- Spring '08
- Work, 3 cm, Standing wave, 2L, 03 m