PHVS/CS www wwai w m i M i WRiGf/T Longtmans' Elementary Science Manuals. CORNELL UNIVERSITY LIBRARY FROM Cornell University Library arV17829 Elementary physics / ,. 3 1924 031 270 352 olin,anx PRINTED BY SPOTTISWOODE AND CO., NEW-STREET SQUARE LONDON ELEMENTARY PHYSICS BY ^ MARK R.^RIGHT HEAD MASTER OF THE HIGHER GRADE SCHOOL, GATESHEAD AUTHOR OF 'sound, LIGHT, AND HEAT' LONDON LONGMANS, GREEN, AND CO. AND NEW YORK : 15 EAST i6"> STREET 1889 ® The original of tliis bool< is in tine Cornell University Library. There are no known copyright restrictions in the United States on the use of the text. http://www.archive.org/details/cu31924031270352 PREFACE The method followed in this work is the same as that pursued in ' Sound, Light, and Heat ' in this series ; the leading facts are brought under the notice of the student by easy experi- ments, that do not demand expensive apparatus. Full .in- structions are given for the construction of the apparatus, in the text, or in the Appendix. The work will serve as a suitable text -book for any class beginning the study of physics. The author believes that in early lessons it is inadvisable to trouble the student either with theories, or with the generalisations that prove such a valuable aid to the advanced student ; little space has therefore been devoted to theoretical considerations. Experience as a teacher suggests that a careful examination of the facts of science is the first duty of a beginner. Many illustrations are new, others are from ' Sound, Light, and Heat,' and from blocks in the possession of the publishers ; several in magnetism and electricity are from Mr. Poyser's work on those subjects. Numerous easy examples will be found throughout the book. M. R. W. Gateshead : October 1889. CONTENTS HEAT CHAPTER PAGE I. HEAT AND TEMPERATURE. THERMOMETERS II. EXPANSION OF SOLIDS, LIQUIDS, AND GASES . III. HEAT AS A QUANTITY. SPECIFIC HEAT IV. LATENT HEAT. FUSION. VAPORISATION . 1 V. TRANSMISSION OF HEAT I 12 22 28 42 SOUND I. PRODUCTION AND SPEED OF SOUND 55 II. TRANSMISSION OF SOUND. WAVE MOTION . . . . 6o IIL INTENSITY AND REFLECTION OF SOUND 68 IV. MUSICAL SOUNDS. PITCH, INTENSITY, QUALITY. . . 74 LIGHT I. RECTILINEAR PROPAGATION OF LIGHT. SHADOWS . . . 83 II. REFLECTION OF LIGHT. MIRRORS 93 III. REFRACTION OF LIGHT. LENSES IO9 IV. COLOUR 126 MAGNETISM L MAGNETIC INDUCTION I3I II. TERRESTRIAL MAGNETISM 145 viii Elementary Physics FRICTIONAL ELECTRICITY CHAPTER PAGE I. ATTRACTION AND REPULSION . . .... 159 11. INDUCTION ... .... 176 III. POTENTIAL. MACHINES . 187 VOLTAIC ELECTRICITY i. the voltaic battery 201 ii. the current. the galvanometer 200 iii. electrolysis. electro-magnets 2l8 Examination Questions 233 Appendix 235 Answers to Examples 244 INDEX 245 HEAT CHAPTER I HEAT AND TEMPERATURE—THERMOMETERS, Heat and Temperature. — The earth is warmed by the heat from the sun. Savages ignite fires by rubbing together pieces of dry wood ; by rubbing a brass button upon a piece of wood, we can heat it sufificiently to render it unpleasant to the hand. When the brake is applied to a railway train, the friction heats the iron wheels, and sparks of molten metal fly from them. The blacksmith, by hammering a hot piece of metal, can raise it from a red to a white heat. Heat is supplied by the earth — notably by volcanoes, geysers, and hot springs. Heat is also generated by chemical action ; for example, the heat evolved when we pour water upon quicklime, and when we burn coal. The principal sources of heat are, the sun, mechanical actions such as friction and percussion, the earth, and chemical action. Other sources will be mentioned in this volume. We test the state of a body with respect to its heat by touching it, or by holding the hands near it. The laundry-maid determines when the iron is sufficiently hot, by holding it near her face. The nurse tests the state of the bath with respect to its heat by putting her hands in it. The state a substance is in, with respect to the heat that affects the senses, is called its temperature. Our own sensations cannot be relied upon to give us exact knowledge of temperature. A warm day, when we are in good health, might be called a cold day if we were ill. A substance B 2 Heat we describe as warm to-day may be in ^ very different state, with respect to its heat, compared with the same substance that we described as warm yesterday. Two persons will not always agree concerning the temperature of a body : the glass-worker -is not greatly distressed when the temperature of the factory in which he is working is unbearable to a visitor. Both hands will not always give the same verdict, — the right frequently feels cold to the left. Plunge the right hand into hot water, the left into cold water ; after a minute plunge both into lukewarm water ; the right hand now feels cold and the left hand warm. Touch pieces of iron, wood, and flannel, in a room shaded from the sun ; the iron feels cold, the wood fairly warm, and the flannel warm. We shall prove afterwards, that all are at the same tempera- ture. The hand may be a good measurer of temperature when confined to the same substance; bath attendants are very expert in determining suitable temperatures of water for baths. We conclude, however, that generally the hand cannot be used for comparing the temperatures of bodies. By mixing I lb. of hot water with i lb. of cold water, we obtain 2 lbs. of lukewarm water. The same amount of heat is there, but the temperature is different from either of the single pounds. Temperature is a state or condition; it is no more heat than the level of the water in a basin is the water itself Heat is analogous to the water in a vessel ; temperature to the level of the water. Heat flows from a body at a high temperature to one at a low temperature, just as water flows from a high to a low level. Heat is the agent which produces the sensation of hotness, warmth, and similar sensations. If a red-hot ball be placed in an exact balance, we can detect no change of weight when it cools, or loses heat. Heat, we infer, is not a material substance like water, that can be poured from one vessel to another. Remembering this, we may conveniently speak of heat flowing from a hot to a cold body, without regarding it as a material substance. Heat and Temperature — Thermometers 3 Expansion of Solids. — In nearly all cases a body expands when it is heated. The platelayer is instructed to leave a space between the ends of rails. A bridge is never fixed at both ends, one end being placed on rollers to allow for the change in length as the temperature changes. We can convince our- selves of the truth of the statement that bodies expand, when heated, by actual experiments. Fig. I. A bar or rod of iron (fig. i) about 18" long .rests upon two blocks of hard wood ; one end of the bar is held firmly by a heavy weight, the other end rests upon a sewing-needle ; a light straw is fastened at right angles to the needle with sealing-wax, and a divided semicircle