Transverse & Longitudinal Vibration of Rod
Ratio of Length

f, f': ratio of frequency ; l, l':ratio of length

f=2^(a/12)

Transverse Vibration l=(1/f)^(1/2)

Longitudinal Vibration l'=1/f'

	transverse vibration			longitudinal vibration
a	musical scale	f	l	musical scale	f'	l'
0	do	1	1.0000	do	1	1.0000
1
2	re	2(2/12)	0.9439
3
4	mi	2(4/12)	0.8909	re	2(2/12)	0.8909
5	fa	2(5/12)	0.8655
6
7	sol	2(7/12)	0.8170
8				mi	2(4/12)	0.7937
9	la	2(9/12)	0.7711
10				fa	2(5/12)	0.7492
11	si	2(11/12)	0.7278
12	do	2	0.7071
13
14	re	2(14/12)	0.6674	sol	2(7/12)	0.6674
15
16	mi	2(16/12)	0.6300
17	fa	2(17/12)	0.6120
18				la	2(9/12)	0.5946
19	sol	2(19/12)	0.5777
20
21	la	2(21/12)	0.5453
22				si	2(11/12)	0.5297
23	si	2(23/12)	0.5147
24	do	4	0.5000	do	2	0.5000