Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world

Transcription

1

2 Pearson Education Limited Edinburgh Gate Harlow Essex CM20 2JE England and Associated Companies throughout the world Visit us on the World Wide Web at: Pearson Education Limited 2014 All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, without either the prior written permission of the publisher or a licence permitting restricted copying in the United Kingdom issued by the Copyright Licensing Agency Ltd, Saffron House, 6 10 Kirby Street, London EC1N 8TS. All trademarks used herein are the property of their respective owners. The use of any trademark in this text does not vest in the author or publisher any trademark ownership rights in such trademarks, nor does the use of such trademarks imply any affiliation with or endorsement of this book by such owners. ISBN 10: ISBN 10: ISBN 13: ISBN 13: British Library Cataloguing-in-Publication Data A catalogue record for this book is available from the British Library Printed in the United States of America

3 222 Chapter 10 String Instruments Reinecke, W. (1973). Ubertragungseigenschaften des Streichinstrumentenstegs, Catgut Acoust. Soc. Newsletter 19: 26. Richardson, B. E., and G. W. Roberts (1985). The Adjustment of Mode Frequencies in Guitars: A Study by Means of Holographic Interferometry and Finite Element Analysis, Proc. SMAC 83 (Royal Swedish Academy of Music, Stockholm). Rossing, T. D., and G. Eban (1999). Normal Modes of a Radially Braced Guitar Determined by Electronic TV Holography, J. Acoust. Soc. Am. 106: Rossing, T. D., J. Popp, and D. Polstein (1985). Acoustical Response of Guitars, Proc. SMAC 83 (Royal Swedish Academy of Music, Stockholm). Schelleng, J. C. (1968). Acoustical Effects of Violin Varnish, J. Acoust. Soc. Am. 44: Schelleng, J. C. (1974). The Physics of the Bowed String, Sci. Am. 230(1): 87. Sloane, I. (1966). Classic Guitar Construction. NewYork: Dutton. GLOSSARY anisotropy The difference in some property when measured in different directions (such as the stiffness of wood along and across the grain). bass bar The wood strip that stiffens the top plate of a violin or other string instrument and distributes the vibrations of the bridge up and down the plate. belly The top plate of a violin. bridge The wood piece that transmits string vibrations to the sound board or top plate. Chladni pattern A means for studying vibrational modes of a plate by making nodal lines visible with powder. compensation (string) An extra length of string added because tension changes when a string is pressed against a fret. f-holes The openings in the top plate of a string instrument shaped like the letter f. Helmholtz resonator A vibrator consisting of a volume of enclosed air with an open neck or port (see Sections 2.3 and 4.7). humbucking pickup A magnetic pickup with two coils designed to minimize hum caused by stray magnetic fields. mobility (mechanical admittance) The ratio of velocity to force (called input admittance or driving point mobility if velocity and force are measured at the same point). nut The strip of hard material that supports the strings at the head end. purfling The thin wood strip near the edge of the top or back plate of a string instrument. saddle The strip of hard material (ivory or bone) that supports the string at the bridge of a guitar. sinusoidal force A smoothly varying force with a single frequency; the waveform is described as a sine wave. sound hole (rose hole) The round hole in the top plate of a guitar that plays an important role in determining the lower resonances of the body. sound post The short round stick (of spruce) connecting the top and back plates of a violin or other string instrument. sul ponticello Bowing near the bridge. sul tasto Bowing near the fingerboard. viol An early bowed string instrument usually having six strings and a fretted fingerboard. viola da gamba A viol played in an upright position. REVIEW QUESTIONS 1. What musical interval separates the open strings of a violin? 2. In what century did Antonio Stradivari and Guiseppi Guarneri make fine violins? 3. Describe the spectrum of a string plucked at its center. 4. Describe the spectrum of a string plucked at one-fifth of its length. 5. During how much of the bowing cycle does the string move with the bow? 6. How does a player increase the amplitude of vibration of a bowed string? 7. How are Chladni patterns created in a free violin top? 8. What is meant by anisotropy in a sheet of wood? 9. What is the approximate frequency of the f-hole (A 0 ) resonance of a violin? 10. What are the approximate frequencies of the first two resonances of a violin bridge? 11. How much below violin strings are viola strings tuned? 226