is fixed behind the straw. If the rod moves to the right or left, the needle will roll, and the pointer will move to the right or left. A very slight movement of the bar will cause a considerable movement of the index. Heat the bar with a spirit- lamp, the temperature rises, and the pointer informs us that the bar is expanding ; on cooling, the pointer moves to the left, showing that the bar is contracting. This experiment illustrates a bridge, one end fixed and the other upon rollers to allow for changes in the temperature. Fig. 2. A more difficult experiment is the following : — A piece of platinum wire 18'' long (fig. 2) is attached to an iron or copper B2 Heat screw ; it passes over a piece of knitting-needle to which an index is attached as in the last experiment ; the wire then passes through a notch in the smooth iron bar upon which the needle rests, and is stretched by a pound weight ; the notch keeps the wire in position. If now one terminal of a pair of Grove's cells be attached to A, and the other terminal touch the iron bar B, a current flows through the wire, heats it, and the elongation is registered by the movement of the index. We may conveniently dispense with the Grove's cell, and merely run the flame of a Bunsen burner along the wire a few times. The heating makes the wire bend if both ends be fixed, but the bending is difficult to observe. Telegraph wires " sag " more in summer than in winter, on account' of expansion due to the weather, not to the electric current. Expansion in length is called linear expansion. A surface having length and breadth will expand in two directions. A window-pane, tightly fixed on a cold day, frac- tures on a warm day, if space has not been allowed for expan- sion. - A solid can expand in three directions ; such expansion is called cubical expansion. Cut a hole in an iron plate so that a 4-oz. flask filled with cold water just passes Fill the flask with hot water ; the area of the section of the flask increases, and the -flask is unable to pass through the hole. A historical experiment is Gravesande's Ring (fig. 3). A ball, a, passes the hole, m, when cold, but not when heated. Move the ball into different positions ; , in no position will it pass ; the ' experiment, then, illustrates the cubical expansion of solids. Expansion of liquids.— The illustration (fig. 4) represents a tube 12'' long, inserted by a round .cork into a 2-oz. flask. The flask is filled with water that has Fig. Heat and Temperature — Thermometers 5 been jjoiled (to expel the air) and coloured with red ink. A paper scale is fastened behind the tube. Place the flask in a dish of warm water ; notice first a slight descent, then a steady rise of the liquid in the Tube. The slight descent is due to the glass expanding before the heat is com- municated to the water. The expansion is readily observed, and we con- clude that liquids expand much more than solids. By fitting up similar flasks and filling them with various liquids, such as alcohol, turpentine, and mercury, we can compare the expansions of liquids. Move the corks, and arrange so that the liquids all stand at the same height. Place all in a dish of lukewarm water. The alcohol expands most, turpentine second, water third, and the mercury the least. Observe that the mercury begins to move first. fig. 4. Examples. I. r. Define Heat and Temperature. Is temperature heat ? 2. What is meant by expansion ? When are the terms linear, square, and cubical expansion used ? 3. How would it affect the rise of the liquid in fig. 4, if a tube be used (a) with a narrower bore {b) with a wider bore ? What would be the effect of using a larger flask ? Suppose the glass did not expand, how would this affect the rise of the liquid ? Thermometers. — A thermometer is an instrument for measuring temperatures. The expansion of solids is so small that they cannot be used for thermometers. Liquids, enclosed in glass tubes, make suitable thermometers. Mercury is preferred, although its ex- pansion is not so marked as water and alcohol ; it expands regularly, and remains a liquid at temperatures at which water and alcohol pass into vapour ; it can be obtained pure, and as we saw in the last experiment, it takes the temperature of a body quicker than the other liquids. In the simple thermometers we have constructed, the bulbs are large and the tubes are open at the top. An open tube would admit dirt and allow Heat evaporation ; it would also allow the pressure of the atmosphere to affect the position of the liquid in the tube. A Mercury Thermometer. ^ — A small bulb is blown at the end of a tube with a fine uniform bore (fig. 5). A small bulb is chosen so that the mercury may quickly receive or lose heat, and a 9wm fine bore that for a slight change in IJ temperature we may have a distinct I /H motion of the mercury. A bulb is blown at the other end, and cut in two, so as to leave a small cup, a. Mercury is placed in the cup, but is unable to run through the fine bore. The tube is warmed, air is expelled, and on cooling, the mercury is forced into the bulb. This is repeated, until the bulb and the tube are full. Finally the mercury is boiled, to ex- pel all air and damp. The tube is next heated near the cup, drawn out, E, and cut off. The bulb is then placed in a bath of boiling oil, till the mercury oozes out at the point. When no more oozes out, a small flame is held to the point until the glass softens ; the flame is then re- moved from the bath, and the end of the tube closed, f. When the thermometer cools it contains only mercury and mercury vapour. The fixed points. — A divided scale behind the tube might serve the purpose of one experimenter, but as different persons wish to compare temperatures, two fixed points have been agreed upon. It is found that (i) the temperature of melting ice is always the same wherever or whenever the experiment is tried ; (2) that; the steam of boiling water is always at the same temperature if the pressure be the same. The standard pressure in England #° 4 Fig. 5. Heat and Temperature — Thermometers is taken as a pressure of 30 inches of mercury on the square inch, on the Continent as 760 milUmetres of mercury on the square millimetre — that is, in England the barometer must either be standing at 30 inches, or allowance must be made for any variation. I. The Freezing-point. — Clean snow or well-pounded ice is placed in a vessel (fig. 6). The thermometer is inserted, so that it is surrounded ; it is left for a quarter of an hour and moved, until the thread of mercury is seen just above the ice ; a scratch is then made with a file ; this is the freezing-point. The water from the melted ice escapes at the bottom. II. TheBoiling-Point. — The bulb is placed in a metallic vessel (fig. 7), so arranged that the tube is heated by steam. By following the 8 Heat B2* ^ I Fig. 8. -y direction of the arrows it will be seen that the inner tube, A, is prevented from cooling by the steam surrounding it. The thermometer is moved until the mercury is just seen above the cork, a ; when it is stationary a mark is made ; this is called the boiling-point. If the barometer be not at 30 inches a cor- rection is made from tables. The Scale. — ^The distance between the fixed points is divided ^ C R into equal parts called degrees. Three methods are followed (fig. 8): 1. Fahrenheit Scale. — ^The freez- ing-point is marked 32 degrees (written 32°) the boiling-point 212". Therefore the distance be- tween is divided into 180 equal parts. This scale is ih common use in England. Fahrenheit be- lieved that his zero, 32° below freezing-point, was the lowest tem- perature experienced on the earth. 