Ordinary Level Physics

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A — ABBOTT

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Ordinary Level Physics

By the same author

Elementary Physics (with M. Nelkon)

Ordinary Level Physics A. F. Abbott, B.Sc. Head of Physics Department, Latymer Upper School, London

With a Foreword by

Sir John Cockcroft, O.M., F.R.S.

“ay

Heinemann

Educational

Books

Ltd Lonpon

Foreword

by Sir John Cockcroft, O.M., F.R.S.

Mr Abbott’s book on physics, taken to the Ordinary Level of the General Certificate of Education, should be

welcomed by teachers of physics for its combination of theoretical and experimental work, and for its practical outlook, which should make the course interesting also for those students who will not take physics beyond the Ordinary Level. The well-illustrated references to the application of physics in industry should also appeal to the more practically minded student. The author has rightly included an introduction to atomic and nuclear physics.

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Steam to turbine generating

rods

Graphite

core

Uranium

rods

—=

u

:

Water

Fic. 54. Gas cooled reactor

bricks (Plate 5). This graphite core has a number of vertical channels which are filled with rods of a very heavy metal called uranium. Interspersed among the uranium rods are a set of boron steel rods which may be raised or lowered in similar channels in the graphite. These are the control rods, and their function will be explained in due course. The uranium used in the reactor consists of a mixture of two different kinds of atoms, of which the most important are called U-235. Quite spontaneously, some of these U-235 atoms explode or disintegrate to

q2

MECHANICS

AND

HYDROSTATICS

form other atoms of smaller mass. When this happens, energy is radiated from the central core or nucleus of the atom together with small high-speed particles called neutrons. If one of the neutrons happens to strike the nucleus of a neighbouring atom this may also disintegrate, with a further evolution of energy and the production of more neutrons. This splitting up of the nucleus is called fission. The graphite of which the core is composed is called a moderator (Plate 5). Its function is to slow down the speed of the neutrons, as it is found that fission of U-235 is more likely to occur with slow neutrons than with fast ones. In a small piece of uranium mixed with moderator most of the e

Neutron

@

Fission product

@) Uranium

atom

This stray neutron starts the chain reaction

Fic. 55. Chain reaction in nena

neutrons

escape

through

the surface.

If, however,

the amount

of

material is increased the chances that a neutron will collide with an atomic nucleus will also increase, since there are more atoms present. Each nuclear fission which occurs produces two or three fresh neutrons which are, in turn, capable of promoting the fission of further nuclei. When the lump of uranium and moderator is above a certain critical size the fission process proceeds cumulatively in what is called a chain reaction (Fig. 55). This is where the above-mentioned boron steel rods play their part. Before the uranium rods are loaded into the graphite core the boron rods are already in position, and these have the property of being able to absorb neutrons which are shot out from the uranium, and so prevent the chain reaction from starting. When sufficient

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60

= 550 ft.-Ib. wt./sec.

To measure personal horsepower Anyone may find the horsepower he is able to develop when running upstairs by measuring the total vertical height of a stairway and using a stopwatch to find the time taken to run up it. Example. A boy who weighs 90 Ib. finds that he can run up a flight of 40 steps each 6 in. high in 4-4 sec. Total work done = = = Power =

Weight x Vertical height raised 90 x 05 x 40 1800 ft.-lb. wt. work done per second

Therefore,

Average power = but

Total work done _ 1800

Sere ft.-Ib. wt./sec.

Time taken

1 H.P. = 550 ft.-Ib. wt./sec.

hence 1800

Average personal H.P. = PASS

0-74 H.P.

This result is very creditable, but it must be remembered that the boy can maintain this very high power only for a comparatively short time. Experiment shows that the average horsepower of a man walking upstairs at an ordinary pace is only about 0:3 H.P.

QUESTIONS:6 1. What is meant by: (a) work; (6) energy; (c) power. between potential and kinetic energy.

Explain the difference

2. Find the time taken by a 10-H.P. engine to raise a load of 440 Ib. wt. to a

height of 25 ft. (1 H.P. = 550 ft.-lb.wt./sec.)

(S.)

76

MECHANICS

AND

HYDROSTATICS

3. What do you understand by the term energy? Indicate the various forms of energy, illustrating your answer by reference to a steam engine, steaming down a slope. (S. part qn.) 4. A steam shovel driven by a 4-H.P. engine lifts 200 tons of gravel an hour to a height of 10 ft. How much work is lost per hour? (1 H.P. = 550 ft.-Ib. wt./sec.)

(C.) 5. State the principle of the conservation of energy.

(J.M.B.)

6. State four of the transformations of energy which occur at a power station which uses coal as its fuel. (S.)

7 : Newton’s laws of motion The study of moving bodies begun by Galileo Galilei in Italy was continued after his death by Sir Isaac Newton in England. In 1687 Newton published a book written, as was the custom in those days, in Latin and given the title, Philosophiae naturalis principia mathematica. Translated, this means, “The mathematical principles of natural philosophy’’. The Principia, as it is familiarly called, is regarded as one of the greatest scientific works ever written. It is devoted mainly to the study of motion, particularly that of the planets and other heavenly bodies. In the first part of the book Newton sums up the basic principles of motion in three laws. In this chapter we shall discuss these laws and consider some of their applications. Newton’s first law of motion

Every body continues in its state of rest or of uniform motion in a straight line unless compelled by some external force to act otherwise. It is a matter of common experience that objects at rest do not begin to move of their own accord. If we place an object in a certain place we expect it to remain there unless a force is applied to it. Some simple parlour tricks are based on this principle. For example, if a pile of draughts or pennies is placed on a table the bottom one can be removed without

disturbing

the remainder,

simply by flicking it sharply with a piece of thin wood or metal. In this case the force of friction between the bottom disc and the one in contact with it acts for too short a time to cause any appreciable movement of the discs above. Incidentally, the use of a ruler is not recommended for this experiment, as the blows it receives will not improve its straight edge. The bottle and coin trick is equally effective in demonstrating the same Fic. 56. effect. A sixpence is put on a card and placed over the mouth of a bottle (Fig. 56). When the card is flicked away with the finger the coin drops neatly into the bottle. For 77

78

MECHANICS

AND

HYDROSTATICS

success in performing this trick the finger should move in a horizontal plane so that the card is not tilted. It is not immediately obvious that a body moving with uniform velocity in a straight line tends to go on moving for ever without coming to rest. The fact is that no one has yet found a means of eliminating all the various outside forces which can retard a moving body. A person riding a bicycle along a level road does not come to rest immediately he stops pedalling. The bicycle continues to move forward, but eventually it comes to rest as a result of the retarding action of air resistance and friction. In a collision between two motor cars the passengers are frequently injured by being thrown against the windscreen. They simply tend to continue their straight-line motion in accordance with Newton’s first law; hence the advantage of safety

harness. When a bullet is fired from a gun its motion is opposed both by air resistance and the pull of the earth. Sooner or later it returns to the earth, but it would be reasonable to suppose that, if air resistance and gravitation could be eliminated, the bullet would go on moving in a straight line for ever. In the early seventeenth century the German astronomer Johann Kepler had shown that the planets move in elliptical paths or orbits round the sun, but he was unable to explain why. It was left to Sir Isaac Newton to offer a satisfactory explanation based on the first law of motion and the law of universal gravitation (see page 14). Newton pointed out that the planets move in curved paths because the sun is attracting them. No slowing up occurs, since there is no retarding force. The planets move in the vacuum of space, carrying their atmospheres with them. If the attraction of the sun suddenly ceased, a planet would continue to move in a straight line making a tangent with its original orbit. It is important to realise that, once a body is moving with uniform speed in a straight line, it needs no force to keep it in motion provided there are no external opposing forces. We shall now go on to discuss the motion of a body when it is being acted upon by a force. Momentum

A truck requires a larger force to set it in motion when it is heavily laden than when it is empty. Likewise, far more powerful brakes are needed to stop a heavy goods vehicle than a light car moving with the same speed. The heavier vehicle is said to possess a greater quantity of motion or momentum than the lighter one. The momentum of a body is defined as the product of its mass and its velocity.

