Vibroacoustic Behaviour of Harp Sound Boxes - Daltrop

Click here to load reader

  • date post

    06-Apr-2015
  • Category

    Documents

  • view

    83
  • download

    0

Embed Size (px)

Transcript of Vibroacoustic Behaviour of Harp Sound Boxes - Daltrop

Vibroacoustic Behaviour of Harp Soundboxesby Shira Daltrop

A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF BACHELOR OF SCIENCE in The Faculty of Science (Physics)

THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2009 c Shira Daltrop 2009

All rights reserved. This work may not be reproduced in whole or in part, by photocopy or other means, without permission of the author.

ii

AbstractThis project involves studying the acoustic velocity eld around a soundbox of a musical string instrument. The relationship between the low frequency modes of the air in sound holes and the soundboard is important in determining the quality of sound production of an instrument. Using an impact hammer to apply a force, an accelerometer to measure the movement of the soundboard, and a velocity probe to measure the movement of the air, this relationship is examined. This study is focused on the harp, however a guitar was also measured to ensure this method can reproduce previous results. The lowest air and wood modes were examined and the results agreed with theory. From looking at the phase dierence between the soundboard velocity and the acoustic velocity, it is determined when the soundboard and sound holes are in and out of phase at the four lowest resonances.

iii

Table of ContentsAbstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii iii v 1 2 4 4 4 5 9 10 10 11 11 12 12 13 13 13 15 15 19 26 27

Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 Soundboxes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.1 2.2 2.3 Sound Radiation From a Point Source . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vibration of Plates . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Vibration of a Shell and a Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

3 Previous Work on Harps

4 Experiment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 4.2 4.3 4.4 The Impact Hammer The Velocity Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Method . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Calibration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.4.1 4.4.2 4.4.3 Accelerometer and Impact Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . Velocity Probe . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Converting From Decibels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

4.5

Error

5 Analysis and Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 5.2 HarpIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Aoyama Amphion Harp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

6 Conclusion

Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

Table of Contents

iv

AppendicesA Aoyama Ampion Harp: Another Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . B Aoyama Amphion Harp: Holes H2-5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 31

v

List of Figures1.1 2.1 2.2 2.3 2.4 2.5 2.6 4.1 4.2 4.3 4.4 4.5 4.6 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 The Conguration of a Harp . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 5 6 6 7 7 8 10 11 12 12 13 14 15 16 16 17 17 18 18 20 20 21 21 22 22 23 23 24 24

The Amplitude and Power of a Spherical Monopole . . . . . . . . . . . . . . . . . . . . . . . Admittance of a Violin Plate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Admittance of a Guitar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acoustic Velocity Divided by the Force of a Guitar . . . . . . . . . . . . . . . . . . . . . . . Phase Dierence Between the Plate Velocity and Acoustic Velocity of a Guitar . . . . . . . Schematic Diagram of the Guitar Soundbox . . . . . . . . . . . . . . . . . . . . . . . . . . . The Impact Hammer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Velocity Probe in a Sound Hole . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Accelerometer on the Soundboard . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . The Inertance From a 200g Mass . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase Dierence of Plate Velocity and Acoustic Velocity . . . . . . . . . . . . . . . . . . . . Phase Dierence of Soundboard Velocity and Force of Aoyama Amphion . . . . . . . . . . . Conventions for Analysing Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acceleration Versus Time of HarpIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acoustic Velocity Versus Time of HarpIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . Increasing Resonances of a Harp Soundboard . . . . . . . . . . . . . . . . . . . . . . . . . . Admittance of HarpIII . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Acoustic Velocity Divided by the Force of HarpIII . . . . . . . . . . . . . . . . . . . . . . . Phase Dierence Between Acoustic Velocity and Soundboard Velocity of HarpIII . . . . . . Admittance of Aoyama Amphion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Phase Between Soundboard Velocity and Force of Aoyama Amphion . . . . . . . . . . . . .

5.10 Acoustic Velocity Divided by the Force of Hole H1 of Aoyama Amphion . . . . . . . . . . . 5.11 Phase Dierence of Acoustic Velocity and Soundboard Velocity of Aoyama Amphion at 297mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.12 Phase Dierence of Acoustic Velocity and Force of Hole H1 of Aoyama Amphion . . . . . . 5.13 Phase Dierence Between Acoustic Velocity and Soundboard Velocity at 223Hz . . . . . . . 5.14 Phase Dierence Between Acoustic Velocity and Soundboard Velocity at 195Hz . . . . . . . 5.15 Phase Dierence Between Acoustic Velocity and Soundboard Velocity at 183Hz . . . . . . . 5.16 Phase Dierence Between Acoustic Velocity and Soundboard Velocity at 342Hz . . . . . . . 5.17 Phase Dierence of Acoustic Velocity and Soundboard Velocity of Aoyama Amphion at 712mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

List of Figures 5.18 Schematic Representation at 223Hz and 180Hz . . . . . . . . . . . . . . . . . . . . . . . . . 5.19 Schematic Representation at 342Hz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.20 Schematic Representation at 458Hz and 500Hz . . . . . . . . . . . . . . . . . . . . . . . . . A.1 Phase Dierence of Acoustic Velocity and Soundboard Velocity of Aoyama Amphion at 1145mm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A.2 Phase Dierence Between Acoustic Velocity and Soundboard Velocity at 458Hz . . . . . . . A.3 Phase Dierence Between Acoustic Velocity and Soundboard Velocity at 500Hz . . . . . . . A.4 Schematic Representation at 577Hz and 635Hz . . . . . . . . . . . . . . . . . . . . . . . . . B.1 Acoustic Velocity Divided by the Force of Hole H2 of Aoyama Amphion . . . . . . . . . . . B.2 Phase Dierence of Acoustic Velocity and Force of Hole H2 of Aoyama Amphion . . . . . . B.3 Acoustic Velocity Divided by the Force of Hole H3 of Aoyama Amphion . . . . . . . . . . . B.4 Phase Dierence of Acoustic Velocity and Force of Hole H3 of Aoyama Amphion . . . . . . B.5 Acoustic Velocity Divided by the Force of Hole H4 of Aoyama Amphion . . . . . . . . . . . B.6 Phase Dierence of Acoustic Velocity and Force of Hole H4 of Aoyama Amphion . . . . . . B.7 Acoustic Velocity Divided by the Force of Hole H5 of Aoyama Amphion . . . . . . . . . . . B.8 Phase Dierence of Acoustic Velocity and Force of Hole H5 of Aoyama Amphion . . . . . .

vi 25 25 25

28 29 29 30 31 31 32 32 33 33 34 34

1

AcknowledgementsI would like to thank my supervisor, Dr. Waltham, for his guidance and support. I would also like to thank the School of Music for the use of their Aoyama Amphion harp.

2

Chapter 1

IntroductionA harp is made up of a base, a column, a string arm, a soundbox with sound holes in it and strings which are attached to a soundboard (Figure 1.1). What makes harps dierent from most other string intruments is the fact that the plane of the strings is perpendicular to the soundboard as opposed to parallel. As well, there is no bridge present in the harp to connect the strings and the soundboard as in other string instruments. Instead the strings connect directly to the soundboard, therefore it needs to be thick enough to support the force of the strings. In string instruments, the soundboard is present as a sound radiator, while the stri