2. Centigrade Scale. — Freezing- point is 0°, boiling-point 100°. This scale is in common use on the Continent, and in general use for scientific purposes. 3. Reaumur's ^a/t;.— Freezing-point is 0°, boiling-point 80°. This scale is in common use in Germany. The divisions are continued above and below the fixed points, the division below 0° being indicated as — i", —\o°^ -15°, &c. One hundred and eighty divisions on the Fahrenheit scale are equal to 100 divisions on the Centigrade. Therefore 9 divisions F.=5 divisions C. (*) A thermometer reads 60° F. grade scale ? 60° F. is 60 - 32, or 28 divisions F. above freezing-point, is 28 X I C. divisions above freezing-point. /. the reading is 28° ^ | or iS'S" C. What is the reading on the Centi- That Heat and Temperature — Thermometers g Change 12° C. into the Fahr. scale: — 12° Cent, above freezing-point = ^» or 2 if divisions Fahr. above freezing-point. But as freezing-point is marked 32° on the Fahr. scale, the reading will be (32 + 2i|)° = 43!° Fahr. Express o°F. on the Centigrade scale. o°F. is 32 Fahr. divisions below freezing-point. .•. 32 X I or i7|° C. below freezing-point .". the reading is- 17|° C. Examples. V. 1. Define Heat and Temperature. What is meant by sensible heat ? 2. What is a thermometer ? Describe the construction of a mercurial thermometer. 3. How are the fixed points on the stem of a mercurial thermometer determined ? Into how many parts is the distance between them divided on the Fahrenheit scale ? To what temperature on the Centigrade scale does 179° F. correspond? 4. How many divisions of the Centigrade scale are equal to 54 divisions of the Fahrenheit scale on the same thermometer. 5. Change the following degrees Centigrade into degrees Fahrenheit : SO, 10, - 7. 180, 32-5. 6. Express 90°, 30°, - 15°, 32°, 180° Fahrenheit in the Centigrade scale. Testing Thermometers. — Ordinary thermometers are rarely accurate ; it will form a good exercise to test the thermometers which are in use in the class. The apparatus for testing the freezing-point is readily made out of an ordinary tin, by punching a few holes in the bottom. It is important to use clean ice. After testing with clean ice, add a little salt, and test again. In a class experiment the thermo- meter indicated - 10° C. when salt was added. For verifying the boiling-point, a flask with a long neck and half-filled with water may be used (fig. 9). Pass a thermometer through a cork, through which also passes a bent open tube. The thermometer must not touch the water ; it should merely be sur- rounded with the steam. When the mercury is steady, add a little salt to the water, and note again the height of the mercury when immersed in the steam. Place the thermometer in the salt and water and observe the tem- perature ; also in water containing calcium chloride. lO Heat Example. Freezing-point with clean ice = o° C. „ „ ,, ice and salt =— 10° C. Boiling-point with steam from water = 100-5° C. Error -5° salt and water = 100-5° ^• , ,, calcium chloride and water, the thermometer dipping into the water = 107° C. Impurities affect the boiling-point of water, but do not affect the temperature of the steam from such water. The mercurial ther- mometer can now be used to test the temperature of a body. Suppose it touches a piece of warm iron, heat flows from the iron to the mercury ; the bulb being small the heat lost by the iron is inappreciable ; soon the iron and the thermo- meter are at the same tem- perature, whichis practically that of the piece of iron. With the thermometer test the temperature of va- rious bodies in the room. Show that all are at the same temperature. (See p. 2). When the temperature is steady, the thermometer being surrounded by steam, connect the tubes of a and b with india-rubber tubing (fig. 9). The tube of b dips into water ; therefore the steam has now to overcome a greater pressure ; the mercury rises, showing that the temperature is rising. Le^ the tube of b dip into mercury ; the steam has now to over- come a yet greater pressure, and a further increase of tempera- ture is indicated. The boihng-point depends upon the pressure the vapour has to overcome. In an experiment the thermometer, sur- FiG. 9. Heat and Temperature — Thermometers ii rounded by steam that escaped freely showed loi"; when thp tube dipped into 8" of water the thermometer indicated 102°; when mercury was substituted for water the boiling-point became 108°. Examples. III. 1. Why should care be exercised in securing a tube of uniform bore? 2. What are the objections to constructing a mercury thermometer and leaving the top of the tube open ? 3. How is a thermometer filled ? 4. Why is it necessary to boil the mercury? 5. What is meant by ' the fixed points ' ? What precautions must be taken in obtaining the boiling-point ? 6. Change the following degrees C. into F. : 15°, 30°, 17-5°, 0°, 100°, -30°, - 10°. F. into C. : 180°, 212°, 70°, 60°, - 12°. 7. How would you construct a water thermometer ? How would you graduate it ? 8. Explain how the fixed points on the stem of a mercurial thermometer are obtained. Why is it necessary, in marking the ' upper fixed point,' to take note of the height of the barometer ? 9. How would you show that the boiling point changes as the pressure changes ? 10. Does the thermometer measure heat ? What does it measure ? 11. Why is steam used rather than boiling water in determining the ' upper fixed point ' 2 12. What is meant by a ' degree' of heat, say 14 degrees Centigrade? What is meant by a change of temperature ? 12 Heat CHAPTER II EXPANSION OF SOLIDS, LIQUIDS, AND GASES The linear coefficient of expansion. — ^The general state- ment that solids expand when heated, is insufiScient for prac- tical purposes. We must know how much a given length of iron, say, will increase in length, when heated through a number of degrees. Small as the expansion is, it can be measured by methods, that are explained in advanced works. A bar of iron measured 20" at 0° C, and 20~" at 100° C. A brass rod at I5°C. was 24" long; at 95° C. it was 24j|g" long. To compare the expansions of brass and iron, we calculate the elongation of each, when its temperature rises from 0° to 1° C, and compare the elongation with the original length. For all practical purposes we may calculate the elongation when the temperature rises one degree, beginning at any ordinary tempera- 2" ture. In the above example the elongation of the iron is — 100 for 20" when its temperature is raised 100° .'