Problems

(The normal air pressure is to be reckoned as 14.7 lb. per square inch or 1033.3 g. per square centimeter.)

1. A rubber balloon is placed under the receiver of an air pump. The pump is worked until the volume of the air in the balloon changes from 128 c.c. to 352 c.c. What is the pressure in grams per square centimeter?

2. An air pump having a cylinder holding 60 c.c. is used to pump air from a receiver holding 540 c.c. How much air is taken

out in the first 2 strokes?

3. Suppose the air to be all removed from an air-tight cubical box 2 ft. on each edge. What would be the pressure of the atmosphere tending to crush the box?

4. How much must the volume of air in a pneumatic riveting hammer be compressed to drive it at a pressure of 45 lb. per square inch?

5. What pull would be required to separate the hemispheres used by Guericke, which were 22 in. in diameter, if the air were entirely removed? What would be the crushing force of the atmosphere upon the entire surface?

6. How deep must water be in a box so that its pressure upon the bottom may be the same as that of the atmosphere?

7. If the box in problem 6 were 6 ft. square, how much would the air in it weigh?

8. How much does the external pressure on the receiver of an air pump exceed the internal pressure if its surface is 3550 sq. cm., and the internal pressure sustains a column of mercury 3 mm. long; outside barometer reading, 76 cm.?

9. What is the excess of internal over external pressure on a gas tank 3 ft. high and 10 in. in diameter, if the pressure gauge reads 91 atmospheres?

10. How many foot pounds of work are done by a compressed air engine during each stroke, if its piston is 16 in. in diameter, and the stroke is 18 in., when the gauge shows an air pressure of 4 atmospheres?

11. To what height would the atmospheric pressure sustain a water column if the barometer reading is 29.8 in.?

12. The specific gravity of glycerin being 1.26, what will be the reading of a glycerin barometer when the mercury barometer reads 753 mm.? What change in the height of the glycerin column will correspond to a change of 1 mm. in the mercury column?

13. Assuming the exterior surface of a man's body to be 20 sq. ft., what is the entire pressure of the atmosphere upon it? Why is it not crushed by this weight?

14. Pikes Peak is 14,108 ft. high. According to the graph in Fig. 162, what is the height of the barometer at the summit during fair weather? How does the density of the air there compare with that at the level of the sea?

15. A closed manometer like that in Fig. 166 is attached to a tank of compressed air. The air in the manometer is reduced to one fourth its original volume, and the difference of level in the mercury columns is 30 cm. What is the pressure in the tank in excess of one atmosphere?

16. The difference in the height of the two water columns in an open manometer is found to be 14 cm. when the manometer is attached to a gas jet. By what part of an atmosphere does the pressure of the gas exceed that of the air?

17. Over what height can water be carried by a siphon when the barometer reads 29.1 in.? What effect will it have upon the flow to reduce this height to 10 ft.?

18. What part of the air is left in a bulb which has been exhausted by the use of a Fleuss pump, when the pressure sustains a mercury column only mm. long?

19. A diver is working in 30 ft. of sea water, the sp. gr. of which is 1.025. What pressure must be supplied by the compression pump to counterbalance the water pressure?

CHAPTER VI

SOUND

I. WAVE MOTION AND VELOCITY

188. Simple Harmonic Motion. If a heavy ball, suspended like a pendulum, is given a circular motion in a hori

B

zontal plane, the cord by which it is suspended will describe the surface of a cone, and the arrangement is called a conical pendulum. To an eye at E, in the same horizontal plane as that in which the ball is moving, the ball seems to be moving in a horizontal straight line, projected on the wall at AB.

FIG. 178

Though the ball is

moving with uniform velocity around its circular path, the

a distance so great that the lines EA and EB are practically parallel: divide the circle into any convenient number of parts, 16, for example. From the dividing points 1, 2, 3, etc., drop perpendiculars to the line AB, meeting it at the corresponding points 1', 2', 3', etc. Any body moving to and fro along the line AB in such a way that its position at any time corresponds to the projection on AB of a body moving with uniform velocity around the circle of reference, is said to have a simple harmonic motion. It is evident that the distances 1'-2', 2'-3', etc., are passed over in equal times.

189. Vibrations and Wave Motion. A body or a particle that has simple harmonic motion is vibrating. The greatest distance reached from the position of rest is the amplitude of the vibration. The vibration is longitudinal when this motion has the same direction as the length of the vibrating body; it is transverse when the motion is perpendicular to the length.

When rapid vibrations are set up in one part of an elastic body, they are transmitted to the other parts in the form of waves.

Demonstration.

Procure a half-inch spiral coil of spring brass wire 10 or 12 ft. long, or make one by winding the wire on a piece of

FIG. 180

gas pipe fixed to turn in a lathe. Hook one end of the coil to a screw hook in a post, and taking the other end in the hand, stretch it somewhat. Strike the coil a light, vertical blow near the hand, and a wave will run to the fixed end and return (Fig. 180). The sudden jerk felt by the hand as the reflected wave strikes it shows that the wave transmits the energy of the blow.

190. Wave Length. One particle of a body transmitting waves is in the same phase as another particle when it is mov

ing in the same direc

tion with the same

B

E

velocity at the same time. Figure 181 shows the form of a wave, due to trans

FIG. 181

verse vibrations, moving from left to right. The particle A is moving downward with a certain velocity, and the next particle that is in the same phase is E. The particle C has the same velocity, but is moving upward. The distance between any particle and the next particle in the same phase, measured in the direction of wave motion, as AE, is the wave length. The top of the wave at B is called the crest, while the bottom at D is the trough. The vertical distance from B to the horizontal line (that is, half the vertical distance between B and D) is the amplitude. It is a simple matter to make a body record its own vibrations by tracing a wave form similar to Fig. 181.

Demonstration. Bore a hole near the end of a long piece of whalebone, and fasten it by a screw to the side of a block screwed to a board. Rub a few drops of kerosene or cosmolene on one side of a strip of glass so that the surface is evenly covered with a thin layer. Put some flour in a muslin bag and dust it evenly over

FIG. 182

the glass. Place on the board between two guides and underneath the whalebone. Fix a bristle to the whalebone near the end so that it will just touch the glass. Vibrate the whalebone, and the bristle will make in the flour surface a nearly straight line twice the length