54
ACOUSTICS 0-82 E, in advance of the end. That is, the length of the to be^l'66. Rayleigh and Ramsay {Phil. Trans. A. 1895, part i. pipe must be increased by 0'82 Ebefore applying Bernouilli’s p. 187) also used a single dust-tube with a sounder to find y for theory. This is termed the end correction. Using this argon, and again the value was 1 -66. result Eayleigh found the correction for an unhanged _ When a system is set vibrating and left to itself, the open end by sounding two pipes nearly in unison, each vibration gradually dies away as the energy leaks out provided with a flange, and counting the beats. Then the either in the Avaves formed or through friction. flange was removed from one and the beats were again In order that the vibration may be maintained, Maintencounted. The change in virtual length by removal of the a periodic force must be applied either to aid the Orations flange was thus found, and the open end correction for the internal restoring force on the return journey, or unhanged pipe was 0'6 E. This correction has also been Aveaken it on the outgoing journey, or both. Thus if a penfound by B'aikley by direct experiment (Phil. Mag. vii. dulum always receives a slight impulse in the direction of 1879, p. 339). He used a tube of variable length and motion just about the lowest point, this is equivalent to an determined the length resounding to a given fork, (1) increase of the restoring force if received before passage Avhen the closed end was the first node, (2) when it was through the lowest point, and to a decrease if received after the second node. If these lengths are L and L, then that passage, and in either case it tends to maintain the 7 7 7 . , swing.. If the bob of the pendulum is iron, and if a coil is hj- u ^ 2 and ~~2T~ 18 t^ie correction for the open end. placed just below the centre of SAving, then, if a current passes The mean value found was 0'576 E. through the coil, Adiile and only while the bob is moving Helmholtz investigated the velocity of propagation of sound in pipes, taking into account the viscosity of the air towards it, the vibration is maintained. If the current is on while the bob is receding, the vibration is checked. If Propaga- (Eayleigh, Sound, ii. § 347), and Kirchhoff in- it is always on it only acts as if the value of gravity were tion of vestigated it, taking into account both the increased, and does not help to maintain or check the waves m viscosity and the heat communication between vibration, but merely to shorten the period. ^U the air and the walls of the pipe (Sound, ii. In a common form of electrically maintained Etectrically § 350). Both obtained the value for the velocity fork, the fork is set horizontal with its prongs 'f,0ar,gta,aed in a vertical plane, and a small electro-magnet U(l--r°=), is fixed betAveen them. The circuit of the electro-magnet E, V 27tjN’ p where U is the velocity in free air, E is the radius of the is made and broken by the vibration of the fork in pipe, 1ST the frequency, and p the air density. C is a con- different ways say, by a wire bridge attached to the stant, equal to the coefficient of viscosity in Helmholtz’s loAver prong which dips into and lifts out of two mertheory, but less simple in KirchhofFs theory. Experiments cury cups. The mercury level is so adjusted that the ciron the velocity in pipes were carried out by Schneebeli cuit is just not made when the fork is at rest. When it (Pogg. Ann. cxxxvi. 1869, p. 296), and by Seebeck (Pogg. is set vibrating contact lasts during some part of the outAnn. cxxxix. 1870, p. 104) which accorded Avith this result ward and some part of the inward swing. But partly as far as E is concerned, but the diminution of velocity owing to the delay in making contact through the carriage down of air on the contact piece, and partly owing to the was found to be more nearly proportional to 1ST A Kundt delay in establishing full current through self-induction, also obtained results in general agreement Avith the formula the attracting force does not rise at once to its full value (Eayleigh, Sound, ii. § 260). He used his dust-tube in the outgoing journey, whereas in the return journey method (O. A. § 93). the mercury tends to follow up the contact piece, and the Kundt s dust-tube may also be employed for the determination full current continues up to the instant of break. Hence 0 s ec Specific 2? tI16. raU velocit ^, P ikc heats of a gas or vapour. the attracting force does more work in the return journey heats9 ^Wlth ^ . y °f sound in a gas at pressure P than is done against it in the outgoing, and the balance is ratio. density p, and if waves of length X and frequency N are propagated through it, then the dis- available to increase the vibration. ance between the dust-heaps is In the organ pipe—as in the common whistle—a thin sheet of air is forced through a narroAv slit at the bottom X _U dof the embouchure and impinges against the top 2 2N rgan plpe ' Avhere y is the ratio of the two specific heats. If d is measured edge, which is made very sharp. The disturbance ° made at the commencement of the blowing will no doubt set for two gases in succession for the same frequency N, we have the air in the pipe vibrating in its OAvn natural period, just A2 as any irregular air disturbance will set a suspended body 7i />]P2 df ’ where the suffixes denote the gases to which the quantities relate. SAvinging in its natural period, but we are to consider how If 7i is known this gives 72. Kundt and Warburg applied the the vibration is maintained when once set going. When the method to find y for mercury vapour {Pogg. Ann. clvii. 1876, p. motion due to the vibration is up along the pipe from the 356), using a double form of the apparatus in which there are two embouchure, the air moves into the pipe from the outside, dust-tubes worked by the same sounding rod. This rod is sup- and carries the sheet-like stream in with it to the inside ported at I and f of its length where it enters the two dust tubes, of the sharp edge. This stream does work on the air, aiding the motion. When the motion is reversed and the air moves out of the pipe at the embouchure, the sheet is deflected on to the outer side of the sharp edge, and no Fig- 9. Avork is done against it by the air in the pipe. Hence as represented diagrammatieally in Fig. 9. It is stroked in the middle so as to excite its second mode of vibration. The method the stream of air does work during half the vibration ensures that the two frequencies shall be exactly the same In Avhich is not abstracted during the other half, and so goes the mercury experiment the sounding rod was sealed into the on increasing the motion until the supply of energy in dust-tube, which was exhausted of air, and contained only some blowing is equal to the loss by friction and sound. " mercury and some quartz dust to give the heaps. It was placed The maintenance of the vibration of the air in the m a high temperature oven, where the mercury was evaporated, the second tube containing air was outside. When a known singing tube (described O. A. § 89) has been Sin in £ z temperature was attained the sounder was excited, and d* and d, explained by Eayleigh (Sound, ii. § 322 h) could be measured. From the temperature, Avas known, and as due to the way in which the heat is com“ e‘ 72/7i could then be found. Taking 7l = l-41, -y2 was determined municated to the vibrating air. When the air in a