. the elongation 2" 2" for I "will be ;- 100 = The relation between this 100 1 0000 2" elongation and the original length is =-20' I 0000 I 00000 The fraction -nrwirTr is called the linear coefiScient of ex- pansion of iron. Similarly we calculate that the linear co- %" T efiScient of expansion of brass is -^ — h 80 -;- 24" = - 100 64000 The linear coefficient of expansion for one degree, is the ratio of the increase of length when the temperature is raised one degree, to the original length. Expansion of Solids, Liquids, and Gases 13 Tablk of Coefficients of Linear Expansion for 1° C. Glass = -00030085 = Platinum . = -0000085 = Cast iron . = -ooooi = Wrought iron = -000012 = 120000 I 120000 I lOOOOO I 85000 Brass . = -000016 = Copper == -000017 ~ Lead . =-000028 = Zinc . = -00003 = 64000 I 58000 3S00O I 34000 This table is only approximate as different specimens vary in their expansions. It assumes that the expansion from 0° to 1° C. is — of the expansion from 0° to 100°: this is 100 nearly true, and it is by measuring the expansion for 100°, or some such range of temperature, that the coefficient is deter- mined. The coefficient for 1° F. will be 2. of the above values. 9_ The coefficient of cubical expansion is three times the coefficient for linear expansion. This will be understood by considering fig. 10. Let the lines represent a cube of one foot side, that increases slightly in three directions ; let its co- efficient of linear expansion be -ooi. The increase in volume will be three slabs (Aj, Aj, and A, are the diagonals), three strips (a section of each is shown), and a small cube. The strips and cube will be so small compared with the original volume when the expan- sion is very small, that they may be neglected. The increase in volume will therefore practically be the volume of the three slabs. And the coeffici- ent of cubical expansion (increase in volume -T- original volume) will be -003 c, That is, three times the coefficient of linear expansion. thick very 14 Heat Examples. IV. 1. Find the coefficient of expansion in the following examples : — u. A rod of brass at 15° C. measures 2 feet; at 95° C. it measures 2-003 fs^t- b. A rod of glass at 10° C. measures 5 feet ; at 70° C. it measures 5 -0024 feet. 2. Explain what you mean when you say that the coefficient of linear expansion of iron is o-ooooi2. If an iron yard-measure be correct at the\j temperature of melting ice, what will be its error at the temperature of boiling water ? 3. From London to Edinburgh is 400 miles. Suppose the hottest day in summer to be 90° F. above the coldest day in winter ; find the difference in length in the rails laid on the railway between the two places. 4. A rod of brass just fits between two supports ; ice-cold water is poured over it and the bar falls. Why is this ? The bar is now heated in a boiler and is found to be too long. Why ? 5. A rod of lead, 6 feet long, was fixed between two firm supports on a day in winter. It was examined in summpr and was found bent. Explain why. ■ '> Forces of Expansion and of Contraction. — Solids in ex- panding and contracting do work. AB (fig. 11) is an iron bar passing through sockets in a strong cast-iron frame, CD. The iron bar has a hole at one end, through which passes a small rod, =^^ L Fig. F, of cast iron. At the other end is a screw- thread, A, on which a nut, N, with two arms works. The rod is heated, placed in its sockets, the rod F is inserted, and the nut screwed up tightly. As the temperature falls, the bar contracts, and the force is sufificient to break the rod of cast iron F. The force exerted is enormous ; an iron rod i square inch in section in cooling through 9° C. exerts a force of i ton. A striking illustration is afforded in the case of telegraph wires. An iron wire stretched across a span of 400 feet with a sag of 5 feet at a temperature of 25° C. would have a strain upon it of 13,544 lbs. per square inch. In winter, at a temper- ature of —5° C. the strain would be 34,000 lbs. per square Expansion of Solids, Liquids, and Gases 15 inch, suflficient to permanently stretch the wire. The iron tyres of wheels are placed on red-hot and fit loosely ; on cooling they secure the woodwork tightly, EflEects of expansion and contraction.— Draw out a piece o glass tubing ; cut the end off, leaving a small hole ; insert a piece of platinum wire and heat in the flame. The glass fuses, the hole closes, and on cooling the platinum is found to be firmly imbedded. Try the same experiment with an iron wire — either the glass cracks, or the hole is not closed. The coefficients of expansion of glass and platinum (p. 13) are equal, while there is a marked difference between the ex- pansion of glass and iron. Solder a strip of brass and a strip of iron together, hammer them until they are straight ; heat the compound bar ; it bends, the iron being on the concave side. The coefficient of expansion of brass is ■000016; that of iron = -ooooi. The brass expands more than the iron, and therefore forms the convex side of the bend. The rate of a chronometer depends upon the mass of the balance-wheel (fig. 12), and the distance of the circumference from the centre. The parts B c are made up of a compound strip like the above, the metal having the highest coefficient of expansion being on the outside. When heat'ed the radius a expands, and the chronometer would lose time ; but the heat ^^^ ^^ also causes the strips b c to curve inwards, the masses b are thus brought nearer the centre, and this compensates for the extension of a a. Compensating Pendulums. — Any alteration in the length of the pendulum affects the time of the clock. Pendulums so constructed that they do not alter their number of swings per second as the temperature changes, are called compensating pendulums. In Harrison's gridiron pendulum (fig. 13) a, b, c, d are rods of steel ; h, k are brass. If the temperature rise, a, b, c, and |f period. From o to 12 (e) is one wave-length ; o is in its original position. If after one revolution the particles rest, one wave moves along, Transmission of Sound — Wave Motion 63 and in i-j^g- period the position is f. The wave has advanced half a wave-length from the position in E. If the particles keep moving the waves are repeated as in g. In all these illustrations the particles do not change from their average position ; the form of the wave alone moves forward. Longitudinal waves. — The preceding explains water-waves, the waves that pass along ropes, and, as we shall see later, the waves of light and radiant heat. There is, however, another method by which wayes can be transmitted. Fill a piece of india-rubber tubing 12 feet long and \ diameter with sand, and hang it from the ceiling ; near the top make a dis- tinct chalk mark, hold the end in one hand, so as to