4 Experiments for Home, Laboratory, and Classroom Demonstration How much below violin strings are cello strings tuned? 13. What musical intervals separate the open strings of a guitar? 14. What is the approximate frequency of the lowest resonance of a guitar? 15. How does string tension in a folk guitar with steel strings compare to the tension in those of a classical guitar? 16. Why do most electric guitars have more than one set of pickups? 17. Each fret on a guitar is placed at what fraction of the remaining distance to the bridge? 18. What is meant by string compensation in a guitar? QUESTIONS FOR THOUGHT AND DISCUSSION 1. Does increasing the force on a violin bow increase the loudness of the tone? Explain why. 2. Why does a folk guitar with steel strings play more loudly than the same guitar with nylon strings? 3. How might the resonances of a hollow-body electric guitar affect the tonal output? (Remember that the pickups sense string motion only.) 4. Electric guitars (especially those with a hollow body) are susceptible to acoustic feedback (see Section 24.6), even though they have no microphone. Explain why this occurs and how it can be prevented. 5. Why do classical guitarists hold the back of the guitar away from their body when they play? EXERCISES 1. Continue the sketches in Fig to show the shape of the plucked string during the next half cycle from t = 1 2 T to t = T. 2. In Figs and 10.5, note that plucking a string onefifth the distance from one end suppresses the fifth harmonic, and plucking it at the midpoint (one-half the distance) suppresses the second harmonic. Also note that the phase of the harmonics (indicated by + or ) changes in going through a zero. Using this information, draw a similar diagram to show the addition of modes to obtain the shape of a string plucked at one-third its length. 3. Assuming a frequency of 440 Hz and a bow speed of 0.2 m/s in Fig. 10.7, what is the displacement of the string at its midpoint? What is the speed of the string when it leaves the bow and snaps back? (Hint: First determine the time during which the string moves at the speed of the bow.) 4. Note the similarity between the Chladni patterns in Fig and the holograms in Fig for modes II and V. Sketch a Chladni pattern that one might expect for mode I in Fig If the main resonances (A and T in Fig ) of the alto violin in the new family of fiddles are scaled to those of the conventional violin, near what notes will they lie? (The alto is tuned a fifth below the violin.) Compare these resonances to those of the viola. 6. Determine the musical intervals between the strings of the guitar (see Section 10.9) and those of the electric bass (see Section 10.15). 7. Calculate the two lowest resonance frequencies of a pipe 46 cm long closed at both ends (they are the same as those a pipe open at both ends; see Section 4.5). Do the same for a pipe 33 cm long. Now compare these frequencies to those given for the resonances A 2 and A 4 (longer pipe) and A 3 and A 5 (shorter pipe) in Fig (c). Discuss the significance of the similarity. 8. Carefully measure the distance of each fret of a guitar from the saddle of the bridge, and determine how closely the rule of eighteen has been followed. If done carefully, you can determine how much compensation is included for each string. EXPERIMENTS FOR HOME, LABORATORY, AND CLASSROOM DEMONSTRATION Home and Classroom Demonstration 1. Motion of a plucked string Straddle a steel string (on a guitar or a monocord) with a magnet and display the voltage induced by the moving string on an oscilloscope. Move the magnet to different locations on the string. 227

