1.2 HISTORICAL BACKGROUND

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Because of its connection with music, acoustics has been a field of interest

for many centuries (Hunt, 1978). The Greek philosopher Pythagoras (who

also stated the Pythagorean theorem of triangles) is credited with conducting

the first studies on the physical origin of musical sounds around 550 BC

(Rayleigh, 1945). He discovered that when two strings on a musical instrument

are struck, the shorter one will emit a higher pitched sound than the

longer one. He found that if the shorter string were half the length of the

longer one, the shorter string would produce a musical note that was 1

octave higher in pitch than the note produced by the longer string: an octave

difference in frequency (or pitch) means that the upper or higher frequency

is two times that of the lower frequency. For example, the frequency of the

note ‘‘middle C’’ is 262.6 Hz (cycles/sec), and the frequency of the ‘‘C’’ 1

octave higher is 523.2 Hz. Today, we may make measurements of the sound

generated over standard octave bands or frequency ranges encompassing

one octave. The knowledge of the frequency distribution of the noise generated

by machinery is important in deciding which noise control procedure

will be most effective.

The Greek philosopher Crysippus (240 BC) suggested that sound was

generated by vibration of parts of the musical instrument (the strings, for

example). He was aware that sound was transmitted by means of vibration

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of the air or other fluid, and that this motion caused the sensation of

‘‘hearing’’ when the waves strike a person’s ear.

Credit is usually given to the Franciscan friar, Marin Mersenne (1588–

1648) for the first published analysis of the vibration of strings (Mersenne,

1636). He measured the vibrational frequency of an audible tone (84 Hz)

from a long string; he was also aware that the frequency ratio for two

musical notes an octave apart was 2:1.

In 1638 Galileo Galilei (1939) published a discussion on the vibration

of strings in which he developed quantitative relationships between the

frequency of vibration of the string, the length of the string, its tension,

and the density of the string. Galileo observed that when a set of pendulums

of different lengths were set in motion, the oscillation produced a pattern

which was pleasant to watch if the frequencies of the different pendulums

were related by certain ratios, such as 2:1, 3:2, and 5:4 or octave, perfect

fifth, and major third on the musical scale. On the other hand, if the frequencies

were not related by simple integer ratios, the resulting pattern

appeared chaotic and jumbled. He made the analogy between vibrations

of strings in a musical instrument and the oscillating pendulums by observint

that, if the frequencies of vibration of the strings were related by certain

ratios, the sound would be pleasant or ‘‘musical.’’ If the frequencies were

not related by simple integer ratios, the resulting sound would be discordant

and considered to be ‘‘noise.’’

In 1713 the English mathematician Brook Taylor (who also invented

the Taylor series) first worked out the mathematical solution of the shape of

a vibrating string. His equation could be used to derive a formula for the

frequency of vibration of the string that was in perfect agreement with the

experimental work of Galileo and Mersenne. The general problem of the

shape of the wave in a string was fully solved using partial derivatives by the

young French mathematician Joseph Louis Lagrange (1759).

There are some great blunders along the scientific route to the development

of modern acoustic science. The French philosopher Gassendi

(1592–1655) insisted that sound was propagated by the emission of small

invisible particles from the vibrating surface. He claimed that these particles

moved through the air and struck the ear to produce the sensation of sound.

Otto von Guericke (1602–1686) said that he doubted sound was transmitted

by the vibratory motion of air, because sound was transmitted better

when the air was still than when there was a breeze. Around the mid-1600s,

he placed a bell in a vacuum jar and rang the bell. He claimed that he could

hear the bell ringing inside the container when the air had been evacuated

from the container. From this observation, von Guericke concluded that the

air was not necessary for the transmission of sound. He did not recognize

that the sound was being transmitted through the solid support structure of

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the bell. This story emphasized that we must be careful to consider all paths

that noise may take, if we are to reduce noise effectively.

In 1660 Robert Boyle (who discovered Boyle’s law for gases) repeated

the experiment of von Guericke with a more efficient vacuum pump and

more careful attention to the support. He observed a pronounced decrease

in the intensity of the sound emitted from a ticking watch in the vacuum

chamber as the air was pumped out. He correctly concluded that the air was

definitely involved as a medium for sound transmission, although the air

was not the only path that sound could take.

