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BOARD OF EXAMINERS.
VIII. Sound, Light, and Heat
(Section 1 only of Stage 1)
Professor H. L. Callendar, M.A., LL.D.,
Report on the Examinations in Sound, Light,
Results : 1st Class, 185; 2nd Class, 149; Failed, 90 ; Total, 424. The answers to this paper showed a fair general average of excellence, with comparatively few serious failures. The points of weakness were chiefly those where exact knowledge was required in the answers. This, however, is to be expected in the First Stage. The following remarks on the several questions may be of use to teachers.
SOUND. Q. 1. Describe, with the aid of diagrams, the process by which sound
waves are propagated through the air. Students seem much misled by the analogy of the propagation of waves when a stone is dropped into water. They think that sound is propagated in this way. They are also much misled by the displacement curve. They thus think that sound can be propagated both longitudinally and transversely.
The question states “Describe, with the aid of diagrams ..."; insufficient attention was paid to this. Q. 2. Describe some phenomena which show that sound waves can be
reflected. A sharp tap is sounded in front of a long flight of stairs. What impression will the sound reflected from the stairs
give to an observer in front? The second part of this question was seldom understood clearly. Q. 3. Define what is meant by (a) simple harmonic vibration, (6)
frequency of the vibration, (c) amplitude of the vibration. Illustrate your definitions by reference to the case of a simple
pendulum. When S.H.M. is described with the aid of an auxiliary point moving round a circle, it should be stated that the point moves uniformly. Amplitude is the maximum displacement from the equilibrium point. Q. 4. An observer notes an interval of 4.5 seconds between seeing the
flash and hearing the report of a gun at a distance of one mile. Find the velocity with which the sound has travelled. How
would it be affected by temperature? It should be stated in the answer that light is propagated so quickly that the flash is seen practically instantaneously.
LIGHT. Q. 5. A mirror hangs on one of the walls of a room ; show by means of
carefully drawn diagrams that an observer will see by reflection more and more of the room behind him as he approaches the
mirror. Many of the diagrams were very crude. Q. 6. Find the size of an image of the sun formed by a concave mirror
6 feet in radius, assuming that the distance of the earth from
the sun is 100 times the diameter of the sun. A large proportion of the candidates took the mirror as of 6 feet focal length. Q. 7. State the laws of refraction of light, and show that it follows from
your definition that the direction of a ray after passing through à plate of glass with parallel sides, is parallel to its direction
before entering the glass. Many candidates treated the angle of refraction as the angle of emergence from a parallel slab. Thus, it was stated that the angle of incidence is equal to the angle of refraction. Q. 8. Explain what is meant by an image. What is the difference
between a real and a virtual image! In the case of a concave mirror, find the positions of the object when the image is
virtual. The explanation of an image was, on the whole, very badly done. A large numher of candidates confined themselves to stating that it is a representation of the object. This is not an explanation, but a paraphrase.
Q. 9. Define what is meant by the specific heat of a substance, and
explain how it can be measured.
Equal volumes of water at 100° C. and mercury at 0° C. are shaken up together, what will be the temperature of the mixture ?
Density of mercury 136. Specific heat .03. The specific heat was frequently defined by reference to unit volume. Q. 10. Describe some simple experiments which show that the vaponr of
water exerts an appreciable pressure on the walls of the vessel in which it is contained, and that the vapours of different liquids
exert different pressures at the same temperatures. In the “barometer tube” experiment, care should be taken to state that enough liquid is introduced to saturate the space, if the maximum vapour pressure is required. Q. 1. Define latent heat. The latent heat of steam is 539 at 100° C
How much steam at 100° C. would be required to raise 1 lb. of
water at 0° to the boiling point ? Latent heat should be defined generally, and not with particular reference to the case of water. Q. 12. State the law of the expansion of gases at constant pressure.
Find the alteration in the weight of air in a room 8 metres long, 8 metres broad, and 4 metres high, when the temperature is raised from 0° C. to 20° C.
The height of the barometer is 76 cm.
Weight of a litre of air at 0° C. and 76 cm. = Gases expand, per degree centigrade, by sis of their volume at 0°C. The last point is important, but was often omitted.
STAGE 2. Results : 1st Class, 91 ; 2nd Class, 174 ; Failed, 37 ; Total, 302. The answers to this paper showed in many cases a good average standard of knowledge. There were comparatively few failures. Some weakness was shown in working out numerical results, especially in regard to the relations of units. Subjoined are special details with reference to the Reveral questions. Q. 1. Describe an experiment showing the interference between two
trains of sound waves which are travelling in nearly the same
direction. The best experiments for this are the sound analogues of Lloyd's fringes and Fresnel's Biprism (Rayleigh's Experiment.) That of stationary waves between a source of sound and the wall is not a correct answer, as the two trains are going in opposite directions. Q. 2. The velocity of sound through water is 1440 metres per second ;
find the percentage diminution in the volume of water produced
by an additional pressure of one atmosphere. Boyle's Law does not enter into this question. Many candidates are evidently not at bome in the C.G.S. system of units. They have, therefore, attempted to convert to the F.P.S. gravitational system, and their attempt has usually ended in disaster. Q. 3. Describe carefully the method of Kundt's tube for measuring the
velocity of sound in a gas or in a solid. The adjustment to the best position should be given--this is when the end of the rod is at a node (practically). Q. 5. How would you construct a harmonicon (1) of glass strips of con
stant thickness, (2) of wood strips of constant length. Scarcely attempted. Many candidates treat this as a monochord question. Q. 6. Explain what is meant by resonance, and give examples of reson
ance in (a) mechanical and (6) acoustical systems. Sounding boards in pianos, etc., do not exhibit resonance (in its strict sense), as a rule. It is there a case of forced vibrations. Q. 7. It has been noticed that sound is sometimes transmitted over the
surface of water with greater intensity during the prevalence of rain or fog than in bright sunny weather.
