The Theory of Sound: In Two VolumesMacmillan, 1896 - Sound |
Common terms and phrases
A₁ amplitude aperture approximately axis calculated coefficient condensation condition constant corresponding cylindrical denote density determined dimensions direction distance disturbance e-ikr effect energy equal equation expression finite flame fluid Fn ikr fork function given Green's theorem harmonic heat infinite integral intensity kinetic energy length medium motion mouth nodes normal velocity observed obtained open end P₁ phase Phil pipe piston pitch plane waves plate Pogg potential pressure problem propagation quantity quarter period radius rarefaction ratio reflected refraction resonator result shews simple source solution source of sound sphere spherical spherical harmonics suppose surface symmetrical theorem theory tion tube vanish velocity of propagation velocity of sound velocity-potential vibration viscosity wave-length zero
Popular passages
Page 16 - WAVES. [245. each component wave the direction of propagation is the same as that of the motion of the condensed parts of the fluid. The rate at which energy is transmitted across unit of area of a plane parallel to the front of a progressive wave may be regarded as the mechanical measure of the intensity of the radiation.
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 - ... 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 between velocity and condensation § 245 (3), (4). In a stationary wave-form a loss of velocity accompanies an augmented density according to the principle of energy, and therefore the fluid composing the condensed parts of a wave moves forward more slowly than the undisturbed portions. Relatively to the fluid...
Page 471 - Robison and others had shewn that a quill held against a revolving 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...
Page 232 - ... ceases; but by keeping the gauze hot by the current from a powerful galvanic battery, Rijke was able to obtain the prolongation of the sound for an indefinite period. In any case from the point of view of the lecture the sound is to be regarded as a maintained sound. In accordance with the general views already explained, we have to examine the character of the variable communication of heat from the gauze to the air. So far as the communication is affected directly by variations of pressure...
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 18 - Newton expressed the result in terms of the ' height of the homogeneous atmosphere,' defined by the equation where p and p refer to the pressure and the density at the earth's surface. The velocity of sound is thus *J(gh), or the velocity which would be acquired by a body falling freely under the action of gravity through half the height of the homogeneous atmosphere.
Page 470 - WILLIS'S view of the way in which the cavity tone was superimposed on the reed tone is very explicit. ' According to EuLER, 1 if a single pulsation be excited at the bottom of a tube closed at one end, it will travel to the mouth of this tube with the velocity of sound. Here an echo of the pulsation will be formed which will run back again, be reflected from the bottom of the tube, and again present itself at the mouth, where a new echo will be produced, and so on in succession till the motion is...
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,...