slightly stretch the tube ; with the fingers of the one hand rub it along its length. A wave passes along the tube, as is shown by the move- ment of the mark ; it is reflected at the top and moves back. Wrap a long steel wire round a cylinder of wood 2" diameter, so that the coils are ^" apart. On removing the cylinder a spiral is formed. Suspend the coil horizontally, this is done by attaching two threads to every tenth coil and fastening these threads to the parallel horizontal laths. Gather a few coils at one end into the hand ; on releasing them observe the compression travel to the pther end of the wire. In the last two experiments a wave passes along the tube and helix ; the particles move backwards and forwards in the line of direction, but do not change their average positions. Cut a narrow slit ss'm black paper B (fig. 48). Place it along the dotted line of A. Draw A beneath the slit in the direction of the arrow ; the dot that is seen, vibrates backwards and forwards ; its motion is harmonic, as we see from the form of the sinuous curve. A number of particles moving backwards and forwards, one moving a httle after the other, will produce a wave ; there will be a compression (the particles come together) succeeded by a rarefaction (when the particles move apart, relative to each other) like the compression and rarefaction that travelled along the coil. 64 Sound Place the slit along the dotted line C, fig. 48 ; draw the book in the direction of the arrow. Each curve in c is similar to A. They are arranged so that each dot produced with the slit moves a little later in its path than the preceding dot. The wave of compression and rarefaction will be seen travelling across the slit. Compare the parts of greatest com- pression with crests of waves, the parts of rarefaction with troughs of waves (fig. 49). The wave-length is the distance from one compression to the next (from f to c (i)), or from one rarefaction to the next (from r to r (i)), or from one particle to the next particle in a similar position, and moving in the same direction ; and as in the case of vertical waves, the. wave will move one wave- F16. 48. Transmission of Sound — Wave Motion 65 length in the time it takes a particle to make a complete vibration. Soimd-waves. — Sound-waves are transmitted by the air- particles vibrating in the line of direction. When a body vi- brates with sufficient rapidity, the parti- cles of air surround- ing it are set in '°"*'' motion and sound-waves are formed. The motion is commu- nicated by each particle to the next, the motion of the particles near the ear affect that organ, that is, energy is transmitted by the sound-waves to the ear and a sound is heard. When a gun is fired the sound-waves travel ; there is, however, no tendency Fig. 50. for the smoke to move in straight lines in ajl directions as the sound-waves do. The propagation of sound-waves is not the propagation of air-particles. Insert a funnel in one end of a long wide india-rubber tube, direct the other end towards a lighted candle, and blow a little smoke into this end. Beat two pieces of wood together near the mouth of the funnel ; the candle is extinguished by the sound- wave, but the smoke is not forced through the tube. • Such sound-waves from firing shots in mines (it has been 66 Sound suggested) cause explosions, by forcing impure gas through the meshes of the Davy lamp (see p. 47). Sound travels in all directions. A skylark singing is the centre of a sphere of sound-waves, and every particle in the sphere is vibrating. Fig. 50 gives a rough idea of the sound-waves caused by a bell. At equal distances from the point of disturbance all the particles will be in similar positions, and will form the surface of a sphere ; such a surface forms the front of the wave. If we consider a very small portion of the surface of a sphere, it will practically be a plane surface ; so that the wave-front is a plane surface, and the direction of the wave is at right angles to this surface. Elasticity. — Set a dozen solitaire balls in a groove ; move one and roll it against the eleven ; the end one starts off the row, while the intermediate balls are apparently motionless. In the water-waves, the particles moved upwards on account of the impulse given to the wave (the stone falling in the pond, &c.), and downwards on account of the action of gravity. How can we explain that when a particle moves forward, it returns on its path and moves backwards ? Why do the solitaire balls transmit motion ? Definition. — When a body, after being compressed by a force, recovers its original shape when the force is removed, the body is said to be elastic. It requires a certain force to compress a piece of putty, but on removing the pressure the original shape is not regained ; putty is therefore inelastic. Cover a flat stone with red powder, touch it with a solitaire ball, and notice the dot made. Allow the ball to fall from a height of three or four feet upon the stone and examine the dot made ; it is larger than before, the ball has been flattened, but when the pressure was removed it regained its original shape. The glass ball is elastic. Allow a leaden ball to fall, the flattening remains. Glass is elastic ; lead is inelastic. Each time one prong of a vibrating tuning-fork advances, it gives a push to the air ; the particles are compressed, and by their elasticity resist compression ; they expand, compressing the Transmission of Sound — Wave Motion 6y next set of particles ; these, in their turn compress the next set, so that the compression is propagated. When the prong moves back it causes a rarefaction ; this rarefaction is transmitted in the same way as the compression. The tuning-fork makes a series of backward and forward movements, and thus a series of condensations and rarefactions are produced, which constitute sound-waves. The particles recover themselves on account of their elasticity, and transmit the wave just as the solitaire balls did ; each ball, representing a particle of air, was compressed for a short time, it then expanded on account of its elasticity and communicated the compression to the next ball. Examples. II. 1. Give an example of harmonic motion. 2. Define the terms oscillation, vibration, amplitude, period. 3. Give examples of wave-motion. Explain crest and hollow. 4. Define wave-length. 5. In what direction do the particles in a water-wave move ? 6. There are five crests between a. boat and the shore, a distance of 100 feet. Calculate the average wave-length. 7. What is meant by a wave of sound and by the length of a ■uvmie ? Explain how sound is transmitted through air. 8. Compare the direction of the motion of the particles in a water-wave, and the wave in a wire spiral. 9. Define wave-length. Suppose the amplitude of vibration of the particles be doubled, how Will this aflfect the wave-length ? 10. Explain condensation, and rarefaction. 