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1899.

SUBJECT VIIIa. SOUND.

Advanced Stage and Honours.
EXAMINERS:

PROFESSOR A. W. RÜCKER, M.A., SEC.R.S.,

PROFESSOR W. GRYLLS ADAMS, M.A., D.Sc., F.R.S.,

AND

PRINCIPAL R. T. GLAZEBROOK, M.A., F.R.S.

GENERAL INSTRUCTIONS.

If the rules are not attended to, your paper will be cancelled.

You may take the Advanced Stage, or Part I. of Honours, or (if eligible) Part II. of Honours, but you must confine yourself to one of them.

The marks allotted to each question are given in brackets.
Put the number of the question before your answer.

You are to confine your answers strictly to the questions proposed.

Your name is not given to the Examiners, and you are forbidden to write to them about your answers.

The examination in this subject lasts for three hours.

Advanced Stage.

INSTRUCTIONS.

Read the General Instructions above.

You are not permitted to answer more than seven questions.

21. What experiments would you make to show that the pressure of a gas measures its resistance to compression at constant temperature?

(28.)

On what property of

22. Describe a method of comparing the relative wave-lengths of sound in air and in different gases. the gases do these differences depend?

(28.)

23. How would you test the state of vibration of the air in different portions of an organ pipe when it is in action?

(28.) 24. How would you determine experimentally the pitch of a note given by a musical instrument, and what apparatus would you require for the purpose?

(28.) 25. Explain the squeak which is heard when a sudden sound is produced near a paling with small intervals between consecutive pales.

(30.) 26. Four strings of the same weight and material, and stretched with the same force, give the notes of the common chord. Find the ratios of their lengths to that of the shortest of them. (28.)

27. In Melde's experiment, if the vibrations of the fork are transverse to the string the frequency of the fork is the same as that of the string, but if the vibrations of the fork are parallel to the string, the frequency of the fork is twice that of the string. Explain carefully the cause of this.

(28.) 28. How could you determine by means of resonators the constituent tones which are present in a compound musical note ?

(28.)

29. Write a short essay on Musical Scales and Temperament.

(30.)

HONOURS-PART I.

Read the General Instructions on page 1.

You are not permitted to answer more than five questions.

51. State the laws of transverse vibration of a rectangular bar of metal clamped at one end, and explain in a general manner how the law connecting the frequency with the dimensions and elastic constants of the bar may be obtained.

52. Write an essay on the vibrations of bells.

(60.)

(60.)

53. Give a general explanation of the formation of Chladni's figures in the vibrations of plates.

(60.)

54. Explain why, in accordance with the theory of audition of Helmholtz, beats can only be heard between notes separated by a moderate interval. Discuss the evidence as to the accuracy of this conclusion.

(60.)

55. Write a short essay on Musical Scales and Temperament.

(60.) 56. A string of length and mass m per unit of length is stretched with tension T. Show that the frequency of

1

the fundamental note is

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(60.)

57. Discuss the various causes which influence the audibility of sounds at a distance from the point at which they are produced.

(60.)

HONOURS-PART II.

PAPER I.

NOTE.-No Candidate is eligible for examination in Part II. of Honours who has not obtained a pass in Honours-Part I. in 1898, or a 1st or 2nd Class in Honours of the same subject in a previous year.

INSTRUCTIONS.

Read the General Instructions on page 1.

You are not permitted to answer more than five questions. Candidates who do well in Paper I. will be summoned to South Kensington to undergo a further examination, which will consist of (1) another paper, and (2) a practical examination in the laboratory.

81. Explain why, in accordance with the theory of Helmholtz, beats can only be heard between notes separated by a moderate interval. Discuss the evidence as to the accuracy of this conclusion. (40.)

82. Write a short essay on the propagation of sound in branched pipes. (40.)

83. Discuss and explain some cases of the maintenance of soundwaves by means of heat. (40.) 84. Find the equation to Lissajous' figure produced by two mutually perpendicular simple harmonic vibrations, the frequency of one of which is double that of the other. Deduce from the general case the form of the curve when the phases differ by a quarter of a vibration.

(40.)

85. A number of heavy particles of equal mass are attached at equal distances apart to a stretched string of negligible mass. Obtain an expression for the velocity of wave propagation along the string, and deduce hence the velocity along an unloaded string of uniform deusity. (40.) 86. Show that the work done in producing a strain of simple type, e.g., a uniform compression in an isotropic elastic solid, is half the product of the strain into the corresponding stress.

(40.)

87. Give a general explanation of the formation of Chladni's figures in the vibrations of plates.

(40.)

HONOURS-PART II.

PAPER II.

INSTRUCTIONS.

You are not permitted to answer more than five questions, of which one must be in Section A.

SECTION A.

(40.)

111. Write an essay on the evolution of the musical scale. 112. A musical note is in general due to a combination of tones

corresponding "to vibrations of which the periods are "aliquot parts of the original vibration. The exceptions "to this statement are apparent rather than real."

Discuss the view expressed in the above paragraph, and give fully your reasons for agreeing with or differing from (40.)

it.

SECTION B.

113. Give a general description of the construction of the ear.

114. Write a short essay, with illustrations, on the "normal functions."

(40.)

use of (40.)

115. Discuss the theory and uses of singing and sensitive flames. (40.) 116. Show that if the small quantities of the second order are included in the equation of motion of a plane wave of sound, two notes of frequencies, m and n, will, when sounded together, produce notes of frequencies m + n and (40.)

m-n.

117. Show that in order that there may be no loss in the transmission of sound waves through the air, the conditions must be those which correspond to strictly adiabatic or to strictly isothermal expansion. (40.)

Laboratory Work.

HONOURS (PART II.). PRACTICAL EXAMINATION.

1. Determine the velocity of sound in the given rod by Kundt's method, having given that the velocity of sound in air at a temperature t° C. is

v = 330·6 +0.6 t metres/sec.

2. Find the simple rigidity of the material of the given wire by means of a torsion pendulum.

3. Determine the pitch of an electrically driven fork by means of a stroboscope.

4. Find the ratio of the radii of the two given wires, given a monochord and a tuning fork.

5. Determine the difference in the frequencies of the two given forks by measuring the frequency of the first difference tone by means of a monochord.

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