The Physics Of Music

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The Physics of Music by ALEXANDER WOOD M. A.., I. SG, 3 Late Fellow of Emmanuel College, Cambridge revised by J. 3V1. BOWSHER METHUEN CO LTD 36 ESSEX STREET - STRAND - W. C, 2 PREFACE TO FIRST EDITION i HOPE that this little book may serve as an introduction for some to the very interesting borderland between physics and music.

It is a borderland in which the co-operation of musicians and physicists may have important results for the future of music. The typescript and proofs have been read by Miss Nancy Browne from the point of view of the general reader, and many obscure passages have been clarified. On the technical side I am indebted to Dr Pringle, who has read the proofs and given me valuable criticism and advice.

Miss Cawkewell has helped me with the illustrations, Mr Cottingham has supplied the photographs for Figs. 1.7 to i. io, and my secretary. Miss Sindall, has been responsible for the typing and for the assembly and preparation of the material. Because of the help received from these and others the book is a much better book than it would otherwise have been.

For its remaining imperfections I must take full responsibility. I should like also grateftdly to acknowledge the patience and consideration of the publishers and the way in which they have grappled with the difficulties of the production of a book of this kind in war-time. ALEX WOOD PREFACE TO THE SIXTH EDITION DR WOODS book was first published in 1944 and has enjoyed considerable popularity for many years as an introduction to the physics of sound for musicians.

I have tried to preserve the flavour of the new original book as much as possible, but have felt it necessary to indicate the opinions of other authorities, where these differed greatly from Woods, with additional footnotes. The sections on the recording and reproduction of sound, and on the acoustics of buildings, have been largely rewritten in the light of modern developments.

J. M. BOWSHER December, CONTENTS tSHAP. PAGE 1. THE NATURE OF SOUND . I 2. FORCED VIBRATION AND RESONANCE 23 3. INTENSITY AND LOUDNESS ...... 33 4. PITCH .......... 42 5. MUSICAL QUALITY . . . . . . . 6 1 O. THE EAR ......... 78 7. VIBRATIONS OF STRINGS ....... go 8. ORGAN PIPES . . . . . . . . IIO gT SUNDRY OTHER MUSICAL INSTRUMENTS . . . 132 IP.

DISSONANCE AND CONSONANCE . . . . . - 157 11. SCALES AND TEMPERAMENT . . . . . 171 12. RECORDING AND REPRODUCTION OF SOUND . . . 2O2 13. HALLS AND CONCERT ROOMS . . . . . .223 BIBLIOGRAPHY ........ 252 INDEX OF SUBJECTS ....... 253 INDEX OF NAMES ........ 257 VI ILLUSTRATIONS FIG. PAGE 1.1. Wave-model facing 4 1.2.

Wave diagram to illustrate propagation of waves ... 4 1.3 Simple harmonic motion ....... 4 1.4. Displacement diagram for simple harmonic wave . . . 5 i .5. Two successive positions of a wave to show direction of motion of the medium as the wave passes ..... 6 1.6. Relation between displacement, particle velocity, and density . 7 1.7.

Reflected ripples with the source at one focus of an elliptical reflector and the reflected ripples converging to the other focus ........ . facing 5 1.8. Straight ripples focused by passing over an immersed lens which gives varying depth, and therefore varying speed for ripples facing 5 1.9. Ripples passing through an aperture and showing bending at the rages ....... . facing 5 i. to.

Superposition of two sets of circular ripples showing nodal and antinodal lines . facing 5 i. i i.Stationary waves due to two equal sets of waves travelling in opposite directions ....... 12 1. 1 2. Motion of the air at four successive instants separated by one quarter of a period ....... 13 1.13. Wave diagram to illustrate stationary waves . . . 14 1.14.

Refraction of sound-rays due to reversal of wind or temperature gradient ......... 18 1.15. Diagram of tuning-fork showing compression and rarefactions . 19 9.1. Coupled pendulums 25 2.2. Tuning-fork mounted on resonance box 26 2.3. Resonators used by Helmholtz for the analysis of sounds . facing 36 2.4...