1 1. Give illustrations and experiments to show that when a sound-wave is transmitted, the air-particles do not leave their average position. 12. Explain elasticity ; give examples of elastic and inelastic substances. 13. Explain how the condensation and rarefaction constituting a wave of sound are produced. How is a sound-wave propagated through air ? 14. Take the speed of sound as 1,120 feet per second. Find the wave length (a) if there be 280 vibrations per second, {b) if the period of the particles be jjj second. 15. Sound-waves are i-2 foot long; the air-particles make 1,000 vibra- tions in a second. Find the speed of sound. 16. Explain the action of the toy telephone made of two cardboard boxes connected vrith string. 68 Sound CHAPTER III THE INTENSITY AND REFLECTION OF SOUND Intensity. — The further the ear is from a sonorous body, the feebler is the effect as regards sound upon the ear. As in all cases of straight line motion, the intensity varies inversely as the square of the distance ; that is, the intensity of sound at a distance of 200 yards is one-fourth the intensity at 100 yards. The intensity depends upon the density of the medium in which the sound originates (p. 57). Make the tuning-fork sound, then place the end upon the table, or, better still, on a thin board suspended by threads ; observe how the sound is increased. Sprinkle fine sand upon the thin board ; the sand moves, proving that the board is vibrating. A string stretched tightly over two nails in the wall produces scarcely any sound when it vibrates ; stretch the same string on supports inserted in a box with a thin cover : the sound is increased. The area of a vibrating body may be so small, that the number of air-particles set in motion are unable to affect the ear, or affect it slightly ; when the vibrations are transmitted to a larger area, a larger number of particles are set in vibration and these cause a distinct increase in the intensity. The wall in the experiment is so thick and so firmly fixed that it is unable to vibrate ; the thin wood readily vibrates and increases the in- tensity. For this reason musical instruments are provided with sounding-boards ; in the violin the thin wood forming the belly vibrates when the string is bowed ; the post communicates the vibration to the back, which also vibrates. A tuning-fork held in the hand sounds longer than when its root rests upon a sounding-board ; the energy is communicated to a larger surface The Intensity and Reflection of Sound 69 and is the sooner used up. We gain in the intensity of the sound, but lose in the time the sound lasts. The intensity depends upon the area of the sonorous body. If in fig. 46 we double the diameter of the circle, that is, double the amplitude of vibration, while the period remains as before ; each particle in a b c . . . must move with twice its former speed. The waves will be higher and will have a greater effect upon any obstacle, their capacity for doing work will be four times their former capacity. In a similar way if the ampli- tude of the particles in sound-waves be doubled or trebled, the capacity of the waves for doing work will be four times or nine times their former capacity, and will have four times or nine times their former eiiect upon the ear. The amplitude of the vibrations of the air-particles, will be the amplitude of vibration of the sonorous body. The intensity depends upon the amplitude of the vibration of the particles ; if the amplitude be doubled the intensity is quadrupled ; the intensity varies as the square of the amplitude of the vibrations of the sonorous body. A sensitive flame. — Bend a piece of glass tubing at right angles. Draw out one end ; cut off so as to leave a very small orifice. Connect the other end with the gas supply (fig; 51) ; z" above the orifice place a square piece of brass gauze 6'' side ; turn on the gas, ignite it above the gauze, and surround the flame with a wide piece of glass-tubing about 6" long. Turn the gas-tap until the flame just does not flare. The vibration of the air-particles of sound- waves affect the gas below the gauze, and the flame flickers. Rattle keys, tap on the table, hiss, or whistle, the flame is in every case affected. Fig. 51. Beflection of sound. — Draw a semicircle ' on the table with chalk, graduate it as in fig. 52, and arrange the tin tubes along radii each making 45° with the normal. Place the sensitive flame at the end of one. A, and several 70 Sound damp towels, B, between A and the end of the other tube. Tap two pieces of metal together inside the second tube, adjust the flame, and use more damp towels if necessary until the flame does not respond to the taps. Place a reflecting surface, a plane mirror, a sheet of paper, or the hand, at c. The flame is at once affected by the taps. Remove the 1-eflector, the flame steadies. If a be placed making an angle of 40° with Fig. 53. the normal, then the other tube must make the same angle. The sound-wave which travels down one tube is reflected at c. A watch may be substituted for the taps and the ear for the sensitive flame. Sound is reflected similarly to light (p. 94). The angle of incidence is equal to the angle of reflection. Dry towels, sheets of paper, do not serve as effective screens, 77!^ Intensity and Reflection of Sound 71 and we conclude that they are poor absorbers of sound-waves, while damp towels are good absorbers of sound-waves. By using two large concave reflectors, we can further illus- trate the reflection of sound (fig. 53). When a watch is placed at the focus of one mirror, a person can hear the ticks by placing his ear at the focus of the other mirror, although the distance may be such, that when the second mirror is removed, he is unable to hear the ticks. The sound-waves from the watch strike the near mirror, are reflected parallel to the principal axis, and after meeting the second mirror, are again reflected to its focus. This is the better demonstrated by substituting the taps for the ticks of the watch, and the sensitive flame for the ear. Whispering-galleries. — We can easily understand that if a gallery be of a certain shape, the whisper of a person in one part may be quite audible to another person beyond ordinary range of sound. Regard the two mirrors in fig. 53 as the opposite side of a semicircular gallery. Speaking-tubes. — The use of the tubes in the experiments Fig. 54. is, that the waves of sound reflected are from the interior and are thus prevented from spreading. Instead of the intensity 72 Sound being inversely as the square of the distance, there is but a slight diminution of sound. Reduce the sensitive flame until it is not affected by the taps produced from two pieces of metal, at a distance of 1 5 or 20 feet. Fit the large tin tubes end to end, and place them between the flame and the source of sound so that the taps are made close to one end. The flame at once responds. If we use a long india-rubber tube, half-inch wide, and place one end to the ear, the slightest sound made at the other is distinctly