The New Student's Reference Work/Acoustics

Acoustics (a-kōōs′tĭks). Those phenomena which one detects by the ear are generally studied together under the head of acoustics. But whenever any sound is heard we find that somewhere in the neighborhood there is what we call a sounding body, and this is always found to be a body in rapid vibration. Besides this we find that if the sounding body be supported on a bit of cotton wool, placed under the receiver of an air pump, and the air exhausted, the sound is almost entirely extinguished. We are thus led to believe that two things are always essential to the production of sound, viz., a rapidly vibrating body and an elastic medium, generally air, between that body and the ear.

Accordingly the subject of acoustics is made to include a study of vibrating bodies, such as a piano wire, a violin string, an organ pipe, etc., and also of the bodies which transmit vibrations to the ear, such as air, wooden rods and other elastic media.

The structure of the ear and the sensation of sound are generally studied under physiology, and are seldom included under acoustics.

A VIBRATING STRING

One of the most typical of vibrating bodies is a stretched string, such as is employed in the guitar or the harp. When a string of this kind is plucked by the finger a series of waves is started in the string, and these waves are reflected from the fixed ends of the string in such a way that the string vibrates as a whole, to and fro, in a manner familiar to every one. It has been found by experiment that the number of vibrations which a string will make in one second, i.e., the pitch of the string, depends upon three things only, namely, the length of the string, the force with which it is stretched, and the mass of unit length of the string. This may be described more definitely as follows:

If we denote by n the pitch of the string, whose length is l, by T the stretching force, and by m the mass of unit length, then

$n={\frac {1}{2l}}{\sqrt {\frac {T}{m}}}$

Evidently, therefore, we can raise the pitch of a string in two ways, either by increasing the stretching force, i.e., by increasing T, or by shortening its length, i.e., by diminishing l.

SOUND A WAVE MOTION

The evidence for thinking that the disturbance which we call sound is a wave motion in the air is as follows:

1. Sound is reflected from buildings or hillsides just as water waves are reflected from a wharf. This is the familiar phenomenon of the echo.
2. Two sounds can be added together to produce silence. The simplest method of doing this is to hold a tuning fork near to one ear, front of you, and while it is still vibrating rotate it slowly about its stem as an axis. It is found that there are certain positions in which the disturbance from one prong of the fork will just annul the disturbance from the other prong of the fork, thus adding two sounds together to produce silence.
3. Sound waves can actually be seen by properly illuminating the air with an electric spark. This was first done by Toepler of Dresden. More recently Professor R. W. Wood has succeeded by this method in making instantaneous photographs of sound waves, showing just what portions of the air are condensed and what portions are rarefied at the instant.

SPEED OF SOUND IN AIR

It has been found by experiment that sound waves of all lengths travel in air with the same speed. This is evident, indeed, from the fact that the “time” of an orchestra is just as perfect at long distances as at short distances.

Among the best measures of this speed are the following:

Observer.	Speed of Sound in Meters per sec. Temp. = 0°C.	Method.
Moll and Van Beck	332.77	Eye and ear
Regnault	330.71	Mechanical
Szathmari	331.57	Unison

As a mean we may take 332 meters per second, which is equivalent to 1,089 feet per second, at a temperature of 0° C. Newton and Laplace first showed how the speed of sound may be computed in any gas as soon as its pressure and its density are known. For they proved that if V denotes the speed of sound in a gas in which the density is D and the pressure P, then

$V={\sqrt {\frac {kP}{D}}}$

where k is a constant, which for most gases has the approximate value of 1.4. But it has been found that the value of this constant, k, depends upon the number of atoms in one molecule of the gas. If there is but one atom in the molecule then k = 1.6. Accordingly when chemists wish to determine how many atoms there are in a molecule of any given gas they measure the speed of sound in that gas, then measure the pressure and density, and afterward compute k by the use of the expression given above.

MUSICAL TONES

The sound which is produced by a regular and rapid vibration is called a “musical tone,” while the sound which is produced by irregular vibrations is called a “noise.” Every musical tone possesses three features by which it may be distinguished from all other musical tones. These are loudness, pitch and quality.

1. It has been shown that the loudness or intensity of a sound depends simply upon the amplitude of the vibrating air particles at the ear. The loudness of a sound will therefore, vary not only with the distance of the sounding body, but also with the amount of vibration in the sounding body.

2. The pitch of a note depends simply upon the number of vibrations per second, that is, the frequency of the body which produces it.
3. But even when notes have the same loudness and the same pitch they may be quite different, as, for instance, the difference between middle C on the guitar and on the piano. Two notes of this kind are said to differ in quality. And quality has been shown to depend upon the presence of other notes, called overtones, along with the note under consideration.

THE MUSICAL SCALE

When we consider one tone in relation to other tones we are led to a study of the musical scale. Two definitions are necessary to any understanding of the musical scale, viz.:

1. A musical interval between any two notes is defined as the ratio of their frequencies. Two notes which have the same frequency are said to be in unison. But if the ratio be 2:1 then the interval is said to be an octave.
2. The Major Triad. — It is a very remarkable fact that the ears of all western nations consider any three notes whose frequencies are in the ratio 4:5:6 as harmonious. Such a combination is called the major triad, and is always pleasing to the ear.

The interval between any note and its octave is divided by musicians into a series of seven smaller intervals, called tones and semitones. These tones are called by letters of the alphabet, and together form what is known as the musical scale.

THE MAJOR SCALE.

Name of Note.

C

D

E

F

G

A

B

2C

Name of Note in Vocal Music

do

re

mi

fa

so

la

si

do

Interval

9/8

10/9

16/15

9/8

10/9

9/8

16/15

From inspection of this table it will be readily seen that the entire Major Scale, as it is called, is made up of the three following major triads:

C	:	E	:	G	=	4	:	5	:	6
F	:	A	:	2C	=	4	:	5	:	6
G	:	B	:	2D	=	4	:	5	:	6

For an excellent experimental discussion of acoustics, see Tyndall’s Lectures on Sound (Appleton), and Blaserna’s Theory of Sound (Int. Sci. Series). The great masterpiece in the literature of acoustics is, however, Helmholtz’s Sensations of Tone, trans. by Ellis (Longmans).

Henry Crew.