The sound wave in a cylindrical steel bar, generated by a light tap on one of its ends, is recorded by a microphone located near the other end. A sound analysis software is used to obtain the resonance spectrum of the bar. Longitudinal and flexural vibration frequencies are obtained from the peaks of the spectrum. The speed of sound, Young’s modulus, and Poisson’s ratio of steel are obtained.

1.
M. F.
Mascarenhas
,
C. M.
Spillmann
, and
John F.
Linder
, and
D. T.
Jacobs
, “
Hearing the shape of a rod by the sound of its collision
,”
Am. J. Phys.
66
,
692
697
(
1998
).
2.
J. W. S.
Rayleigh
,
The Theory of Sound
, 2nd ed. (
Dover
,
New York
,
1945
), Vol.
1
, pp.
260
261
.
3.
P. M.
Morse
,
Vibration and Sound
, 2nd ed. (
McGraw-Hill
,
New York
,
1948
), Chap. 4, Sec. 14.
4.
L. D.
Landau
and
E. M.
Lifshitz
,
Theory of Elasticity
(
Pergamon
,
London
,
1959
), Chap. 3, Sec. 25.
5.
T. D.
Rossing
and
N. H.
Fletcher
,
Principles of Vibration and Sound
(
Springer-Verlag
,
New York
,
1997
), Chap. 2, Secs. 2.15 and 2.16.
6.
L. E.
Kinsler
,
A. R.
Frey
,
A. B.
Coppens
, and
J. V.
Sanders
,
Fundamentals of Acoustics
, 4th ed. (
Wiley
,
New York
,
2000
), pp.
80
85
.
7.
M. J.
Moloney
, “
Measuring and calculating bar flexural vibration frequencies
,”
Am. J. Phys.
73
,
439
441
(
2005
).
8.
D.
Bancroft
, “
The velocity of longitudinal waves in cylindrical bars
,”
Phys. Rev.
59
,
588
593
(
1941
).
9.
Reference 3, pp.
293
294
.
10.
S.
Timoshenko
, “
On the correction for shear of the differential equation for transverse vibrations of prismatic bars
,”
Philos. Mag.
41
,
744
746
(
1921
).
11.
G. R.
Cowper
, “
The shear coefficient in Timoshenko’s beam theory
,”
ASME Trans. J. Appl. Mech.
33
,
335
340
(
1966
).
12.
Many software programs for recording and editing sounds can be found on the World Wide Web. In this work, we have used the freeware AUDACITY 1.2.6 for Windows (http://audacity.sourceforge.net/).
13.
The speed of sound in a solid depends on several factors such as its composition and the method of production. Thus, one can find in the literature different values for the speed of sound in steel. For example, one finds a value of 5130 m/s in
R. A.
Serway
,
Physics for Scientists and Engineers with Modern Physics
, 3rd ed. (
Saunders
,
Philadelphia
,
1990
), Table 17.1,
or values in the range of 5000–5200 m/s in the
Handbook of Chemistry and Physics
, 56th ed. (
CRC
,
Cleveland
,
1976
), edited by
R. C.
Weats
, p.
E
41
.
14.
T. D.
Rossing
and
D. A.
Russel
, “
Laboratory observation of elastic waves in solids
,”
Am. J. Phys.
58
,
1153
1163
(
1990
).
15.
H. M.
Ledbetter
,
N. V.
Frederick
, and
M. W.
Austin
, “
Elastic-constant variability in stainless-steel 304
,”
J. Appl. Phys.
51
,
305
309
(
1980
).
16.
R. A.
Serway
,
Physics for Scientists and Engineers with Modern Physics
, 3rd ed. (
Saunders
,
Philadelphia
,
1990
), Table 12.1.
17.
By applying the hit with the hammer perpendicularly to the axis of the bar, at a point on the lateral surface close to one end (lateral hit), one can measure 21 flexural frequencies.
18.
Reference 6, p.
526
.
AAPT members receive access to the American Journal of Physics and The Physics Teacher as a member benefit. To learn more about this member benefit and becoming an AAPT member, visit the Joining AAPT page.