Sir Isaac Newton (1687) compared the transmission of sound and the

motion of waves on the surface of water. By analogy with the vibration of a

pendulum, Newton developed an expression for the speed of sound based on

the assumption that the sound wave was transmitted isothermally, when in

fact sound is transmitted adiabatically for small-amplitude sound waves. His

incorrect expression for the speed of sound in a gas was:

c ј рRTЮ1=2 рincorrect!Ю р1-1Ю

R is the gas constant for the gas and T is the absolute temperature of the

gas. For air (gas constant R ј 287 J/kg-K) at 158C (288.2K or 598F),

Newton’s equation would predict the speed of sound to be 288 m/s (944ft/

sec), whereas the experimental value for the speed of sound at this temperature

is 340 m/s (1116 ft/sec). Newton’s expression was about 16% in error,

compared with the experimental data. This was not a bad order of magnitude

difference at the time; however, later more accurate measurements of

the speed of sound consistently produced values larger than that predicted

by Newton’s relationship.

It wasn’t until 1816 that the French astronomer and mathematician

Pierre Simon Laplace suggested that sound was actually transmitted adiabatically

because of the high frequency of the sound waves. Laplace proposed

the correct expression for the speed of sound in a gas:

c ј р_RTЮ1=2 р1-2)

where _ is the specific heat ratio for the gas. For air, _ ј 1:40.

In 1877 John William Strutt Rayleigh published a two-volume work,

The Theory of Sound, which placed the field of acoustics on a firm scientific

foundation. Rayleigh also published 128 papers on acoustics between 1870

and 1919.

Between 1898 and 1900 Wallace Clement Sabine (1922) published a

series of papers on reverberation of sound in rooms in which he laid the

foundations of architectural acoustics. He also served as acoustic consultant

for several projects, including the Boston Symphony Hall and the chamber

of the House of Representatives in the Rhode Island State Capitol Building.

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Sabine initially tried several optical devices, such as photographing a sensitive

manometric gas flame, for measuring the sound intensity, but these

measurements were not consistent. He found that the human ear, along

with a suitable electrical timepiece, gave sensitive and accurate measurements

of the duration of audible sound in the room.

One of the early acoustic ‘‘instruments’’ was a stethoscope developed

by the French physician Rene Laennee. He used the stethoscope for clinical

purposes in 1819. In 1827 Sir Charles Wheatstone, a British physicist who

invented the famous Wheatstone bridge, developed an instrument similar to

the stethoscope, which he called a ‘‘microphone.’’ Following the invention

of the triode vacuum tube in 1907 and the initial development of radio

broadcasting in the 1920s, electric microphones and loudspeakers were produced.

These developments were followed by the production of sensitive

instruments designed to measure sound pressure levels and other acoustic

quantities with a greater accuracy than could be achieved by the human ear.

Research was conducted during the 1920s on the concepts of subjective

loudness and the response of the human ear to sound. Between 1930 and

1940, noise control principles began to be applied to buildings, automobiles,

aircraft and ships. Also, during this time, researchers began to investigate

the physical processes involved in sound absorption by porous acoustic

materials.

With the advent of World War II, there was a renewed emphasis on

solving problems in speech communication in noisy environments, such as

in tanks and aircraft (Beranek, 1960). The concern for this problem area was

so critical that the National Defense Research Committee (which later

became the Office of Scientific Research and Development) established

two laboratories at Harvard University. The Psycho-Acoustic Laboratory

was involved in studies on sound control techniques in combat vehicles, and

the Electro-Acoustic Laboratory conducted research on communication

equipment for operation in a noisy environment and acoustic materials

for noise control. After World War II ended, research in noise control

and acoustics was continued at several other universities.

Noise problems in architecture and in industry were addressed in the

post-war period. Research was directed toward solution of residential,

workplace, and transportation noise problems. The amendment of the

Walsh–Healy Act in 1969 gave rise to even more intense noise control

activity in industry. This law required that the noise exposure of workers

in the industrial environment be limited to a specific value (90 dBA for an 8-

hour period). If this level of noise exposure could not be prevented, the law

required that the workers be provided with and trained in the use of personal

hearing protection devices.

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