The Theory of Sound, Volume 2Macmillan, 1896 - Sound |
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A₁ amplitude angle aperture approximately axis calculated coefficient condensation condition constant corresponding cylindrical denote density dimensions direction distance disturbance e-ikr effect eikat energy equal equation expression finite flame fluid function Green's theorem harmonic heat HELMHOLTZ'S THEOREM infinite integral intensity investigation kinetic energy medium motion nodes normal velocity observed obtained open end p₁ parallel phase Phil pipe pitch plane waves plate Pogg potential pressure problem propagation quantity quarter period radius rarefaction ratio reflected wave refraction resonator result shewing simple source sinh solution source of sound sphere spherical spherical harmonics suppose surface symmetrical theorem theory tube V₁ vanish velocity of propagation velocity of sound velocity-potential vibration viscosity wave-length zero аф
Popular passages
Page 370 - ... which in the case of a nearly vertical direction of motion cannot stop short of actual contact. Regular vibration has, however, the effect of postponing the collisions and consequent scattering of the drops, and in the case of a direction of motion less nearly vertical may prevent them altogether.
Page 33 - ... be propagated relatively to the undisturbed parts of the gas without undergoing an alteration of type. Nevertheless, when the changes of density concerned are small, (5) may be satisfied approximately ; and we see from (4) that the velocity of stream necessary to keep the wave stationary is given by •(6), which is the same as the velocity of the wave estimated relatively to the fluid. This method of regarding the subject shews, perhaps more clearly than any other, the nature of the relation...
Page 61 - The subject of sensitive flames with and without pipes is treated in considerable detail by Prof. Tyndall in his work on Sound; but the mechanics of this class of phenomena is still very imperfectly understood. We shall return to it in a subsequent chapter. 261.] EXPERIMENTS OF SAVART AND KONIG. 61 harmonics, twelfth, higher third, &c., corresponding to the various subdivisions of the column of air. In the case of the twelfth, for example, there is a node at the point of trisection nearest to the...
Page 471 - U, etc., so that it would appear as if in simple sounds, that each vowel was inseparable from a peculiar pitch, and that in the compound system of pulses, although its pitch be lost, its vowel quality is strengthened." . . . "Having shown the probability that a given vowel is merely the rapid repetition of its peculiar note...
Page 240 - ... becomes posterior. If the rate of alternation o'f the body's motion be taken greater and greater, or, in other words, the periodic time less and less, the condensation and rarefaction of the gas, which in the first instance was utterly insensible, presently becomes sensible, and...
Page 471 - ROBINSON and others had shown that a quill held against a toothed wheel, would produce a musical note by the rapid equidistant repetition of the snaps of the quill upon the teeth. For the quill I substituted a piece of watch-spring pressed lightly against the teeth of the wheel, so that each snap became the musical note of the spring. The spring being at the same time grasped in a pair of pincers, so as to admit of any alteration in length of the vibrating portion. This system evidently produces...
Page 36 - ... easier and the backward slopes steeper. At a time equal to the greatest positive value of dx/du, antecedent to that at which the curve is first contemplated, the velocity would be discontinuous. The exception is now a wave of condensation, involving a passage always from a less to a greater density. When discontinuity sets in, a state of things exists to which the usual differential equations are inapplicable ; and the subsequent progress of the motion has not been determined. It is probable,...
Page 227 - ... tube, were noticed soon after the discovery of the gas and have been the subject of several elaborate inquiries. The fact that the notes are substantially the same as those which may be elicited from the tube in other ways, eg by blowing, was announced by Chladni. Faraday proved that other gases were competent to take the place of hydrogen, though not without disadvantage. But it is to Sondhauss that we owe the most detailed examination of the circumstances under which the sound is produced....
Page 36 - Stokes*, who pointed out the difficulty which ultimately arises from the motion becoming discontinuous. If we draw a curve to represent the distribution of velocity, taking x for abscissa and u for ordinate, we may find the corresponding curve after the lapse of time t by the following construction : — Through any point on the original curve draw a straight line in the positive direction parallel to x, and of length equal to (a + u) t, or, as we are concerned with the shape of the curve only, equal...
Page 307 - WAVES. 307 made to vibrate, place a sheet of paper, or the blade of a broad knife, with its edge parallel to the axis of the fork, and as near to the fork as conveniently may be without touching. If the plane of the obstacle coincide with either of the planes of symmetry of the fork, as represented in section at A or B, no effect is produced ; but if it be placed in an intermediate position, such as C, the sound becomes much stronger1.