Page 35 - Singiresu S. Rao-Mechanical Vibrations in SI Units, Global Edition-Pearson (2017)

32 Chapter 1 Fundamentals oF Vibration
String
1 2 3

Weight

FiGure 1.2 Monochord.

a monochord. In the monochord shown in Fig. 1.2, the wooden bridges labeled 1 and 3
are fixed. Bridge 2 is made movable while the tension in the string is held constant by
the hanging weight. Pythagoras observed that if two like strings of different lengths are
subject to the same tension, the shorter one emits a higher note; in addition, if the shorter
string is half the length of the longer one, the shorter one emits a note an octave above the
other. Pythagoras left no written account of his work, but it has been described by oth-
ers. Although the concept of pitch was developed at the time of Pythagoras, the relation
between the pitch and the frequency was not understood until the time of Galileo in the
sixteenth century.
Around 350 b.c., Aristotle wrote treatises on music and sound, making observations
such as “the voice is sweeter than the sound of instruments,” and “the sound of the flute
is sweeter than that of the lyre.” In 320 b.c., Aristoxenus, a pupil of Aristotle and a musi-
cian, wrote a three-volume work entitled Elements of Harmony. These books are perhaps
the oldest ones available on the subject of music written by the investigators themselves.
In about 300 b.c., in a treatise called Introduction to Harmonics, Euclid wrote briefly about
music without any reference to the physical nature of sound. No further advances in scien-
tific knowledge of sound were made by the Greeks.
It appears that the Romans derived their knowledge of music completely from the
Greeks, except that Vitruvius, a famous Roman architect, wrote in about 20 b.c. on the
acoustic properties of theaters. His treatise, entitled De Architectura Libri Decem, was lost
for many years, to be rediscovered only in the fifteenth century. There appears to have been
no development in the theories of sound and vibration for nearly 16 centuries after the
work of Vitruvius.
China experienced many earthquakes in ancient times. Zhang Heng, who served as a
historian and astronomer in the second century, perceived a need to develop an instrument
to measure earthquakes precisely. In a.d. 132 he invented the world’s first seismograph
[1.2–1.4]. It was made of fine cast bronze, had a diameter of eight chi (a chi is equal to
0.237 meter), and was shaped like a wine jar (Fig. 1.3). Inside the jar was a mechanism
consisting of pendulums surrounded by a group of eight levers pointing in eight directions.
Eight dragon figures, with a bronze ball in the mouth of each, were arranged on the outside
of the seismograph. Below each dragon was a toad with mouth open upward. A strong
earthquake in any direction would tilt the pendulum in that direction, triggering the lever
in the dragon head. This opened the mouth of the dragon, thereby releasing its bronze
ball, which fell in the mouth of the toad with a clanging sound. Thus the seismograph
enabled the monitoring personnel to know both the time and direction of occurrence of the
earthquake.