E.—la.

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No. 43. — Sound, Light, and Heat. — For Class D. Time allowed: Three hours. [Candidates may answer questions either in Sound and Light or in Heat, but not in both. All answers should be illustrated, where possible, with diagrams.] A.— Sound and Light. 1. How has the velocity of sound in air been ascertained ? Point out the sources of inaccuracy in the method which you describe, and .show how the errors may be minimised or eliminated. 2. Explain the statement that a sound-wave consists of longitudinal vibrations. The wave-length of a certain note in air is found to be double that of a second note in the same medium : show how the pitch of the first note is related to that of the second. 3. State what you know about resonance. 4. What is the law connecting the intensity of illumination of a given plane surface with the distance from the source of light ? How can the truth of the law be experimentally tested ? 5. A- gas flame of sixteen-candle power is 75 centimetres from a standard candle: what is the nearest position to the candle at which a screen can be placed so as to be equally illuminated by both sources of light ? 6. Define the terms " refractive index " and " critical angle." A scratch on the under surface of a horizontal glass plate appears to be 3 in. from the upper surface when viewed normally from above :if the refractive index of the glass is l - 5, what is the real thickness of the plate ? 7. Make a careful diagram of the path of the rays from an object placed 3 in. in front of a doubleconvex lens and coming to a focus at the same distance behind it. Deduce from your diagram the focal length of the lens. 8. Describe and explain the changes in the nature of the image seen by an observer as he approaches a large concave mirror from a considerable distance. B.—Heat. 1. Define the terms: Unit of heat, coefficient of linear expansion, specific heat, latent heat of vaporisation, radiation. 2. In what respects is the expansion of water anomalous ? Describe and show graphically the nature of the volume changes which a piece of ice would undergo if gradually heated from -10° C. to 120° C. 3. What do you understand by the boiling-point of a liquid ? What circumstances affect the boiling-point of a liquid ? How would you determine the boiling-point of benzine ? 4. Make a sketch showing the application of a hot-water system to the heating of a two-storied school. Explain the principle of the apparatus, and point out the probable effects which would result if the circulating-pipes became frozen overnight. 5. Into 100 grams of oil at 80° C. 60 grams of ice (at its melting-point) were dropped; after careful stirring the mixture showed a uniform temperature of 5° : what was the specific heat of the oil? 6. Describe three experiments which you would perform in order to convince your class that steam contains more heat than the same weight of water at the same temperature. 7. How would you propose to measure temperatures above the boiling-point or below the freezingpoint of mercury ?

No. 44. — Sound, Light, and Heat. — For Class C and for Civil Service Senior. Time allowed: Three hours. [Candidates may answer questions either in Sound and Light or in Heat, but not in both. All answers should be illustrated, where possible, with diagrams.] A.—Sound and Light. 1. How would you construct a simple sonometer and demonstrate with it the laws of the transverse vibrations of strings ? 2. Describe any method whereby the relative velocity of sound in air and in glass can be determined. 3. Explain the formation of musical notes in open and in closed pipes. A narrow closed pipe gives a fundamental note the pitch of which is 256 vibrations a second : if the velocity of sound in air is 1,100 ft. a second, what is approximately the length of the pipe ? 4. State the laws of reflection of light, and show how they may be applied to find the angular elevation of the sun. 5. How can a hollow acute-angled prism be used for determining the refractive index of a transparent liquid ? Calculate the refractive index of a substance in which the critical angle is 30°. 6. Explain the action of the eye as an optical instrument. What is the physical meaning of " shortsightedness," and how can this defect be remedied by spectacles ? 7. Draw a clear diagram of the path of rays of sunlight through a spectroscope to an observer's eye. What is the spectroscope used for ? B.—Heat. 1. Thermometers are sometimes found to indicate correctly at 0° C. and at 100° C, but to be incorrect at intermediate temperatures : how can this be accounted for, and how could the exact error at 50° be ascertained ?