NEWTON’S

LAWS

OF MOTION

719

When two bodies, a heavy one and a light one, are acted upon by the same force for the same time, the light body builds up a higher velocity than the heavy one. But the momentum they gain is the same in both cases. This important connection between force and momentum was recognised by Sir Isaac Newton and expressed by him in a second law of motion. Newton’s second law of motion The rate of change of momentum of a body is proportional to the applied force and takes place in the direction in which the force acts. In Chapter 2 we mentioned the use of the pound weight and kilogram weight as gravitational units of force and explained why they are unsuitable for accurate scientific purposes. We shall now show how Newton’s second law of motion enables us to define an absolute unit of force which remains constant under all conditions. Suppose a force F units acts on a body of mass m gm. for a time f¢sec. and causes its velocity to change from u cm./sec. to v cm./sec. The momentum changes uniformly from mu to my units in ¢ sec.

my — mu

Therefore, the rate of change of momentum = ae

: el. cm./sec.?.

By Newton’s second law, the rate of change of momentum is proportional to the applied force and hence

Fo

amu t

Factorising,

at

Fome—# 5 »)

(v — 4) __ Change in velocity __ 4 cceleration t

Time

== iC. /SeC.-

therefore

F ox ma

This relationship can be turned into an equation by putting in a constant. Thus,

F = Const. X ma

It is this equation which enables us to define an absolute unit of force. If m=1 gm. and a= 1 cm./sec.?, the value of the unit of force is chosen so as to make F = 1 when the constant = 1. This unit of force is called the dyne (C.G.S. unit), and may be defined as follows, A dyne is the force which produces an acceleration of 1 cm./sec.? when it acts on a mass of 1 gm.

80

MECHANICS

AND

HYDROSTATICS

Thus when F is in dynes, m in gm., and a in cm/sec.”, we have F=

ma

Absolute systems of units Systems of units for scientific measurements are based on the three fundamental units of length, mass and time and, there are three systems in use, namely, the C.G.S. system based on the centimetre, the gram and the second; the M.K.S. system based on the metre, the kilogram and the second; and the F.P.S. system based on the foot, the pound and the second.

The M.K.S. system has a number of advantages over the others, but a discussion of the reasons for this is beyond the scope of this book.

Absolute units of force The C.G.S. unit of force, the dyne, has already been defined. The M.K.S. unit of force is called the newton and is the force which produces an acceleration of 1 metre/sec.” when it acts on a mass of 1 kg. The F.P.S. unit of force is called the poundal and is the force which produces an acceleration of 1 ft./sec.? when it acts on a mass of 1 Ib. All three of these units are easy to remember, since they are all defined in the same way, and differ only in the units of length and mass on which they are based. Also, the equation F = ma applies to all systems provided the correct units are used, i.e., centimetres go with grams and metres with kilograms. One cannot, of course, mix centimetres and pounds in the same equation.

To verify experimentally that F oc ma Newton’s second law may be verified by means of Fletcher’s trolley. One form of this apparatus consists of a three-wheeled trolley whose mass can be varied by adding rectangular metal blocks. It runs over a sheet of paper placed on a smooth horizontal board (Fig. 57). Various accelerating forces may be applied by means of a string which passes over a pulley and carries a scale pan and weights. Affixed to the trolley is a strip of spring steel fitted with an inked brush. This is set in vibration and makes a wavy line on the paper when the trolley is in motion. The vibrating strip acts as both clock and

NEWTON’S

distance measurer.

LAWS

OF

MOTION

81

It takes the same time for each complete vibration,

and therefore the lengths of the waves on the paper represent the distances moved by the trolley in successive equal intervals of time. We shall explain presently how the acceleration is calculated from the trace.

Before each experiment it is necessary to compensate for friction, which retards the trolley’s motion. This is done by adding small weights Vibrating steel strip

Loading masses

Smooth board

Applied forceN

|

a

Fic. 57. Modified Fletcher’s trolley

gradually to the scale pan until the trolley moves with uniform velocity after having been given a slight push. This will be achieved when the waves made on the paper are all of the same length. The resultant force on the trolley is now zero, and any extra load added to the pan will produce acceleration. Alternatively, friction may be compensated for by slightly tilting the base board until the trolley will run down it with uniform velocity. Experiment 1. To show that a « F when the mass, m, is constant

Having made the preliminary adjustment to compensate for friction, a 10-gm. weight is placed in the pan to act as an accelerating force F, and a wave trace obtained as already described. The periodic time of 4——§, cm. —>+_——._ S, cm. ———}

Fic. 58. Trace from Fletchers’ trolley experiment

vibration of the steel strip is also found by timing a large number of vibrations, as in the case of a simple pendulum (see page 60). In order to find the acceleration, a straight line is drawn down the centre of the trace and the lengths of successive waves are measured by a millimetre scale (Fig. 58).

82

MECHANICS

AND

HYDROSTATICS

Consider two such waves of lengths s, and s, cm. respectively.

If the

time for one vibration of the brush is ¢ sec., then

: ! iY Average velocity over the distance s; = ricm./sec., and ; : Ss Average velocity over the distance sz = - cm./sec.

er are So S S—S Hence, the Gain in velocity in ¢ sec. = z— ; == ; 1 cm./sec. Therefore, the Acceleration =

Gain in velocity :

5, —Ss , 1 cm./sec.?

Time

t

Usually several pairs of values of s, and s, may be measured from a trace and a mean value of s, — s, obtained for calculating the acceleration. The experiment is carried out several times using different accelerating forces and the results recorded as shown in the table. Acceleration

(Extend table sections as required)

If a o F, then the results should show that

a

constant or, alter-

natively, the graph of a against F should be a straight line through the origin. .

is i

: 1 Experiment 2. To show that a « — when the accelerating force F is

constant

Me

In this experiment a suitable constant accelerating force is used and

the mass of the trolley is varied by adding the loading masses one at a time. Owing to the fact that friction varies with the weight of the trolley, it will be necessary to make a fresh adjustment to compensate for friction

NEWTON’S

LAWS

OF MOTION

each time the mass of the trolley is altered. a table as below.

The results are recorded in

Nea;

S_ cm.

(Ss. = 54) cm,

83

c rati Acceleration

Gs)

a=

cm,

(Extend table sections as required)

Ifac = then the results should show that ee = ma = constant.

1/m

Alternatively, the graph of a against should be a straight line through the origin. fe Summary. The two experiments described above show, respectively,

that axcFk

and

ae m

Combining the two results,

aoa F xX =

whence

F cma

Weight of a body expressed in absolute force units Galileo showed that all bodies, whatever their mass, have the same acceleration when they fall freely under the action of gravity. In equations, the acceleration due to gravity is usually denoted by the letter g. Thus, g has the value 981 cm./sec.?, or 9-81 metres/sec.?, or 32 ft./sec.?, according to the system of units we are using. The force which causes a falling body to accelerate is its weight. Hence, substituting in the equation,

Force = Mass x Acceleration we obtain Weight = mg (in appropriate units) If we consider unit mass, then m = 1 and therefore

in C.G.S. units in M.K.S. units

1 gm. weight = 981 dynes; 1 kg. weight = 9-81 newtons;

in F.P.S. units

1 Ib. weight = 32 poundals.

84

MECHANICS

AND

HYDROSTATICS

Newton’s third law of motion

To every action there is an equal and opposite reaction. This law has already been mentioned on page 17 with reference to the reaction force which a table exerts on)a weight stood upon it. We shall now discuss another aspect of the law. When a bullet is fired from a gun equal and opposite forces are exerted on bullet and gun during the time the bullet is passing down the barrel. Since, therefore, both bullet and gun are acted upon by equal forces for the same time, they will, in accordance with the second law of motion, acquire equal and opposite momenta. The backward momentum of the gun itself is shown by its kick or recoil. Hence,

Mass of bullet x Muzzle velocity = Mass of gun x Recoil velocity It is to be noted that momentum is a vector quantity, ie., it has direction as well as magnitude. The momenta of the bullet and gun are equal but in opposite directions. Consequently, the sum total of their momenta is zero. This illustrates an important principle arising out of Newton’s second and third laws which is known as the Law of the conservation of momentum When two or more bodies act upon one another, their total momentum remains constant, provided no external forces are acting.

