ticles and the motion of the wave are at right angles to each other (Art. 224).

Sound is transmitted by longitudinal waves in air.

229. How We Hear. When sound passes into the opening of the ear,. it produces periodic changes in the pressure of the air in front of the ear drum. The drum is thus set into vibration, and its vibrations are passed along by a very delicate mechanism, till they excite the extremities of the auditory nerve, producing the sensation of hearing.

The ear is extraordinarily sensitive. The "ear power," i. e., the rate at which energy is supplied to the ear when a faint sound is just audible, has been measured, approximately,

and it is found to be something like

1

100,000,000

gram-cen

timeter a second. If energy flowed continuously at this rate into a cubic centimeter of water, and if all of it were converted into heat, and retained in the water, it would take rough y 100,000 years to heat the water 1°C.

DEFINITIONS AND PRINCIPLES

1. When vibrating freely, every body vibrates in its natural period.

2. The greater the frequency of a tone, the higher its pitch.

3. The speed of sound in air at 0°C. is 1088 feet per second. 4. The speed of sound in air increases 2 feet per second for every degree C. rise in temperature.

5. In order that a body be set into vibration by resonance, the period of the impulses given it must be the same as its own natural period of vibration.

6. Waves transmit energy from one place to another.

7. The particles of the elastic medium in which waves travel do not move forward with the waves; but each one merely vibrates over a small space on either side of its position of rest.

8. The speed with which a wave travels is found by multiplying the wave length by the frequency.

9. Waves will not travel in a medium unless it has both elasticity and inertia.

10. Waves are transverse when the particles of the medium vibrate at right angles to the direction in which the wave travels, and longitudinal when the particles vibrate in the same direction in which the wave travels.

11. Sound is transmitted by longitudinal waves in air.

QUESTIONS AND PROBLEMS

1. Why must the impulses be given to a swing at regular intervals .n order to make it swing?

2. Does a rocking chair rock more slowly when some one is sitting in it than it does when empty? Why?

3. Why is it difficult for a tall person to walk comfortably with a short person?

4. When a circular saw starts through a board the pitch of the buzzing tone is high. Why does the pitch fall soon after the saw enters the 'board?

5. If you know the number of teeth on the saw in question 4, can you determine how many revolutions per second it is making from the tone that you hear? How?

6. Can a fog-horn on a steamer be heard astern? Why?

7. If the moon were inhabited, could we ever make enough noise to be heard by the inhabitants? Why?

8. When a tree falls in a lonely forest, and no animal is near by to hear it, does it make a sound? Why?

9. If someone scratches one end of a table with a pin, can you hear it when your ear is close to the other end? Why?

10. When you tap with a key on a steam-pipe in the basement, can the sound be heard upstairs? Why?

11. Why do processions always "break step" while marching across a bridge?

12. Do you get a higher note when you blow across the mouth of a arge Dottie than when you blow across the mouth of a small one? Why?

13. How does the energy from a passing steamer do the work of rocking a small boat a considerable distance away?

14. A toy boat is adrift 20 feet from the shore. Can its owner get it back by throwing stones into the water on the far side of it so as to make waves that travel toward the shore? Why?

15. Why does clapping your hands make a noise, while waving them does not?

16. Why does burning loose gunpowder make practically no noise, while shooting it in a cannon makes a loud noise?

17. If you fill a paper bag with air, hold the mouth shut, and strike it, it explodes with a bang. What happens if you strike it without holding the mouth shut? Explain.

18. Sound spreads in every direction from the source. Why does it become fainter as you get farther away from the source?

19. How does a megaphone or a speaking tube act so as to make sounds louder at a distance from the source?

20. Which travel faster, high or low notes? Why do you think so? 21. The speaking tone of the average man's voice has a frequency of about 160. How long are the waves that he emits at 16° C?

22. The average length of the waves that transmit the sound of a woman's voice is 3% feet at 16° C. What is the period of the corresponding tone?

23. Do women talk faster than men? Why?

24. A thunder clap is heard 7 seconds after the lightning flash is If the temperature of the air was 15° C, how far off was the flash?

seen.

25. If a sunset gun was fired at exactly 6:30 P. M. at a fort, what time was it when the report was heard 20 miles away, the temperature of the air being 25° C?

26. If you remain still in a row boat, the waves come in and strike the boat at regular intervals. If you row out towards the approaching waves, do they strike the boat more frequently or less frequently?

27. If (question 26) you turn round and row in toward the shore how about the frequency with which the waves now strike the boat?

28. Can you explain why the pitch of a tone from a locomotive whistle rises as you rapidly approach it and falls as you recede from it?

CHAPTER XII

MUSIC

230. The Piano. The most familiar of all devices for the production of music is the piano. On its keyboard there are usually 88 keys. Each key, when struck, produces a note of definite pitch. When certain of these keys are struck successively, we hear a pleasing succession of tones called a melody; and when several keys are struck together, we hear chords which may be either pleasing and harmonious or discordant, depending on which particular keys are struck. The piano cannot give tones of all possible pitches, but only those tones to which its strings have been tuned.

When we open the piano case, we find a large number of wires of various lengths and thicknesses. We also find that each key is connected by a very ingenious system of levers with a little felt hammer, which, when the key is pressed, strikes a wire and sets it into vibration, thus producing the note that corresponds to that particular key. The longer and thicker the wire, the lower the pitch of the tone it produces.

One end of each wire is wound around and fastened to a pin, which can be turned with a wrench so as to loosen or tighten the wire. By this means the strings are tuned, since tightening the string raises the pitch of its tone, while loosening the string lowers its pitch.

231. Sounding Board. Directly beneath the strings, with its edges fastened to the frame over which the strings are stretched, is a large, thin board called a sounding board. The vibrations of a string are transmitted through the frame to the sounding board, forcing it to vibrate in the same period with the string. Since the sounding board has a much larger

area than the string, it is able to set into vibration a larger mass of air than the string alone can. Consequently, a much louder tone is produced with the aid of the sounding board than could be produced without it.

232. Other Stringed Instruments. Like the piano, the violin, the violoncello, the mandolin, and the guitar consist of sets of strings tuned to give certain notes, and wooden bodies which serve as sounding boards, to make the tones from the strings louder. These instruments differ from the piano in that they have but few strings, and that these are set into vibration by picking or by bowing them instead of by striking them with hammers.

In instruments of the violin type, each string is made to furnish a large variety of different notes, by pressing a finger on it at various places, thereby changing its length. Since the finger may be placed on a string at any point, an instrument of this kind can give not only all those tones given by piano strings whose pitches are higher than that of its lowest string, but also notes of any intermediate pitches. Yet the notes actually used in playing stringed instruments are practically the same as those given by the strings of a piano. Thus, although the piano is tuned to give notes of only 88 different pitches, while the instruments like the violin can easily be made to give a far greater number than this, yet practically all musical instruments use only those few notes found in the piano scale. There must be some peculiar charm about this particular series of notes,-else why should we use these and no others? To answer this question, we must find out how strings vibrate.

233. How Strings Vibrate. Stationary Waves. The jump-rope is a vibrating string familiar to all children. Most of us know that when the rope is turned at a moderate rate, it swings in a single loop as shown in Fig. 127. It is not necessary to have two to turn the rope; one end may be tied to a tree, and so remain fixed while the rest of the rope vibrates.