2. Wave motion: in coiled spring, in air, on water.

3. Reflection of waves: law, echoes.

Exercises

1. A hunter hears an echo in 8 seconds after firing his gun. How far is the reflecting surface if the temperature is 20C.?

2. How far is the reflecting surface of a building if the echo of one's footsteps returns in 1 second at 10C.?

3. Why is it easier to speak or sing in a room than out of doors?

4. Draw a curve that represents wave motion. Make it exactly three full wave lengths, and state why your curve shows this length. Indicate the parts of the curve that correspond to a condensation and to a rarefaction.

5. How long does it take the sound of the "pin drop" to reach a person at the farther end of the building mentioned at the end of Art. 327?

6. An echo is heard after 6 seconds. How far away is the reflecting surface, the temperature being 70F.?

7. Why are outdoor band-stands generally made with the back curving over the band?

8. A man near a forest calls to a friend. In 4 seconds the echo comes back. How far away is he from the forest?

9. Would it be possible for us ever to hear a great explosion upon the moon? Explain.

10. If a sunset gun was fired exactly at 6:00 P.M. at a fort, at what time was the report heard by a man 25 miles away, if the temperature was 10C.?

(3) INTENSITY AND PITCH OF SOUNDS

[Ill.u.s.tration: FIG. 321.--Graphic representations of (_a_) a noise, (_b_) a musical sound.]

=328. Musical Sounds and Noises Distinguished.=--The question is sometimes raised, what is the difference between a _noise_ and a _musical sound_? The latter has been found to be produced by an even and regular vibration such as that of a tuning fork or of a piano string. A noise on the other hand is characterized by sudden or irregular vibrations such as those produced by a wagon b.u.mping over a stony street. These differences may be represented graphically as in Fig. 321, (a) represents a noise, (b) a musical tone.

[Ill.u.s.tration: FIG. 322.--Curve _b_ represents a tone of greater intensity.]

=329. Characteristics of Musical Sounds.=--Musical tones differ from one another in three ways or are said to have _three characteristics_, viz., _intensity_, _pitch_, and _quality_. Thus two sounds may differ only in intensity or _loudness_, that is, be alike in all other respects except this one, as when a string of a piano is struck at first gently, and again harder. The second sound is recognized as being louder. The difference is due to the greater _amplitude_ of vibration caused by more energy being used. Fig. 322 shows these differences graphically. Curve _b_ represents the tone of greater intensity or loudness, since its amplitude of vibration is represented as being greater.

=330. Conditions Affecting the Intensity of Sound.=--The intensity of sounds is also affected by the _area_ of the vibrating body. This is shown by setting a tuning fork in vibration. The area of the vibrating part being small, the sound is heard but a short distance from the fork.

If, however, the stem of the vibrating fork is pressed against the panel of a door or the top of a box, the sound may be heard throughout a room.

The stem of the fork has communicated its vibrations to the wood. The vibrating area, being greater, the sound is thereby much increased in intensity, producing a wave of greater amplitude. The same principle is employed in the sounding boards of musical instruments as in the piano, violin, etc. It is a common observation that sounds decrease in loudness as the distance from the source increases. This is due to the increase of the surface of the spherical sound waves spreading in all directions from the source. Careful experiments have shown that in a uniform medium _the intensity of a sound is inversely proportional to the square of the distance from its source_. If a sound is confined so that it cannot spread, such as the sound moving through a speaking tube, it maintains its intensity for a considerable distance. An _ear trumpet_ (see Fig. 320) also applies this principle. It is constructed so that sound from a given area is _concentrated_ by reflection to a much smaller area with a corresponding increase in intensity. The _megaphone_ (Fig. 323), and the _speaking trumpet_ start the sound waves of the voice in one direction so that they are kept from spreading widely, consequently by its use the voice may be heard several times the usual distance. The intensity of a sound is also affected by the _density_ of the transmitting medium. Thus a sound produced on a mountain top is fainter and thinner than one produced in a valley. The sound of a bell in the receiver of an air pump becomes weaker as the air is exhausted from the latter. _Four_ factors thus influence the intensity of a sound, the _area_ of the vibrating body, its _amplitude_ of vibration, the _distance_ of the source and the _density_ of the transmitting medium.

It is well to fix in mind the precise effect of each of these factors.

[Ill.u.s.tration: FIG. 323.--The megaphone.]