Rocket propulsion Let us now think of a toy rubber balloon which has been blown up with air and its mouth secured with string. The compressed air exerts a force on the inside walls which is exactly balanced by the reaction of the walls on the air. If the string be now removed so that the air can escape rapidly, the balloon will, if released, dart round the room until all the air has gone. It behaves as a simple rocket. The rockets which form a familiar feature of firework displays contain solid chemicals which burn to produce a high-velocity blast of hot gas. Space rockets which are designed to travel large distances have tanks of liquid fuel together with a supply of either liquid oxygen or some other liquid which produces oxygen to enable the fuel to burn. In either case, a chemical reaction takes place inside the rocket and

creates a large force which propels the gaseous products of combustion out through the tail nozzle with tremendous velocity. The reaction to this force propels the rocket forwards. Although the mass of gas emitted is comparatively small, it has a very large momentum on account of its high velocity. An equal momentum is imparted to the rocket in the opposite direction, so that, in spite of its large mass, the

rocket also builds up a high velocity.

NEWTON’S

LAWS

OF MOTION

85

Jet engines An aircraft jet engine works on the same principle as a rocket. The difference between them is concerned only with the method of obtaining the high-velocity gas jet. Fig. 59 shows, in simplified form, the construction of an axial-flow gas turbine or jet engine. The fuel used in these engines is kerosene (paraffin). This is sprayed through burners into combustion chambers, where it burns in a blast of compressed air and produces a high-velocity jet of gas which emerges from the exhaust nozzle. The air supply is drawn in at the front of the engine and compressed by a turbine compressor. A turbine is simply a special kind of fan Double

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Fic. 287. Crova’s disc to illustrate longitudinal wave motion

366

SOUND

To construct a longitudinal wave model (Crova’s disc) The manner in which oscillatory motion of the air layers gives rise to the compressions and rarefactions of a sound wave may be illustrated by a simple device known as Crova’s disc. A circle of radius about 0-75 cm. is drawn on a piece of stout paper or thin card and eight equidistant points are marked round its circumference. These are numbered 1 to 8. Using these points successively as centres, a set of circles of progressively increasing radii are drawn as shown in Fig. 287. When completed, the disc is cut out with scissors and pinned through its centre to a strip of card with a slit cut in it. The disc is then rotated and viewed through the slit. The portions of the circles seen through the slit represent adjacent layers of air in a sound wave and, as the disc rotates, compressions followed by rarefactions will be seen to travel across. Each individual layer, however, simply oscillates about a mean position.

An experiment on the reflection of sound Two metal or cardboard tubes are set up, inclined to one another in a horizontal plane, and pointing towards a vertical flat surface of any hard material, e.g., a drawing board (Fig. 288). A ticking watch is placed near the end of one tube and the ear is presented to the end of the other tube. Sound waves pass down the first tube and are reflected from the board. The loudness of the sound heard through the second tube is found to be a maximum when the board is adjusted so that the normal to it lies in the plane of the Waten Ear Wee and makes equal angles with their

a

gars Sees ee

Under these conditions the incident

and reflected waves and the normal are in the same plane and the angle of incidence is equal to the angle of reflection. Sound thus obeys the same laws of reflection as light. Echoes

Echoes are produced by the reflection of sound from a hard surface such as a wall or cliff. Let us suppose that a person claps his hands when standing some distance from a high wall and listens for the echo. The time which elapses before the echo arrives will, of course, depend on the distance away of the wall. Now, in order that the echo may be heard separately

PRODUCTION

AND

PROPERTIES

OF

SOUNDS

367

from the original clap it must arrive at least =4; sec. later. Since sound travels at about 1100 ft./sec., the reflected wave must have travelled a total distance of at least 110 ft., and consequently the minimum distance of the wall must be about 55 ft. When the reflecting surface is less than this distance the echo follows so closely upon the direct sound wave that they cannot be distinguished as separate sounds. One merely receives the impression that the original sound has been prolonged. This effect is called reverberation.

The acoustics of buildings Reverberation is particularly noticeable in cathedrals and other large buildings where multiple sound reflections can occur from walls, roof and floor. For example, in St. Paul’s Cathedral, London, it takes about 6 sec. for the notes of the organ to die away after the organist has stopped playing. Excessive reverberation in a concert hall is undesirable, as it causes music and speech to sound confused and indistinct. On the other hand, it is not a good thing to have no reverberation at all. Speakers and singers who have practised in an empty hall are often disconcerted by the seeming weakness of their voices when they perform in the same hall full of people. The soft clothing of the audience absorbs the sound instead of reflecting it, and consequently the music and speech appear to be weaker. Some degree of reverberation is therefore useful, as it prevents a hall from being acoustically “dead” and improves the hearing obtained in all parts of the building. The characteristics of a building in relation to sound are called its acoustics, and the pioneer work in this field was carried out in the early twentieth century by Professor W. C. Sabine of Harvard University. The most important property of a concert hall is its reverberation time, which is defined as the time taken for sound of a specified standard intensity to die away until it just becomes inaudible. Sabine began his investigations by measuring the reverberation time of a number of empty halls and churches. For this purpose he used a small organ pipe which gave a note of the required intensity. Further experiments were then carried out with cushions placed on the seats and with various types of wall and floor coverings in order to ascertain which reverberation time gave the best results. For the majority of halls this was found to lie between 1 and 2 seconds. From his results Sabine obtained a formula relating the reverberation time to the volume of a hall, the surface area of its walls, ceiling and so on, and also the sound-reflecting properties of these surfaces. Later on, this formula was found very useful in planning new concert halls. Research has been continued on the foundations laid by Sabine, and nowadays no architect should draw up plans for a new hall without

368 paying of the Here, panels

SOUND attention to its acoustic design. Plate 12 shows part of a wall Royal Festival Hall, London, during the course of construction. reverberation is controlled by covering the walls with leather put on over a layer of sound-absorbent glass fibre.

Anechoic and soundproof rooms For certain special purposes, e.g., investigation of the properties of loud-speakers and other sound equipment, it is necessary to have rooms whose walls absorb completely all sound energy falling upon them. This is achieved by lining the walls, ceiling and floor with anechoic wedges composed of glass fibre encased in muslin (Plate 12). Efficient sound insulation is necessary for the comfort of those who dwell in blocks of flats. In modern building practice the spaces between floors and ceilings are usually filled with some inelastic material which absorbs the sound instead of transmitting it.

To measure the velocity of sound by an echo method In places where a clear space extends for about 100 yd. from a high wall the velocity of sound may be found by measuring the time taken for a sound to travel to the wall and back again. The experiment is best carried out by two persons working together, one to make the sound and the other to carry out the timing. One observer claps together two small wooden blocks held one in each hand and listens for the echo from the wall. Having obtained some idea of the time interval, he continues to clap the two blocks together and adjusts the rate of striking until each clap is made simultaneously with the arrival of the echo from the previous clap. The time interval between successive claps is then equal to the time taken for sound to travel twice the distance between observer and wall. When the correct rate of striking has been achieved the second observer uses a stop-clock or watch to measure the time occupied by thirty or more clap intervals. It is, of course, important to begin the timing by counting from nought. The distance from the wall is measured by a tape or other means. Let

Distance from wall

= s ft.

No. of clap intervals = n Time

=a

SCC.

Sound travels 2s ft. in “sec.

hence

Velocity of sound = eae Time

pees

t

ft./sec.

PRODUCTION

AND

Several determinations should velocity of sound calculated.