5 224 Chapter 10 String Instruments 2. String force Place a guitar force transducer on the saddle of a guitar bridge and note the force waveform when the string is plucked. An inexpensive force transducer can also be placed under a monocord string. 3. Motion of a bowed string Orient a magnet with its magnetic field passing vertically through a steel string so that it senses the horizontal motion. Bow the string at various points and note the waveform on an oscilloscope. Move the magnet to different locations on the string. 4. Following bow Set up Schelleng s following-bow demonstration (see Fig ). 5. Plate vibrations Chladni patterns on square and rectangular plates of wood and metal can be displayed by supporting the plate on pieces of foam over a loudspeaker. Alternatively, the plate can be mounted on an electromagnetic vibrator. Of particular interest are the modes with nodal lines forming patterns such as +,,and. 6. Violin and guitar plates Chladni patterns of free violin and guitar plates can be made in the same manner as in Demonstration 5. (Apparatus suppliers sell a flat metal plate cut in the shape of a violin plate, but a carved plate is better.) 7. Tap tone frequencies If an FFT spectrum analyzer is available, the tap-tone frequencies of violin and guitar plates can be determined. A guitar top plate without bracing typically has its lowest resonance around 50 Hz; with bracing this rises to around 80 or 90 Hz. A complete guitar has its lowest resonance around 100 Hz. 8. Fret locations Measure the distance L 0 from the bridge saddle to the nut and the distance L 1 from the saddle to the first fret. The ratio L 1 /L 0 should be close to The ratio Laboratory Experiments Acoustics of a guitar (Experiment 17 in Acoustics Laboratory Experiments). Acoustics of bowed string instruments (Experiment 18 in Acoustics Laboratory Experiments). L 12 /L 0 for the twelfth fret should be close to 2 (an octave). 9. Electric guitar output Feed the output waveform of an electric guitar to an oscilloscope as well as into the guitar amplifier. Show the difference between plucking in the horizontal plane and in the vertical plane. Show the different signals from each of the pickups and relate each one to the velocity waveform of the string at that point. 10. Longitudinal string vibrations Rather faint scratch tones can be excited on wrapped strings of a guitar by scratching them longitudinally with a fingernail. Stopping the strings at the frets raises the pitch of these scratch tones (in fact you can play a tune), but changing the tension on the string does not. 11. Bowing at different positions Show the effect of bowing a violin at different positions along the string. 12. Violin mute Show the effect of loading a violin bridge with a mute or other added mass. 13. Fret buzz Show that a strong upward pluck of a guitar near the sound hole causes the string to buzz against the frets, whereas a downward pluck does not. 14. Partials of a guitar string Second part of Demonstration28intheAuditory Demonstrations CD. 15. Harmonics of touching the string When a plucked guitar string is lightly touched at its center to damp out the fundamental, you hear the second harmonic an octave higher. Similarly, touching it at one-third of its length produces tones with frequencies 1.5 times and 3 times the fundamental, which sound a fifth and a twelfth (octave plus a fifth) above the fundamental. Vibrations of plates (Experiment 7 in Acoustics Laboratory Experiments). 228

6 CHAPTER 11 Brass Instruments In Chapters 11 and 12, we will discuss a wide variety of wind instruments, or aerophones, which differ widely in their construction and in their acoustical properties. It is customary to classify them into two families, the brasses and the woodwinds. When a brass instrument is played, the player s lips act as a valve, introducing puffs of air at just the right time to maintain oscillations of the air column. When a woodwind is played, an oscillating air stream or an oscillating reed excites the air column. The brass instruments radiate sound from a flared end of the tube, called the bell; woodwinds usually radiate sound from several holes in the sides of the air column. Other differences will become clear in these next two chapters. In this chapter you should learn: About the acoustic impedance of various brass instruments; How a player s lips function as a pressure-controlled valve; About functions of the mouthpiece, bell, and valves; About sound spectra of brass instruments. In ancient times, people blew animal horns, which served as sound sources for religious ceremonies and as warnings of danger. Attempts to use these horns to play music, however, apparently began during the Middle Ages. Later, wood and metal tubing were substituted for the horns of animals, and mouthpieces were added to simplify playing. Among the brass instruments that have survived from the Renaissance and Baroque eras are the valveless posthorn; the cornett, played with side holes; and the sackbut, forerunner of the trombone INSTRUMENTS OF THE BRASS FAMILY The principal members of the brass family are the trumpet, French horn, trombone, and tuba (see Fig. 11.1(a)). Their playing ranges are indicated in Fig. 11.1(b). Other important brass instruments are the cornet, fluegelhorn, bugle, and baritone horn. Brass instruments have four sections: a mouthpiece, a tapered mouthpipe, acylindrical section, and a bell, as shown in Fig The trumpet, French horn, and trombone have cylindrical sections of considerable length, as indicated in Table 11.1, whereas the fluegelhorn, baritone, and tuba, often referred to as instruments of conical bore, are tapered throughout much of their length. From Chapter 11 of The Science of Sound, Third Edition. Thomas D. Rossing, Richard F. Moore, Paul A. Wheeler. Copyright 2002 by Pearson Education, Inc. All rights reserved. 229

7 226 Chapter 11 Brass Instruments (a) (b) FIGURE 11.1 FIGURE 11.2 A cross section of a brass instrument. 230 (a) Tuba, trombone, French horn, and trumpet; (b) their playing ranges. (Courtesy of C. G. Conn, Ltd.)