=331. Pitch.=--The most characteristic difference between musical sounds is that of _pitch_. Some sounds have a high pitch, such as those produced by many insects and birds. Others have a low pitch as the notes of a ba.s.s drum or the sound of thunder. How notes of different pitch are produced may be shown by the siren (Fig. 324). This is a disc mounted so as to be rotated on an axis. Several rows of holes are drilled in it in concentric circles. The number of holes in successive rows increases from within outward. If when the siren is rapidly rotated air is blown through a tube against a row of holes a clear musical tone is heard. The tone is due to the succession of pulses in the air produced by the row of holes in the rotating disc alternately cutting off and permitting the air blast to pa.s.s through at very short intervals. If the blast is directed against a row of holes nearer the circ.u.mference the pitch is higher, if against a row nearer the center the pitch is lower. Or if the blast is sent against the same row of holes the pitch rises when the speed increases and lowers when the speed lessens. These facts indicate that the pitch of a tone is due to the number of pulses or vibrations that strike the ear each second; also that _the greater the rate of vibration, the higher the pitch_.

[Ill.u.s.tration: FIG. 324.--A siren.]

=332. The Major Scale.=--If a siren is made with eight rows of holes, it may indicate the relation between the notes of a _major scale_. To accomplish this, the number of holes in the successive rows should be 24, 27, 30, 32, 36, 40, 45, 48. If a disc so constructed is rapidly rotated at a uniform rate, a blast of air sent against all of the rows in succession produces the tones of the scale. These facts indicate that the relative vibration numbers of the notes of any _major scale_ have the same relation as the numbers 24, 27, 30, 32, 36, 40, 45, 48.

The note called middle C is considered by physicists as having 256 vibrations a second. This would give the following _actual vibration_ numbers to the remaining notes of the major scale that begins with "Middle C" D.-288, E.-320, F.-341.3, G.-384, A.-426.6, B.-480, C'.-512.

Musicians, however, usually make use of a scale of slightly higher pitch. The _international_ standard of pitch in this country and in Europe is that in which "A" has 435 vibrations per second. This corresponds to 261 vibrations for middle C.

=333. The Relation between Speed, Wave Length, and Number of Vibrations per Second.=--Since the notes from the various musical instruments of an orchestra are noticed to harmonize as well at a distance as at the place produced, it is evident that notes of all pitches travel at the same rate, or have the _same speed_. Notes of high pitch, having a high vibration rate produce more waves in a second than notes of low pitch, consequently the former are shorter than the latter. The following formula gives the relation between the speed (_v_), wave length (_l_), and number of vibrations per sec. (_n_):

_v_ = _l_ _n_, or _l_ = _v/n_

that is, _the speed of a sound wave is equal to the number of vibrations per second times the wave length, or the wave length is equal to the speed divided by the number of vibrations per second_. This formula may also be employed to find the _number_ of vibrations when the wave length and speed are given.

Important Topics

1. Difference between noise and music.

2. Factors affecting intensity: area, amplitude, density, distance.

3. Pitch, major scale, relative vibration numbers.

4. Relation between speed, wave length and vibration rate.

Exercises

1. Give an ill.u.s.tration from your own experience of each of the factors affecting intensity.

2. Write the relative vibration numbers of a major scale in which _do_ has 120 vibrations.

3. What is the wave length of the "A" of international concert pitch at 25C.? Compute in feet and centimeters.

4. At what temperature will sound waves in air in unison with "Middle C"

be exactly 4 ft. long?

5. Explain the use of a megaphone.

6. What tone has waves 3 ft. long at 25C.?

7. What is the purpose of the "sounding board" of a piano?

8. Two men are distant 1000 and 3000 ft. respectively from a fog horn.

What is the relative intensity of the sounds heard by the two men?

9. The speaking tone of the average man's voice has 160 vibrations per second. How long are the waves produced by him at 20C.?

(4) MUSICAL SCALES AND RESONANCE

=334. A musical interval= _refers to the ratio between the pitches[O] of two notes_ as indicated by the results of the siren experiment. The simplest interval, or ratio between two notes is the _octave_, C':C, or 2:1 (48:24). Other important intervals with the corresponding ratios are the _fifth_, G:C, or 3:2 (36:24); the _sixth_, A:C, or 5:3 (40:24); the _fourth_, F:C, 4:3 (32:24); the _major third_, E:C, or 5:4 (30:24); and the _minor third_, G:E, 6:5. The interval between any two notes may be determined by finding the ratio between the vibration numbers of the two notes. Thus, if one note is produced by 600 vibrations a second and another by 400, the interval is 3:2, or a _fifth_, and this would be recognized by a musician who heard the notes sounded together or one after the other. Below is a table of musical nomenclatures, showing various relations between the notes of the major scale.