PROPERTIES

OF

be made

a mean

and

SOUNDS

369

value for the

Echo sounding An echo sounder or fathometer is a device used on a ship for the purpose of measuring the depth of the sea in fathoms. A detailed explanation of the apparatus is beyond the scope of this book, but the basic principle involved is comparatively simple. An electrical device fitted to the bottom of the ship sends out regular sound impulses which are reflected back from the sea-bed and received by a hydrophone.* Obviously the time interval between the emission of a signal and its arrival back to the ship depends directly on the depth of the sea. A special electric circuit utilises the time intervals to control the movement of a stylus over a moving strip of graph paper marked with a scale in fathoms. The stylus thus plots a curve which is a scale contour of the sea-bed, giving a continuous indication of depth as the ship proceeds on its way. This information is of great value to the pilot, as it permits the safe navigation of the vessel through uncharted waters, particularly where shallows or sandbanks are likely to be encountered. Another device based on the same principle is the Asdic, which was used in time of war for locating enemy submarines. It consists of a sound transmitter attached to the bottom of a warship. This is rotated continuously so that the sea is swept over a complete circle. Any submarine or even a mine which happens to be within range of the sound waves will reflect the waves back to the ship. Here, the recording apparatus automatically gives the range and position of the submerged object. It isimportant to note that the sound impulses sent out by a fathometer or asdic have a frequency of the order of 50,000 cycles per sec. (c/s). High-frequency waves of this type are said to be ultrasonic, as they cannot be heard by the human ear. In this connection they have a twofold advantage. First, they cannot be confused with engine noises or other sounds made by the ship. Secondly, very-high-frequency waves can be confined to very narrow beams, and hence can penetrate sea-water to large distances without undue loss of energy.

OUlS

TTONS:: 20

1. What is the nature of a sound wave? How is it propagated? Describe experiments, one in each case, to show: (a) that the source of a sound is a vibrating body; (b) that a material medium is necessary to transmit sound. (J.M.B.) * A hydrophone is a microphone designed to work in water (see page 593).

370

SOUND

2. What is an echo? When a stationary fog-bound ship sounds a short blast, an echo from the coast is heard 5 sec. later. If the velocity of sound in air is 1100 ft./sec., how far is the ship from the coast? (J.M.B.) 3. Describe an experiment which can be performed in the laboratory to show that sound can be reflected in a manner similar to light. Two men, 4 and B, stand in a line perpendicular to a cliff. A being nearer to it and B 825 ft. from A. A fires a gun and hears its echo after 1 sec. When B fires a gun, A hears the echo after 1:75 sec. Find: (i) the velocity of sound, and (ii) the distance of A from the cliff. ~ (S.)

4. Explain how sound waves travel through a gas and describe carefully an experiment which shows that a material medium is necessary for the transmission of sound. A and B are two observers 1 km. apart. There is a steady wind blowing. When a gun is fired at A the time interval between the flash and the report observed at B is 3:04 sec. When a gun is fired at B the interval between the flash and report observed at A is 2:96 sec. Calculate the velocity of sound in air and the velocity component of the wind in the direction BA. (O.C.) 5. Deduce a relationship between the velocity of sound, and the frequency and wavelength of a note. (S.) 6. An experiment is carried out as follows: An observer A fires a pistol. An observer B stands 50 yards away and, by means of a stop-watch, determines the time between seeing the flash and hearing the sound. The speed of sound in air is determined by dividing the distance by the time. State reasons why the result is likely to be inaccurate and suggest ways in which the experiment could be improved. The whistle is blown on the engine at the front of a train 300 ft. long travelling at 60 m.p.h. Determine the time which elapses before the sound is heard by the guard at the rear of the train. (Speed of sound = 1100 ft/sec.)

(W.) 7. State the laws of reflection of sound and explain how an echo may be produced. Two men stand facing each other, 200 metres apart, on one side of a high wall and at the same perpendicular distance from it. When one fires a pistol the other hears a report 0-60 sec. after the flash and a second report 0:25 sec. after the first. Explain this and calculate: (a) the velocity of sound in air; (b) the perpendicular distance of the men from the wall. Draw a diagram of the positions of the men and the wall. (0.C.)

8. Explain how sound is transmitted through the air. Describe an outdoor method for finding directly the velocity of sound in air, pointing out any precautions which are necessary. What will be the effect on the velocity, of: (i) a rise in temperature, and (ii) replacing the air by a denser gas? A and B are two observers in a line between a church bell and a wall. A hears the echo from the wall 1 sec. after hearing the bell, while B hears it 0-2 sec. after the bell. Find the distance between A and B. (The velocity of sound in air is 1100 ft./sec.) (i)

30 : Musical sounds Pitch and frequency In the previous chapter it was mentioned that the pitch of a note, i.e., its position in the musical scale depends on the frequency of vibration of its source. This was demonstrated early in the nineteenth century by Felix Savart, who held a card against a rotating toothed wheel and showed that the pitch of the note emitted depends on the speed of rotation (Fig. 289). As the teeth strike the card it vibrates with a frequency equal to the number of teeth multiplied by the number of revolutions of the wheel per second. If four wheels with teeth numbers in the ratio 4:5 :6:8 are run at constant speed on the same shaft the notes given out are doh, me, soh,

Savart’s wheel Disc siren for notes of common

frequency ratio

chord

4:5;6:8

Fic. 289. Pitch depends on frequency

doh’. This well-known sequence of notes can be recognised whatever the constant speed of the shaft, showing that the musical relation between notes depends on the ratio of their frequencies rather than their actual frequencies. Another device, the disc siren, is a rotating metal plate with holes drilled in concentric rings. When a jet of air is directed against the plate, puffs of air escape through the holes and produce a note of frequency equal to the product of the number of holes in a ring and the number of revolutions per second. 371

372

SOUND

Music and noise

A sound of regular frequency is called a tone or musical note, and music is a combination of such sounds. Certain combinations of notes do, however, produce an effect of emotional tension, or dissonance,

and this has played an important part in the vocabulary of music throughout the ages, in varying degrees. Noise is not easy to define but fairly general agreement may be expected with the definition that it is a sound or combination of sounds of constantly varying pitch, or irregular frequency. Musical scales

As the art of music developed through the ages it came to be accepted that notes of certain frequency relationships gave a pleasing result when played together, while others produced a harsh effect. This experience led to the establishment of musical scales consisting of a series of notes whose pitch relationships enabled the maximum number of pleasing combinations to be obtained. Ch

Og

fe

(a5) (€5) KEYBOARD

ay

(95) (a%) (65)

SCALE

(equally tempered) a compromise with the Diatonic Scale

Frequency 13 notes

ratio between and

the next

each of the is 1:0595

(chromatic semitone) Staff notation -O-

Ronee Soicke

doh ray me

Frequencies

256 288 320 341 ~~

fah soh

eee l

Int

Tones

te

doh

384 427 480

512

SCALE

DIATONIC (Scientific)

lah

BinMinor Lheetha th, Bis oe Semi Major Minor Major Semitone

S)

110)

16

9

10

Major

Fic. 290.

Music evolved along various lines in different parts of the world, and scales were adopted which differed both in the number as well as the pitch of the notes they contained. From the middle of the sixteenth to the middle of the nineteenth centuries European music, in particular, came to be based on the diatonic scale. This consists of eight notes which may be represented in various forms of notation (Fig. 290).

MUSICAL

SOUNDS

373

For scientific purposes, the diatonic scale has been standardised as a series of notes ranging from middle C (c’), 256 c/s to upper C (c’”’), 512 c/s. Most of the tuning forks found in laboratories are in scientific pitch, but these are unsuitable for tuning musical instruments, as will be explained in due course. At the outset it must be understood that, as far as music is concerned, the actual pitch of the notes has never been regarded as being so important as the ratio of the pitches of the various notes of the scale. Thus, during the eighteenth century it would be rare to find two organs whose middle C pipes had the same frequency, although, of course, the ratio of the pitches of the different pipes would be substantially the same for all instruments. However, with the development of orchestral music, attempts were made at various times to establish a uniformity of pitch acceptable to musicians in all countries. In the year 1939 an international committee agreed that standard musical pitch should be based on a frequency of 440 c/s for a’. Musical intervals

The ratio of the frequencies of two notes is called the musical interval between them. Certain recognised intervals have been given special names.