explain this result? The two chief causes of this effect are (i) the upward refraction caused by the warm air near the surface of the water when the sun is shining, and (ii) the acoustic clouds caused by evaporation and convection. Many candidates think a proof of an increase of the velocity sufficient. Q. 8. An observer notes the time on his chronometer at which he hears
a time gun, and the chronometer appears 25 seconds slow. If the gun is at a distance of a mile, and the temperature of the air is 15° C., find the error of the chronometer. *(Velocity at 0°
C., 330 metres per second.) Candidates should use the numerical value of the velocity supplied, and not some remembered formula. The temperature reduction should be given as the square root of the absolute temperature. Q. 9. Describe carefully how the velocity of sound in free air has been
measured, and discuss the errors to which the method you describe is liable.
How would you
Any tube (e.g. a resonance tube) experiment is not a correct answer to this question, as the latter refers to free air-even Regnault's sewer experiment is not quite satisfactory. The chief errors are (i) the wind—a cross wind is not got rid of by reciprocal observations, (ii) temperature, (iii) hygrometric state, and (iv) the personal equation.
STAGE 3. Results : 1st Class, 10 ; 2nd Class, 24 ; Failed, 16 ; Total, 50. On the whole the answers were decidedly above the average, though owing to the comparatively small syllabus in this subject, a higher standard ought to be attained than in such subjects as Heat, Light, and Magnetism and Electricity, where the ground to be covered is so much larger.
Taking the questions in detail :-
a gas and the velocity of mean square of the molecules of a gas. This question was frequently well answered, and nearly all those who attempted it were acquainted with the fundamental ideas underlying the
Q. 2. Discuss the way in which determinations of the velocity of sound
in a gas are used to obtain information as to the number of
atoms in a molecule of gas. Fairly well answered, though many candidates were hardly sufficiently explicit as to why the value of the ratio of the specific heats decreases as the molecule becomes more complex. Q. 3. Write a short essay on the theory and method of production of
singing flames and their use in acoustical investigations. The answers to this question were incomplete though diffuse. Q. 4. Prove that the velocity of propagation of a pulse along a stretched
string is equal to NT/p, where T is the tension and p the mass
of unit length of the string. Well answered. Q. 5. Describe some of the methods used to study the small movements
of vibrating systems such as strings or tuning forks. Answers very incomplete. Many candidates simply described methods of determining the frequency of the fundamental of a fork. Q. 6. Discuss the relation between the intensity of a sound and the rate
of its propagation through various media. Seldom attempted. Q. 7. Explain why the diatonic scale is unsuited for varied music, and
describe the system of temperament in which the interval of a
fifth is maintained perfect. The answers to this question were for the most part unsatisfactory. The first part was sometimes answered fairly well. In the second part alniost without exception the method of equal temperament was described.
Results : Ist Class, - ; 2nd Class, 1; Failed, 3; Total, 4. Out of four candidates, one did sufficiently well in the first paper to justify further examination. In the second paper he showed some knowledge of the mathematical theory, but little acquaintance with details of recent experimental work, although the practical paper showed that he was a very fair experimentalist.
STAGE 2. Results : 1st Class, 39 ; 2nd Class, 194 ; Failed, 126 ; Total, 359. The general character of the answers was about the same as in previous years. A little more time spent in thinking out the manner in which the answer is to be given would in most cases repay the candidate. The following notes on the answers to individual questions may be of interest to the teachers. Q. 1. Describe carefully how you would arrange an experiment to
illustrate the interference of light so that it may be visible to a
large audience. The answers to this question were not very good. A large number of candidates described apparatus for the production of interference bands, but failed to describe how the bands could be thrown upon a screen.
The theory of the production of the bands was often given in a slipshod way. Q. 2. How would you distinguish between ordinary light and plane
polarised light ? Give some method of determining the plane
of polarisation. The first part was well done, but the answers to the second part were incomplete and very rarely clear. Several planes were often mentioned and mixed up, and it was sometimes difficult to follow the answers. Q. 3. Explain the differences between the spectrum produced by a prism
and one produced by a grating. Mention some of the
advantages and disadvantages of each of these methods. The fact that in a diffraction spectrum the deviation is proportional to the wave length appears to be well known. Many candidates stated that one disadvantage of a prisni was the impossibility of obtaining a pure spectrum without using a focussing lens. Many curious advantages and disadvantages were invented for the purposes of answering the question. The high dispersion of a grating spectrum and the brightness of the prism spectrum were often referred to. Q. 4. Describe a simple astronomical telescope and explain carefully,
with the help of a diagram, what determines (1) the magnifying
power, and (2) the field of view. The majority of the candidates knew the essential parts of a simple astronomical telescope, but the diagrams were often very poor. Several candidates placed the object close up to the object glass. The part of the question referring to the magnifying power was fairly well done, but only one or two knew anything about the factors which determine the field of view. Q. 5. What is meant by total internal reflection? Describe how this
phenomenon may be employed to measure the refractive index
of a liquid. The first part of this question was well done, but the second part was not so good. A large number of candidates described unworkable methods, one of frequent occurrence involving total internal reflection at the surface of a film of liqnid enclosed between two parallel glass plates. Q. 6. Explain how caustics are formed. Give a careful drawing to scale
showing the caustic due to a concave mirror when the luminous point is half-way between the principal focus and the centre of
the mirror. Fairly well answered. Some very good caustics were drawn. Q. 7. What is meant by the terms illuminating power, intensity of
Describe some method by which each of these quantities may be measured.