heard. Bending the tube, provided it be not closed, does not affect the experiment. The speaking-tubes used in offices are made of strong caoutchouc, provided at each end with an ivory or bone mouthpiece (fig. 54). Echoes. — Reflection of sound is the cause of echoes. The sound-wave travels to a reflectirig surface — such as the walls of a building, the sides of a mountain, or the trees at the edge of a forest — is reflected, and travels back to the ear ; the sound now heard is called an echo. It is difficult to distinguish words that strike the ear at less intervals than one-tenth of a second — that is, the wave must travel ^^ feet, or no feet, therefore the sur- ' 10 ' ' _ face must not be less than 55 feet distant. Standing between two reflecting surfaces, the Sound-wave, reflected from each, proceeds to the opposite surface, and is again and again re- flected, each echo being fainter than the preceding one. Two or more echoes may also be caused by two or more parts of a reflecting surface at different distances .from the observer, as, for example, from the parts of the edge of a wood at varying distances. Examples. III. 1. Explain the meaning of intensity of sound ; how does the intensity vary with the distan'ce from the sonorous body ? If the intensity at a distance of 100 feet be 90, what will it be at a distance of 150 feet? 2. State the conditions that affect the intensity of sound. What is a sounding-board ? Why is it used ? 3. How could you illustrate the reflection of sound ? Describe a speaking-trumpet. Explain the principle of a speaking-tube. 4. What is an echo ? An echo from a building is heard 30 seconds later than the sound ; how far is the building distant ? The Intensity and Reflection of Sound 73 5. A person is walking between two parallel walls which are near ■ together, and hears a prolonged echo of each footstep ; explain how the echo is produced. 6. Compare the intensities of sound at two places, one 1,100 feet, the other 1,800 from the origin of sound. 7. Explain any method by means of which the ticking of a watch may be made audible to a person at the other end of a large room. 8. What is an echo ? What is essential for the production of a single, and what of a multiple, echo ? 9. How could you prove, by experiments or observations, that, when sound is produced and heard at a distance, the air has not actually travelled to the point where the sound is heard ? 10. How is it that sound is transmitted for long distances, by speaking- tubes? 11. How would you show by experimen that, when a bell rings, the metal is in motion 2 74 Sound CHAPTER IV MUSICAL SO UNDS-PITCH— INTENSITY- Q UALITY Pitch. — Certain sounds are pleasant to the ear, and are called musical sounds. Take the toothed wheel and fix it to the whirling-table, or use the humming-top (Appendix). Turn very slowly and hold a card against the teeth. At first we hear a number of taps ; as the speed increases a musical sound is heard ; this sound continues as long as the wheel moves steadily : as the speed changes, the sound changes. Turn the wheel very rapidly ; the sound becomes painful, and at length we are unable to detect it by the ear, A musical sound is caused by regular vibrations. An ordi- nary person hears a sound when the vibrations are not less than 40 to the second, nor more than 20,000 to the second ; (compare light) ; others can detect sounds caused by vibrations above and below these limits. In place of the toothed wheel use the siren (Appendix). Turn and blow through a piece of bent tubing, the end of which is pointed over one set of holes ; when the motion is very slow, a series of puffs is heard. As the speed increases a note is sounded ; it rises in pitch, and at length the ear is unable to detect it. As in last experi- ment a number of regular vibrations produces a musical sound. Fix a knitting-needle in a vice and make it vibrate, change the length until a sound is heard ; the pitch does not change as it vibrates, although the intensity of the sound does. Does the needle vibrate a definite number of times in a second ? This is best shown with a long strip of steel (use a steel straight-edge) that vibrates more slowly than the short needle. Fasten a stiff bristle to the end of the straight-edge. Smoke a long piece of glass. Arrange that the bristle touches the glass, and make the rod vibrate (fig- SS) ; it traces a line across the glass as it vibrates. Move the Musical Sounds — Pitch — Intensity — Quality 7 5 glass quickly ; a curve is traced, resembling the sinuous curve on p. 61, and the conclusion is that the rod vibrates with harmonic motion^ Stretch a string slightly between two points and pluck it ; the string vibrates slowly, but no sound is heard. Tighten it and a sound is produced. Judging from the result with Savart's wheel and the Fig. 55. siren, the string, seeing that it gives a sound, should be vibrating regularly. Twist a pin round the stretched cord (wire) ; fasten it with sealing-wax so that the pin points horizontally ; pluck the wire vertically, and draw the smoked glass rapidly past the point. Examine the curve ; tighten the wire, and try again. The number of the vibrations increases as the pitch rises. If we move the smoked glass with uniform speed, the wave- lengths traced by a vibrating body producing a certain note will be equal, they will decrease in width as the note dies away. The period of vibration of the body remains constant while the amplitude of the vibration diminishes. A musical sound is produced by a body vibrating a definite number of times per second. The number of the vibrations determines the pitch of the note. These vibrations are transmitted by the air to the ear. Suppose a string vibrates 560 times in a second ; at the end of one second the vibrating air-particles will extend from the string to a distance of 1,120 feet, as sound travels about 1,120 feet in one second. Therefore, each wave-length will be 5-^° feet, or 2 feet long. The wave-length deterinines the pitch ; the higher the pitch the shorter the wave-length. The Musical Scale. — Attach the siren wheel (Appendix) to the whirling-table and turn steadily ; force air through a piece of glass tubing (one encl bent at an angle of 135°) upon the inner row of holes, calling the sound heard Doh. Move the tube to the second row ; we recognise the Me of the musical scale. The third row gives the Soh, and with the outside row, the Doh', or octave, is heard. The ^6 Sound number of holes in the rows are as, 4, 5, 6, 8. Turn the wheel at a different rate ; when steady repeat the experiment. Again, if the first note be called Doh, the Me, Soh, Doh' are heard. When the number of the vibrations per second is doubled, the octave of the scale is produced. If 400 vibrations per second give the fundamental note, 500 give the third, 600 the fifth, and 800 the octave. The diatonic musical scale consists of seven sounds; tlie note of lowest pitch is called the fundamental, and the eighth note the octave to the fundamental. By experiments similar to those performed, the relation between the vibration numbers of the notes of the scale has been found. 