Thus, a ratio of 9 : 8 is called a major tone, 10 :9 a minor tone

and 16: 15 a Those who For example, 2 : 1, is called and so on.

semitone. have studied music will be familiar with other intervals. the interval between the top and bottom notes of the scale, an octave. The interval between c’ and g’, 3 : 2, is a fifth

The problem of tuning a keyboard instrument The lowest (or highest) note on the scale is called the tonic or keynote. Now it is an easy matter to make a change of key when singing, since the voice can be pitched to any frequency within its natural compass. Also the same principle applies in the case of stringed instruments, where the length of the vibrating strings can be adjusted by fingering; or with the trombone where the player manipulates the length of the slide. But with a keyed instrument such as a piano or organ a difficulty arises. The scale represented in Fig. 290 begins with c’ (middle C), which is given by a white key near the centre of the keyboard. The rest of the scale is given by the next seven white keys in order. Ife’ is taken as the key note, an ascending scale cannot be played on a succession of white notes, as the intervals do not now come in the correct order. For example, the interval between e’ and the next white key f’ is only a semitone, whereas the interval between the first and second notes of a

374

SOUND

diatonic scale must be a major tone. Similar difficulties arise with other intervals, and hence, in order to play a correct diatonic scale beginning with e’, it would be necessary to have four extra keys. If sufficient extra keys were provided to enable diatonic scales to be played in all other possible keys we should end up with a piano which had so many keys that it would be impossible to play it. Some compromise is therefore necessary. Space does not allow a detailed discussion of the various attempts which have been made in the past to overcome the difficulty. Suffice it to say that a satisfactory solution of the problem has been effected by substituting the chromatic or equally tempered scale for the diatonic scale. Five black keys, known as sharps (#) or flats (p) are added to each octave of white keys, making in all a range of thirteen notes each separated from its predecessor by an interval of 2% or 1-0595 : 1. This interval is called a chromatic semitone. While these notes do not allow true diatonic scales to be played, the differences are so small that only those with extremely sensitive musical ears claim to be able to detect them. The actual frequencies employed in the equally tempered scale are shown in Fig. 290.

To measure the frequency of a tuning fork A wooden framework supports a vertical smoked glass plate by a length of cotton passing over two hooks (Fig. 291). The plate may be _Adjustable hook Lamp blacked glass plate Bristle

Tuning fork

Clamping

We

screw

Fic. 292. Trace from the fallingplate experiment

Fic. 291. The falling-plate experiment

smoked either by burning camphor or else by means of a small wick lamp containing white spirit (turpentine substitute).

MUSICAL

SOUNDS

BTS

The tuning fork has a short bristle fixed to one of its prongs with a ittle wax and is clamped horizontally with the bristle lightly touching the lower part of the plate. The fork is bowed steadily, and, when a good amplitude of vibration has been built up, the supporting cotton is burnt through with a lighted match. The plate falls freely under gravity and the vibrating bristle leaves a wavelike trace in the soot. If a permanent record of the trace is required, a strip of paper should be fixed to the plate with self-adhesive tape before smoking it. At the end of the experiment the trace is fixed by running weak shellac varnish over it from a piece of drawn-out glass tube. Calculation of the frequency. The distances s, and s, cm. occupied by two successive sets AB and BC of ten complete waves are measured by a millimetre scale (Fig. 292). 1 If the frequency of the fork is f c/s it makes one vibration in 7 Sec. Hence the plate falls through each of the distances s, and s, cm. in

t= > sec. Suppose the velocity of the plate when the bristle is at A is u cm./sec. Then, when the bristle is at B the velocity is u + gt cm./sec. Applying the equation s = ut + 4gf? we have Sy SSI

+

tet?

and

Sg =(u+ gt)t +4¢2?

by subtraction

Spas

hence or

ae

10

So — 8

ue

g

t= 34= J—— = 10, / g

S2 — Sy

c/s;

Intensity and loudness of sound The intensity of a sound wave is defined as the rate of flow of energy per unit area perpendicular to the direction of the wave. By mathematical treatment which is outside the scope of this book it may be shown that the intensity of a sound wave in air is proportional to: (a) the density of the air; (b) the square of the frequency; and (c) the square of the amplitude. From the practical point of view we have to take the density of the air as we find it, and, therefore, for a sound of given frequency the most important factor is the square of the amplitude. Consequently, when the amplitude of vibration of a tuning fork or loudspeaker diaphragm is doubled the sound energy is not doubled but made four times as great. Obviously, the Joudness of a sound will depend on the intensity, but

376

SOUND

it does not follow that loudness is directly proportional to intensity. In the first instance, loudness depends on the varying pressure exerted on the eardrum by the incoming wave, and this will depend on the energy conveyed by the wave. But this is) not the only factor involved. The ear varies in its sensitivity to sounds of different frequencies. Generally speaking, the ear is more sensitive to the higher frequencies.

Quality or timbre of a musical note If a particular note on the scale is played on, say, a piano and a flute, it is easy to distinguish the tone of one instrument from that of the other. The two tones are said to differ in quality or timbre. Generally speaking, instruments do not give tones which are pure in the sense that they consist of single frequencies only. In the majority of cases a musical note consists of several different frequencies blended together. The strongest audible frequency present is called the fundamental and gives the note its characteristic pitch. The other frequencies are called overtones, and these determine the quality of the sound.

The notes of a trumpet possess a quality derived from the presence of strong overtones of high frequencies, while the flue pipes of an organ have a mellow tone. In the case of the latter, practically all the sound energy is centred in the fundamental frequency and the overtones are fewer in number and of smaller intensity. Much experience and craftsmanship go into the design and construction of a piano with the aim of suppressing unwanted overtones and enhancing the desirable ones. The same can be said about other instruments, particularly the violin. Beats

When two notes of nearly equal pitch are both sounded together a regular rise and fall occurs in the loudness of the tone heard. These alternations in loudness are called beats. This may be demonstrated with organ pipes, or singing tubes may be used instead. Two glass or metal tubes about a metre long and 4 or 5 cm. in diameter are clamped in a vertical position and have small gas flames inside them about a quarter of the way up from the bottom. For this purpose, suitable burners may be made from drawn-out glass tubing, as shown in Fig. 293. After adjusting the flame height and position for the best results, the tubes will give out a loud, continuous note. Usually, the tubes are not exactly the same length, so their frequencies are slightly different and strong beats are heard. By sliding a paper collar over the lower end of one tube its frequency may be altered as desired, with a corresponding change in the number of beats heard per second.

MUSICAL

SOUNDS

OTT

In the days when the majority of aircraft were powered by two or more piston-type engines a throbbing sound could often be heard owing to beats between the engine notes. Piano tuners sometimes utilise beats G...

for tuning a piano string to the pitchof a standard tuning fork. If the pitch of the string is not equal to that of the fork, beats will be heard when they are sounded together. The tension of the string is now altered until the beats disappear, showing that the two notes are in unison. Two tuning forks of equal frequency may also be used to produce beats, if the frequency of one of them is reduced slightly by loading its prongs with tiny pieces of wax or plasticine. Let us suppose that two forks A and B, of frequency 256 c/s., are sounded together, but that B has had its frequency reduced

to 252 c/s. in the manner described.

types

Sliding «

Mg

xn

clNee

Magnesium

Electron

nucleus

(8 particle)

The fact that sodium-24 decays into the harmless magnesium-24 renders it particularly suitable as a tracer in blood circulation studies. The use of radioisotopes in medicine is discussed more fully on page 638. x

638

THE

NATURE

OF

MATTER

Nuclear fission

The examples of neutron capture just described are concerned with the disintegration of nuclei into two parts of unequal size. In 1939 Hahn and Strassman investigated the action of neutrons on uranium-235 and found that it was split into two roughly equal pieces, one of which proved to be barium and the other krypton. Otto Frisch coined the expression “nuclear fission” to describe such cases as this. The importance of fission is that it is accompanied by the release of about ten times as much energy as in the case of ordinary disintegration, where only a small piece is broken off the nucleus. The uranium fission reaction was first used successfully to produce heat energy on a large scale by the Italian physicist, Enrico Fermi, at the University of Chicago in 1942. In Chapter 6 we have already described the fission process which goes on inside a commercial nuclear reactor used to produce heat for the production of electric energy. The reactions which go on inside these reactors are, of course, highly complex, but the one responsible for the bulk of the heat production is:

*gU + in —> SU —> Ba + BKr + 2. jn + energy Artificial isotopes Many of the end products resulting from the capture of neutrons by various elements are radioactive and have proved to be beneficial to mankind in the spheres of medicine and industry. Radioactive isotopes are manufactured mainly by irradiating substances with neutrons in a nuclear reactor, but they can also be made by bombardment with high-energy particles (e.g., protons or deuterons) from an accelerator. In the previous chapter we mentioned the use of X-rays for the treatment of cancer. It is now possible to employ suitable artificial isotopes for the same purpose. One of the most important of these is radio-cobalt ({7Co). Ordinary cobalt has a nucleus containing 27 protons and 32 neutrons ({3Co). If placed in a reactor where there is an abundance of neutrons a large proportion of the cobalt atoms capture an extra neutron and turn into cobalt-60. This decays, with the emission of beta rays together with very highenergy gamma radiation equivalent to that obtainable from 2:5million-volt X-rays. When properly shielded by lead the rays from cobalt-60 may be brought under control and employed instead of the more elaborate X-ray equipment for cancer therapy (Plate 24). These cobalt units or gammatrons are now being used to alleviate human suffering in hospitals all over the world. Certain other radioisotopes are taken internally, where they are selectively absorbed by certain organs, and so concentrate the radiation

SPLITTING

THE

NUCLEUS

639

where it is most required. Radio-iodine, for example, is absorbed mostly by the thyroid gland. Radioisotopes are also used as tracers. Small quantities of lowactivity substances are administered by injection to patients, and their passage through the body and location in diseased tissue may be ascertained by means of a Geiger counter (Fig. 486). Originally designed by Geiger for the purpose of counting ionising particles, this device has come to be one of the standard methods for detecting radioactivity. It is reported that Geiger was driven to invent this counter to save himself from the tedium of counting particles by the Aluminium

tube (-ve

Central

electrode (+ ve)

Tube contains argon

with a trace of bromine

To loud speaker or scaler Fic. 486. The Geiger counter

scintillation method (page 619). The essential part is a tube containing argon at low pressure, in which are two electrodes connected to a battery and amplifying circuit. If an alpha or beta particle or a gamma photon enters the tube it causes ionisation of the air. The ions formed are quickly attracted to the electrodes, with the result that a tiny current flows. This is magnified by the amplifying circuit and fed into a small loudspeaker, which gives a click every time a particle or gamma photon enters the tube. The rapidity of the clicks is an indication of the intensity of the radiation received. Alternatively, the amplified current is used to actuate an automatic counting and recording device known as a scaler.

Radioactive isotopes in industry Tracer techniques employing radioactive isotopes have found increasing application in industry. They are used to investigate such things as the flow of liquids in chemical plants and for the study of wear in machinery. In the latter case a small quantity of a radioisotope is incorporated in metal parts, e.g., bearings, piston rings, etc., and the rate of wear may then be calculated by measuring the activity of the abraded material carried away in the lubricating oil. Elsewhere, the ability of substances to absorb gamma radiation has

640

THE

NATURE

OF

MATTER

been adapted to give automatic control of the thickness of paper, plastic and metal sheeting as it goes through the production plant. Cobalt-60 and other gamma emitters are used as an alternative to X-ray apparatus for the examination of forgings and the welded seams of boilers and other pressure vessels. The main advantage here is that of easier portability and the fact that a supply of electricity at high voltage is not required.

Safety precautions The need for extreme care when dealing with radioactive substances cannot be too strongly emphasised. People soon learn to keep away from fire because the pain is immediate and obvious, but the great danger where radioactivity is concerned is that one can receive a severe dose of radiation without being aware of it. A number of small doses received over a long period build up cumulatively in the system, and may eventually lead to leukaemia or cancer later in life. Marie Curie and Enrico Fermi both died in this way. One of the earliest commercial applications of radium compounds was in the manufacture of luminous paint for the numbers on watch and other instrument dials. The paint consists of a minute quantity of a radium salt mixed with zinc sulphide, which glows in the dark as a result of scintillations from alpha particles. Incidentally, the individual scintillations may be seen if the luminous numbers on a watch dial are viewed through a microscope in a dark room. The girls who painted the dials had a habit of applying the brush to their lips in order to put a fine point on it. Unfortunately the danger was not realised in those early days and, over a long period, some of the workers absorbed enough radium to produce fatal illness many years later. Dangers of this sort do not, of course, attend the use of radioisotopes under proper medical control. The isotopes used have half-lives measured in days or weeks only, and hence cease to act after their proper function has been completed. Also these isotopes either decay into harmless substances or else are eliminated from the system. Radium, on the other hand, remains in bones in the body. If has a halflife of 1622 years, and consequently undergoes negligible decay over a normal lifetime. The same objection applies to many other substances, particularly the radiostrontium and radiocaesium from atomic bombs, which can ultimately find its way into the food we eat. Nowadays the strictest safety precautions are taken in nuclear research laboratories and nuclear power stations so that the workers there receive no more than the permitted maximum level of radiation. No one, of course, can avoid receiving the normal “‘background radiation” which originates from radioactive compounds in the earth’s crust and from particles and rays entering the earth’s atmosphere.

a

SPLITTING

THE

NUCLEUS

641

Radioisotopes are handled by mechanical tongs operated by remotecontrol equipment from behind thick walls made of lead, concrete or other suitable material which absorbs the dangerous radiations. For transport, thick-walled lead containers are employed, and in laboratories radioactive samples are carefully shielded in lead castles built of lead bricks. This form of protection works both ways; in some experiments a lead castle is used to keep the background radiation out!

List of elements Atomic number | Symbol

Atomic number | Symbol 7b,

Name

Palladium Silver Cadmium Indium

Hydrogen Helium Lithium Beryllium Boron Carbon Nitrogen Oxygen Fluorine Neon Sodium Magnesium Aluminium Silicon Phosphorus Sulphur Chlorine Argon Potassium Calcium Scandium Titanium Vanadium Chromium Manganese Tron Cobalt Nickel Copper Zinc Gallium Germanium Arsenic Selenium Bromine Krypton Rubidium Strontium Yttrium Zirconium Niobium Molybdenum Technetium Ruthenium Rhodium

Tin

Antimony Tellurium Iodine Xenon Caesium Barium Lanthanum Cerium Praseodymium Neodymium Promethium Samarium Europium Gadolinium Terbium Dysprosium Holmium Erbium Thulium Ytterbium Lutetium Hafnium Tantalum Tungsten Rhenium Osmium Tridium Platinum Gold Mercury Thallium Lead Bismuth Polonium Astatine Radon Francium Radium Actinium Thorium

642

e

LIST

OF

Atomic

ELEMENTS

643

Atomic

Aes

Symbol

Name

91 92 93 94 95 96 97

Pa U Np Pu Am Cm Bk

Protactinium Uranium Neptunium Plutonium Americium Curium Berkelium

number | Symbol TZ. 98 99 100 101 102 103

The elements printed in italic do not occur produced artificially.

Gi E Fm Mv No Lw

naturally,

Name Californium Ejinsteinium

Fermium Mendelevium Nobelium Lawrencium

but have been

QUESTIONS:47 1. State the laws of radioactive decay. What happens when an atomic nucleus disintegrates with the emission of : (a) an alpha particle; (b) a beta particle? Give one example of each process. 2. What do you understand by the terms: (a) transformation series; (b) halflife? 3. What is meant by the expression, “‘splitting the atom’? Should this be replaced by a more precise phrase? If so, suggest an alternative and give your reasons.

