MODES OF VIBRATION OF A LOUDSPEAKER CONE

94 Pages·09.901 MB·English

by  PARTRIDGE, GORDON R

This dissertation has been 66—38
microfilmed exactly as received
PARTRIDGE, Gordon R., 1925-
MODES OF VIBRATION OF A
LOUDSPEAKER CONE.
Yale University, Ph.D., 1950
Engineering, general
University Microfilms, Inc., Ann Arbor, Michigan
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C opyright by
GORDON R. PARTRIDGE
1966
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
MOEES OF VIBRATION
OF A
LOUDSPEAKER GONE
Gordon Radford P artrid g e
B. E. Yale U niversity 194-6
M. Eng. Yale U niversity 1947
A D issertatio n P resented to the Faculty of
The Graduate School of Yale U niversity
in Candidacy fo r
The Degree of Doctor of Philosophy
New Haven, Connecticut
May, 1950
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
MO EES OF VIBRATION.
OF A
LOUDSPEAKER GONE
Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.
i l l
PREFACE
I have been extrem ely fo rtu n ate throughout the course
of th is study in having the opportunity to seek the counsel
of P rof. W alter J . Cunningham. W ithout h is h elp fu l advice
and continued in te re s t, the work would hardly have been
p o ssib le. I t is a pleasure to acknowledge the guidance
he has given me. ■
A word of thanks is also due my w ife, Dorothy Oakes
P a rtrid g e , who was of great help to me in recording the
re s u lts of the experim ental work and in the p rep aratio n
of the m anuscript.
G-. R. P.
New Haven, Connecticut
May, 1950
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iv
TABLE OF CONTENTS
L ist of F igures v
L is t of Tables v i i i
A bstract ix
I. In tro d u ctio n 1
II . M athem atical A nalysis of the Cone 7
I I I . Experim ental Equipment and Techniques 34
IV. Experim ental R esu lts 53
V. Conclusions 68
B ibliography 79
L ist of Symbols 81
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V
LIST OF FIGURES
1 . The cone in sp h erical coordinates 11
2. Chart of the ro o ts of the equation J^ (ar) = 0 21
3. A method fo r estim ating the number of resonant 23
inodes in a sp e c ifie d frequency bandwidth
4. V alues of v r and (v r)2 th a t sa tis fy Eq. (50) 32
5. Assembly drawing of the A lteo-Lansing Model 36
415 loudspeaker
6 . Approximate dim ensions of cone of Model 415 37
A ltec-L ansing loudspeaker
7. The cone mounted in the loudspeaker a fte r 38
a p p lica tio n of gold le a f
8a. Polystyrene probe body 4 l
8b. Brass probe tip s 41
.
9 C athode-follow er p ream p lifier 42
10. The assem bled probe 44
11. D etail of th e probe tip 45
12. Mounting stru c tu re for the probe and speaker 46
13. D etail of the probe, rack-and-pinion m ounting, 47
and d ia l gauge in p o sitio n over the loud­
speaker cone
14. Block diagram of m easuring apparatus 48
15. a.O scillogram of waveforms of driving signal 51
(larg e am plitude) and probe output voltage
(sm all am plitude) showing the phase re la tio n ­
ship fo r which the cone motion is a rb itra rily
c alle d p o sitiv e .
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Vi
15"b. Tli© same waveforms showing the phase re la tio n - 51
ship fo r which the cone motion is a rb itra rily
c alle d negative.
16. The components of m otion at a given po int on 55
the surface of the cone.
17. Displacement of cone w ith dust cover, frequency 59
297 cycles per second
18. Displacement of cone w ith dust cover, frequency 60
303 cycles per second
19. Displacement of cone w ith dust cover, frequency 61
320 cycles per second
20. Displacement of cone w ith dust cover, frequency 62
380 cycles per second
21. Displacement of cone w ith dust cover, frequency 63
439 cycles per second
22. Four tru e nodes at 49.5 cycles per second 65
23. Eight tru e nodes at 7^.5 cycles per second 65
24. Four tru e nodes at 78 cycles p er second 66
25. Six tru e nodes at 91.5 cycles p er second 66
26. Eight tru e nodes at 106 cycles per second 67
27. Comparison between calcu lated and observed 69
values of a rmin (here shown c o rre la te d w ith
frequency) at which c e rta in nodal p a ttern s
occur.
28. Displacement of the cone measured in the ra d ia l 72
d irec tio n along the g en eratrix at f6 = 60°
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vii
29. Displacement of the cone measured in the ra d ia l 72
d ire c tio n along the g en eratrix at jtf = 60°
30. D irections of motion of the cone surface fo r 74
free v ib ra tio n at 4-9.5 cycles per second
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viii
LIST OF TABLES
I. W avelength and v e lo c ity of sound in a paper cone 2
II. R elatio n sh ip between ap ical angle and v ario u s 16
valu es of mu
I I I . Nodal p a tte rn s and the frequencies at which 68
they occur
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