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Evaluating wood samples.
Two important properties of wood for instruments (and any engineering
applicaton) are stiffness (modulus of elasticity, E) and density
(mass per unit volume). E is the ratio of stress divided by strain
which is a measure of how much a sample bends or deforms under a
given load.
The ratio of longitudinal sound velocity to density 
where  ,
is called acoustical admittance (reciprocal of impedance). For radiating
plates, the higher the admittance the more sound energy radiated.
If we make a strip of wood as in Fig.1, then the formula for calculating
the resonant frequencies of the bar is:
where the velocity  ,
the radius of gyration  .
Fig.1
The table below shows various physical properties of some forty
wood samples I have tested. I have used a spreadsheet for my calculations,
but using rationalised dimensions for the wood strips allows anyone
to more easily derive the figures.
Furthermore, having a collection of wood strips of identical size
is a great way to compare the sound they produce. By holding a piece
0.22 L from the end and striking it with a Xylophone mallet you
can find the exact pitch with a strobe tuner. This then must be
converted to Hz. using the Frequency to Cents book available from
C.G. Conn Ltd.
The strip sizes I use are Length: 288mm x Width 34.8mm x Thickness
8.0mm.
At these dimensions the speed of sound transmission C=10 times the
frequency (Hz) of the bar and the density  =
105/8 x mass of sample (Kgs.per cubic metre.) This results
in deriving the admittance of the sample (all measurements must
be in SI units).
The results obtained are consistant with the impression gained from
striking the sample with the mallet.
|
Sample
|
Grain
Angle
|
Pitch
|
Mass
(Kg)
|
f
(Hz)
|
C
(m/sec)
|
D
(Kg/m3)
|
E
(GN/m2)
|
C/D
|
|
Beefwood
|
45
|
E4+35
|
0.077
|
336.4
|
3364
|
962.5
|
10.89
|
3.50
|
|
Belah
|
70
|
F#4+23
|
0.103
|
375
|
3750
|
1281.25
|
18.02
|
2.97
|
|
Black Wattle (Early)
|
85
|
C#5-30
|
0.075
|
545
|
5450
|
937.5
|
27.85
|
5.81
|
|
Blackwood (Gippsland)
|
85
|
A4-15
|
0.058
|
436
|
4360
|
725
|
13.78
|
6.01
|
|
Blackwood (Otways)
|
85
|
G#4-10
|
0.057
|
412
|
4120
|
712.5
|
12.09
|
5.78
|
|
Brazillian Mahogany
|
90
|
B4+10
|
0.043
|
497
|
4970
|
537.5
|
13.28
|
9.24
|
|
Ebony
|
45
|
G#4-35
|
0.087
|
407
|
4070
|
1087.5
|
18.01
|
3.74
|
|
Gidgee
|
90
|
F4+40
|
0.103
|
357.4
|
3574
|
1287.5
|
16.45
|
2.78
|
|
Gombriera
|
45
|
A#4
|
0.099
|
466
|
4660
|
1237.5
|
26.87
|
3.77
|
|
Honduras Rosewood 1
|
80
|
C5-5
|
0.084
|
521.7
|
5217
|
1050
|
28.58
|
4.97
|
|
Honduras Rosewood 2
|
10
|
A4+50
|
0.084
|
453
|
4530
|
1050
|
21.55
|
4.31
|
|
Indian Rosewood
|
80
|
G4+45
|
0.071
|
402.5
|
4025
|
887.5
|
14.38
|
4.54
|
|
Jarrah
|
45
|
B4+5
|
0.075
|
495
|
4950
|
937.5
|
22.97
|
5.28
|
|
Jarrah Jarrah
|
75
|
F#4-35
|
0.064
|
363
|
3630
|
800
|
10.54
|
4.54
|
|
Leopard Wood
|
80
|
G4 - 40
|
0.067
|
383
|
3830
|
831.25
|
12.19
|
4.61
|
|
Mineritchie
|
45
|
F# - 28
|
0.070
|
364
|
3640
|
868.75
|
11.51
|
4.19
|
|
Mountain Ash (Fb)
|
90
|
F#4+40
|
0.045
|
378.6
|
3786
|
562.5
|
8.06
|
6.73
|
|
Myrtle
|
70
|
A#4+20
|
0.059
|
445.1
|
4451
|
737.5
|
14.61
|
6.04
|
|
Native Cherry
|
80
|
F4+10
|
0.061
|
351
|
3510
|
762.5
|
9.39
|
4.60
|
|
New Guinea Rosewood 1
|
80
|
A4+10
|
0.052
|
443
|
4430
|
650
|
12.76
|
6.82
|
|
New Guinea Rosewood 2
|
45
|
B4-15
|
0.051
|
490
|
4900
|
637.5
|
15.31
|
7.69
|
|
Norfolk Pine
|
50
|
C5+10
|
0.036
|
526
|
5260
|
450
|
12.45
|
11.69
|
|
Palm
|
90
|
B4-20
|
0.102
|
488
|
4880
|
1275
|
30.36
|
3.83
|
|
Poplar
|
80
|
B4+50
|
0.040
|
508
|
5080
|
500
|
12.90
|
10.16
|
|
Queensland Walnut
|
90
|
A4-10
|
0.058
|
437.5
|
4375
|
725
|
13.88
|
6.03
|
|
Queensland Walnut- 2
|
70
|
G4-30
|
0.049
|
385
|
3850
|
612.5
|
9.08
|
6.29
|
|
River She-Oak
|
80
|
F#-40
|
0.057
|
361.5
|
3615
|
712.5
|
9.31
|
5.07
|
|
Rock Maple
|
80
|
G#4+20
|
0.058
|
420
|
4200
|
725
|
12.79
|
5.79
|
|
Sitka Spruce
|
70
|
C5-10
|
0.031
|
520.2
|
5202
|
387.5
|
10.49
|
13.42
|
|
Wandoo
|
40
|
G#4+5
|
0.090
|
417
|
4170
|
1125
|
19.56
|
3.71
|
|
Western Red Cedar
|
90
|
B4+20
|
0.035
|
500
|
5000
|
437.5
|
10.94
|
11.43
|
|
Huon Pine
|
90
|
F4-40
|
0.041
|
341
|
3410
|
512.5
|
5.96
|
6.65
|
|
Syrian Cedar
|
45
|
B4+10
|
0.032
|
497
|
4970
|
400
|
9.88
|
12.43
|
|
Kamper
|
80
|
C5+5
|
0.061
|
525
|
5250
|
762.5
|
21.02
|
6.89
|
|
Sengon
|
40
|
A4-40
|
0.031
|
430
|
4300
|
387.5
|
7.16
|
11.10
|
|
Senu
|
40
|
B4-35
|
0.037
|
484
|
4840
|
462.5
|
10.83
|
10.46
|
|
Akasia
|
40
|
G4+10
|
0.049
|
394
|
3940
|
612.5
|
9.51
|
6.43
|
|
Sono
|
80
|
A4-20
|
0.060
|
435
|
4350
|
750
|
14.19
|
5.80
|
|
Waru
|
40
|
G4+50
|
0.041
|
403
|
4030
|
512.5
|
8.32
|
7.86
|
|