4. Describe Rutherford’s experiments on the disintegration of nitrogen nuclei by means of alpha particles. Write, in symbols, the nuclear reaction which takes place and explain the meaning of the symbols you use. 5. Describe and explain Cockcroft and Walton’s experiment on the bombardment of lithium by protons. How did this experiment demonstrate the validity of Einstein’s equation relating to the equivalence of mass and energy? 6. With the aid of a diagram, explain the construction and action of the Van de Graaff electrostatic generator and show how it is used to obtain a beam of high-energy deuterons.

7. Describe and explain the action of one type of particle accelerator. For what purposes are accelerators used? Name two different kinds of particles which could be used in the method you have described. 8. What is meant by nuclear fission? Describe the process of a chain reaction and briefly give details of the method used to control it in a nuclear reactor. (Refer also to Chapter 6.)

9. What are artificial isotopes? Mention two methods for producing them. Give ONE example in each case of their application in: (@) medicine; (6) industry. 10. Describe the construction of a Geiger counter. for what purposes is it used?

How does it work and

h

Definitions and Laws (with page numbers, in the order in which they occur in the text)

Mechanics and Hydrostatics Metre, 4, 11, Plate 1 Kilogram, 7 Weight, 7 Litre, 9 Second, 10 Yard, 11

Potential energy, 69 Power, 74 Newton’s laws of motion, 77, 79,

84 Momentum, 78

Dyne, 79

Pound, 11 Force, 14

Law of gravitation, 14 Coefficient of static friction, 19 Coefficient of sliding friction, 19 Resultant force, 21 Scalar quantity, 21 Vector quantity, 21 Parallelogram of forces, 23 Triangle of forces, 28 Moment of a force, 33 Principle of moments, 35 Couple, 36 Centre of gravity, 38 Speed, 49 Displacement, 49 Velocity, 50 Uniform velocity, 50 Acceleration, 50 Simple pendulum, 58 Parallelogram of velocities, 62 Work, 68 Energy, 68 Kinetic energy, 69 645

Newton, 80 Poundal, 80 Law of conservation tum, 84 Erg, 86

of momen-

Joule (Newton-metre), 86 Foot-poundal, 86 C.G.S. unit of power, 86 Watt, 86 F.P.S. unit of power, 86 Horsepower, 86 Machine, 96 Mechanical advantage, 96 Velocity ratio, 101 Efficiency, 101 Density, 112 Specific gravity, 115 Pressure, 119 Pascal’s principle, 107, 137 Archimedes’ principle, 145 Law of flotation, 150 Graham’s law of diffusion, 159 Surface tension, 161 Cohesion, 161 Adhesion, 161 Hooke’s law, 165

646

DEFINITIONS

AND

LAWS

Heat Temperature, 169 Upper fixed point, 170 Lower fixed point, 170 Fundamental interval, 170 Coefficient of linear expansion,

Focal length of spherical mirror, 288 Real and virtual images, 291 Conjugate foci, 291 Magnification, 297 Laws of refraction, 304

180 Coefficient of absolute expansion, 189 Coefficient of apparent expansion, 189 Boyle’s law, 198 Coefficient of expansion of a gas at constant pressure, 200 Charles’s law, 202, 206 Pressure coefficient of expansion of a gas at constant volume, 202

Refractive index, 306 Critical angle, 311 Principal axis of lens, 320 Principal focus of lens, 321 Focal length of lens, 322 Angular magnitude, 333 Spectrum, 341 Dispersion, 341 Candela, 350

Pressure law, 204, 206 Calorie, 227 British thermal unit, 227 Therm, 227 Thermal capacity, 229 Water equivalent, 230 Specific heat, 231

Latent heat of vaporisation, 237 Latent heat of fusion, 238 Saturated vapour, 249 Boiling point, 252 Dew point, 254 Relative humidity, 256 Mechanical equivalent of heat, 265

Light Ray, 273 Beam, 273 Laws of reflection, 277 Parallax, 279 Principal axis, 287

Principal focus of spherical mirror, 288

Luminous flux, 350 Lumen, 350 Lux; 351 Foot-candle, 351 Inverse square law (light), 352

Sound Pitch, 359, 371 Amplitude, 363 Wavelength, 363 Frequency, 363 Tone, 372 Noise, 372 Musical interval, 373

Quality or timbre, 376 Resonance, 385

Magnetism and Electricity Magnetic pole, 395 Magnetic axis, 395 Magnetic meridian, 396 Magnetic field, 402 Line of force, 402 Geographic meridian, 405 Declination, 405

DEFINITIONS

Inclination or dip, 407 Neutral point, 412 Surface density, 437 Tons, 439 Electric line of force, 444

Electrodes, 508 Anode, 508 Cathode, 508 Faraday’s laws

of

electrolysis,

511 Chemical equivalent, 512 Atomic weight, 512 Valency, 512 Electrochemical equivalent, 514 Fleming’s left-hand rule, 523 Resistivity, 549 Joule’s heating laws, 558

Capacitance, 456 Farad, 456

Relative permittivity, 460 Polarisation, 468 Local action, 468 Ampere, 477 Coulomb, 478

Volt, 478 Electromotive force (simple defn.),

force

647

LAWS

Electrolyte, 508

First law of electrostatics, 424

468 Electromotive defn.), 478

AND

(formal

Ohm’s law, 480

Ohm, 481 Ampere’s swimming rule, 496 Maxwell’s screw rule, 498

Right-hand grip rule, 498 Rule for polarity of coil, 499 Electrolysis, 508

Kilowatt, 564 Kilowatt-hour, 565 Faraday’s law of electromagnetic induction, 576 Lenz’s law, 576

Fleming’s right-hand rule, 578 The Nature of Matter Mass number, 624 Atomic num ber,624

Half-life, 626 Laws of radioactive decay, 627

NATURAL SINES 24'|30'|36'|42’| 48/5 4’| 1’ 0122 |0140

So

0297 | 0314

0541 |0558 0715 | 9732

0889 | 0906

1063 | 1080 1236 | 1253 ON WNH AUR

O157

0332

O471 | 0488 0645 |0663

0506

0819 0993 1167 1340 1513

| 0837 | IOII | 1184 | 1357 | 1530

0854 1028

1685 | 1702

1719 1891

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©

Answers to problems QUESTIONS : 1 (page 12) 3. 12:27 cm.; 3:63 in.

4. 3-47 mm.; 17-74 mm.

QUESTIONS : 3 (page 30)

2. 30 Ib. wt. 3. 13-4 lb. wt. 5. (a) 86°6 lb. wt.; (6) 174 lb. wt. 7. 120 lb. wt.; 50 1b. wt. 9. 10. 11. 13.

4. 130 lb. wt.; 63-6 Ib. wt. 6. 120°. 8. (a) 10-4 lb. wt.; (6) 6 Ib. wt.

(a) T cos 20; (4) T sin 20. (a) 2:08 lb. wt., 16° with vertical; (6) 0-58 Ib. wt. 5-8 lb. wt.; 11-6 lb. wt. 12. 5:8 Ib. wt. 59 lb. wt.; 51 1b. wt. 14. 7:5 lb. wt.; 2-5 lb. wt.

1Se2-Sicwt

QUESTIONS : 4 (page 46) 1. 2), 5. 7. 10. 13. 14.

54 1b. wt.; 36 Ib. wt. 2. 140 lb. wt.; 110 Ib. wt.; 1-2 ft. Silo Vas Slo Wie, 4. 6 ft. 10 in. from A; 6 in. from B. 3-75 lb. wt.; 6-25 Ib. wt. 6. (a) 10:31 gm. wt.; (6) 0-11 gm. wt. 44:8 lb. wt. 9. 8 in. from centre, midway between long sides. 5:2 ft. 11. 26° 34’. 12. 4 Ib. wt. On axis 2 ft. 1:5 in. from B. (a) 3 of the distance AB from A; (5) 36° 52’.

16. 0:57 in. from the centre, on diameter through centre of hole, and on side opposite to hole.

QUESTIONS : 5 (page 65) 2. (a) 64 ft./sec.; (b) 64 ft. 3. 200 ft./sec.; 6:25 sec. 4. 1100 ft. 5, 22:5 m.p.h. 6. 540 ft.