4 5 24 27 30 32 Doh Ray Me Fah CD E F 6 36 40 Soh La G A 8 45 48 Te Doh' B C 'he absolute value of C is immaterial ; it can be decided arbitrarily ; thus the C i 5 is frequently taken as 256 ; it has been below 250 and as high as 270 ; the number 264 is in common use. To find the vibration number of a vibrating body.— Sup- pose we take an ordinary whistle. A siren (of a more expensive form than that used in previous experiments), so constructed that it registers the number of turns per second, is required. Let us suppose the siren sounds the same note as that made by the whistle when it turns five times in a second, and that there are 96 holes. The vibration numbev of the whistle will be 96 X 5, or 480 per second. Tuning-forks are stamped with their vibration number. Suppose the sound made by a fly moving its wings, is a fifth above a fork marked 264. The vibration number of the wings will be 264 x|, that is, the wings are vibrating 396 times in a second. Musical Sounds — Pitch — Intensity — Quality J7 Examples, IV. 1. What are the physical differences (l) between a loud and a gentle sound, (2) between a shrill and a deep sound ? 2. A bell when struck emits a note of a certain pitch. Is the wave- length in air corresponding to this note the same on a warm day as on a cold day ? Give full reasons for your answer. 3. Taking 1,120 feet per second as the velocity of sound in air, find the number of vibrations which a middle C tuning-fork (which vibrates 264 times per second) must make before its sound is audible at a distance of 154 feet. 4. What are the three characteristics of musical sounds ? How is the movement of the air-particles affected by (a) change of pitch, (b) change o) intensity ? 5. A tuning-fork is set in vibration and you hear its note. The sound is conveyed to your ear by the motion of the air-particles in the room. Explain how, and in what direction, the particles move, and state how their motion would be modified if the fork were made to give a louder sound. 6. Describe a method of determining the number of vibrations required to produce a note of given pitch. Transverse vibrations of strings.— We have already pro- duced sounds by causing strings to vibrate transversely, and have shown that the vibrations are made with harmonic motion. The large number of stringed musical instruments makes the study of vibrating strings important. An exami- nation of a stringed instrument will give a general idea of the laws on which the pitch depends. ,-In a violin the first string is thin, it is used to produce the high notes ; the second and third strings are thicker, while the fourth string is made of wire. We infer that the thinner the string the higher the pitch, and the denser the material the lower the pitch. A player plays a higher note by shortening the length of the vibrating string, and we infer that the shorter the string the higher the pitch of the sound produced. If the note of a string be too high or too low, the player slackens or tightens the string to remedy the defect. We conclude that the greater the tension the higher will be the pitch of the note. The Sonometer.— In order to examine the laws relating to strings, an instrument called a sonometer is used. 78 Sound Two strings of the same material and thickness are stretched side by side ; they pass over the fixed bridges A and B, then over pulleys, and have equal weights attached to them (fig. 56). Fig. 56. On plucking or bowing each string, notes of the same pitch are heard ; each string is vibrating as a whole, and is producing its fundamental note. Call this note Doh. Insert one of the movable bridges D midway between the fixed bridges, so as to halve one string. Pluck one half and we recognise the octave. The octave is caused by twice the number of vibrations of the fundamental (p. 76). By halving the length we have doubled the number of vibrations. By means of the movable bridges make one string two-thirds the length of the undivided string ; this length vibrating produces the Soh. That is, when the lengths are as 3 to 2, the vibration-nunibers are as 4 to 6, or 2 to 3. Move the bridge until a length is found that on vibrating gives the Me ; it will be found to be four-fifths of the undivided string. Collect these results. Length Note Vibration-number I 4 1 Fundamental Doh Third Me Fourth Fah Fifth Soh Octave Doh' 24 or I 30.. 4 32.. - 36,, 48 „ 2 First Law. — Other conditions being equal, the number of vibrations per second is inversely as the length of the string. Musical Sounds — Pitch — Intensity — Quality 79 Use the full length of each string, and vary the stretching force. Attach 16 lbs. to each string, and add weights to one until on plucking, the octave is heard. You will find that the total weight is 64 lbs. That is, in order to double the number of vibrations we must quadruple the weights. Verify your first law. On halving the stretched string with 16 lbs. attached, you should double the number of vibrations, and both strings should give the same note. Begin again. Attach 16 lbs. to each string ; add weights to one until the Me is heard ; the weight will be 25 lbs. When the Sohis heard the weight will be 36 lbs. Stretching force Note Vibration-number 16 25 Fundamental Doh Me Soh Doh 4 = a/i6 5= ^25 6= ^36 8= V'64 Second Law. — Other conditions being equal, the vibration number is proportional to the square root of the stretching force. Combine the two laws ; stretch one string with a weight of 16 lbs., the other with 36 lbs. Move the bridge of the first until the same note is heard from both strings ; the length of the one will be two-thirds that of the other >/i6 X 2^= «/36 X - 3 '■ The vibration-number also depends upon the thickness of the strings, that is upon the diameters ; this is not easy to verify, it being difficult to measure diameters ; careful experiments have shown the truth of the third law. If the diameter be doubled or trebled, the vibration number is divided by two or three. Third Law.— Other conditions being equal, the vibration- number is inversely as the diameter. The fourth law refers to the density of the strings. If a 8o Souna catgut string and a copper wire (length, diameter, and stretching force the same in both cases) be used on the sonometer, the copper wire gives the lower note. For this reason the fourth string of a violin, and the lower wires of a piano are wrapped round with wire, so as to increase their density. Fourth Law. — ^The vibration-numbers are inversely pro- portional to the square roots of the densities. Densi- ties Diame- ters or radii Stretch- ing ■forces Lengths The vibration-numhers vary If in 2 strings X X X O X X X X o X X o X X X Inversely as the lengths Directly as the square roots of the stretching forces Inversely as the diameter or radii Inversely as the square roots of the densities For X r6a