7. 44 ft./sec.?; 4 mile. 11. 13. 14. 15.

8. 600 ft./sec.

10. 110 sec.; 70 m.p.h.

120 cm./sec.?. 12. (i) 400 ft.; (ii) 8 sec. 60 m.p.h.; 14 miles; 25 miles; 24 miles. 4-95 m.p.h., N. 19° W.; 9-9 miles. Upstream, 41° 24’ with bank; 3 min. 52 sec. -

16. N. 77° 10’ E.; 20-5 min.

QUESTIONS : 6

(page 75)

945 2) EC,

4, 3-44 x 108 ft.-Ilb. wt. 654

ANSWERS

TO

PROBLEMS

655

QUESTIONS : 7 (page 92) 2. (a) 4 ft./sec.?; (6) 4000 pdl. or 125 lb. wt.

Sh S22 fta/secre.

4. 22 ft./sec.?; 1 min.; 20 m.p.h.; 22,400 pdl. or 700 lb. wt. 5. (a) 135 lb. wt.; (6) 120 lb. wt. 6. 80 ft. Oaabiee. set UME witssal2) HPs 8. 2 sec.; 19-2 joules. 9. (a) 24 pdl.; (6) 288 ft. pdl. or 9 ft.-lb. wt. 10. (a) 4:9 cm./sec.?; (6) 14:7 cm./sec.; (c) 22:05 cm.; 648,270 ergs. 11. (a) 6571 pdl.; (6) 16-43 H.P. 12. 72 fti/secz: 2592 ft-pdl. or 81 Ib=wt-;736 ft:; 1-5 sec. 13. (a) 64 ft./sec.; (b) 6-875 lb. wt. 14. (a) 32 ft.-lb. wt.; 96 ft.-lb. wt.; (6) zero; 128 ft.-lb. wt. 15. 27 ft. 16. (a) 64 ft./sec.; (6) 40 ft.-lb. wt.; (c) 40 ft.-lb. wt.; (d) 60 ft.; 960 Ib. wt. 17. (a) 240 pdl.; (6) 7:5 lb. wt.; 44 sec.; 49 ft. 18. (a) 8 ft.; (6) 1 sec. 19. 44 Ib. ft./sec.; 968 ft.-pdl. 21. 1900 ft.-lb. wt.; 480 lb. wt. 22. 1100 pdl.; 34-375 H.P. 23. 98,000 ergs.; 99 cm./sec. 24. (i) 6 lb. wt.; (ii) 9-6 ft./sec.?; (iii) 30 ft.

QUESTIONS : 8 (page 108)

1. 4. 7. 9. 11. 13. 14. 17.

(a) 5; (6) 3. 480 Ib. wt. 3-75 Ib. wt.; 375 ft-lb. 134 Ib. wt.; 1600 ft.-Ib.

2. (a) 18; (b) 90%. 3. 10%. 5. (a) 5; (b) 343 (©) 663%; 80%. wt. hee wt. 10. 334 1b. wt.

(a) 56%; (0) 25 H.P. 12. 453; 64 lb. wt./sq. in. (a) 50 gm. wt./sq. cm.; (6) 2500 gm. wt.; (c) 0:8 cm. 720; 3060 lb. wt. 16. (a) 16 lb. wt.; (6) 320 ft.-lb. wt. 12-4 lb. wt.

QUESTIONS : 9 (page 117) 1. 1-8 gm./c.c. 5. 13-66 cu. ft. 8 Sips) feonl

3. 604-8 kg.; 1330-56 lb. Th WPS8 2S). 10. 2°32 gm./c.c.

4. 108 Ib. wt. 8. 62:3 Ib./cu. ft. 11. 0-89 gm./c.c.

QUESTIONS : 10 (page 131) 1. 2. 4, 7. 9, 11.

4 gm. wt./sq. cm.; 720 gm. wt. (a) 27:2 gm. wt./sq. cm. or 27:2 cm. of water; (6) 136 gm. wt. 186 cm. of mercury. Se Sisqein: 6. 14-9 lb. wt./sq. in. (a) 245 gm. wt.; (b) 409 gm. wt.; 164 gm. wt. (to 3 sig. fig.). 388,000 dynes; 29,100,000 dynes (to 3 sig. fig.) 80 cm. of mercury. 13. 0-949 cm. of mercury.

QUESTIONS 1. 1034 cm. 5. 10:34 m. 8. 4-9 cm.

: 11 (page 142) 2. 930 cm. or 30:5 ft. 3. 9900 ft.-lb. wt.; 0-3 H.P. 7. 0:289 Ib. wt.; 2:604 Ib. wt./sq. ft. 9. 7-5 in. 10. 0:8; 18-75 in.

656

ANSWERS

QUESTIONS 1. 3. 5. 6. 9. 12. 14. 16. 20. 21.

TO

PROBLEMS

: 12 (page 155)

8. 2. (a) 7:1 gm./c.c.; (6) 178-2 gm. wt. (a) 51:6 gm. wt.; (6) 28 gm. wt. 4. 600 kg.; 45 kg. 1020 gm., 8:5 gm./c.c.; 96 gm., 0:8 gm./c.c. (a) 12 gm.; (6) 16 gm. 7. 2:15 in. 8. 0:8. 116 gm. wt. 10. 3-89 gm. wt. 11. 0-1024. 18 gm. wt. 13. (a) 190-4 gm. wt.; (6) 0-864. 0-6. 15. 18-3 lb. wt.; 29-2 lb. wt. 25 gm. wt.; 0-8. Mel 2icte 19. 0:45 gm./c.c. 448,000 cu. ft.; 438,000 cu. ft.; 285 tons. (i) 5 sq. cm.; (ii) 10 cm. 22.42 ¢.c.3 17:3 cm.

QUESTIONS

: 14 (page 175)

1. 54-6 mm. 4. (a) 25 deg. C.; (6) 45 deg. F. Ten @) ida ©osn(D) AGiieetis

Dm— 40° Ch S200F: 5. 2 deg. high.

5.30 36:9°-C; 6. 40° C.; 140° F.

QUESTIONS : 15 (page 185) 1. 19 in. 4, 70 cm. 9. 126-4° C.

2. 800° C.; 40:4 cm. 6. 38 cm. a. 102 10. 0-44 cm.; 0-0528 sq. cm.

Teen

3. 209 deg. C. 8. 0-107 in. 11, 765 76,

12. (a) 0:000027/deg. C; (6) 0-000015/deg. F.; 0-0036 pints. QUESTIONS

: 16 (page 194)

3. 0:000187/deg. C. 4. 9-55 cm. 6. 0-:0000272/deg. C. (using g = y, — Y.) or, 0:0000268/deg. C. principles). 8. 2:6 cm. 9. 0:05184 c.c.; 0:04536 c.c.; 28-00648 c.c.

(from

Ist

QUESTIONS : 17 (page 208) Pe cue an: 2. 300 litres. Sop lS) Lins ithe 4, 75 cm. of mercury. 5. (a) 70 cm.; (6) 63:6 cm. of mercury. 6. 34-1 Ib. wt./sq. in. Tel 62@? 8. 20:3 cm. 10. 10-3 atm.; 4-11 atm. 11. 25-8 lb. wt./sq. in. 12. Pressure doubles in each part. ISS ESTE: 14. 54c.c. WS a1S3ieic: 16. 1121 c.c. 17. 7 atm.; 114 atm. 18. 1092° C.; 15 litres; —91° C.

QUESTIONS : 19 (page 235) 1292 © 74, 4. 2 min. 30 sec. §. 6. (a) 98-1 cal./deg. C.; (6) 20 ih US fa 8.

SOLES 3. 665° C. 0:2 cal./gm./deg. C. gm.; (c) 0:92 cal./gm./deg. C. 102 cu. ft.; 98d.

\;

ANSWERS

TO

PROBLEMS

657

QUESTIONS : 20 (page 246) 1. 14,500 cal. 4, 24 gm. 4