Wave Effects Caused by Mechanical Motion

Transcription

1 International Journal o Advanced Research in Physical Science (IJARPS) Volume 1, Issue, June 014, PP 8-13 ISSN (Print) & ISSN (Online) Wave Eects Caused by Mechanical Motion Branko Mišković Independent Novi Sad, Serbia aham.brami@gmail.com Abstract: Instead o various explanations o particular wave eects, they are here uniied into the same theory. Going rom the simpler, towards more complex eects, each ollowing relies on the preceding explanation. Not only that these explanations are thus more understandable and convincing, but their similarities and distinctions are compared through a ew classiication principles. Though physical essences o particular waves slightly inluence the exposition, some artiicial exceptions are here overcome and inally reuted. Keywords: Doppler, Mach, Cherenkov, Fizeau, Michelson, Sagnac. 1. INTRODUCTION Unlike the ideally homogeneous medium, each its structural non-homogeneity causes partial relection and/or reraction o the propagated waves. In the case o the sharp discontinuity, the two sides are treated as the two distinct media, separated by the boundary surace. Starting by the waves initialized in the ormer medium, these considerations are reduced to mutual relations o the direct and relected wave beams. One or more relectors may be ound on the beam path, rom its emitter up to the signal detector. I relective suraces be perpendicular to the direct beam, the reverse one propagates in the opposite direction o the same path. At motion o one o the mentioned types o technical elements with respect to the medium o propagation there appear some variations o the physical parameters o the propagated wave and/or o the received signal. During the development o physics, rom one to another opportunity, such particular cases were registered, as the separate wave eects. Irrespective o their ull or partial explanation, these eects are usually applied in technical practice. The arrangement o the science and respective education demand their convenient uniication into one theory. Possible particular inconsistencies or mistakes would be thus also overcome. Such a problematic situation aroused at introduction o special relativity. Namely, any medium o light propagation could not be itted into the postulates o this speculative theory. Formerly understood vacuum medium o EM waves is denied and proclaimed as the misconception o the classical physics. Moreover, by the concept o the dual light nature, physical essence o EM waves is totally mystiied. Though the vacuum medium was thus expelled rom the science, the inluence o matter, as the cruder medium layer, could not be neglected. With artiicial ormal simpliications, respective approximate or un-testable equations were then ormulated.. POSSIBLE CLASSIFICATIONS Irrespective o their separate registrations and distinct explanations, the wave eects can be classiied according to a ew division principles: 1. a moving technical element,. the orm o its motion, 3. the variable and invariant quantities and 4. some chronological order o their registration. Each o these principles emphasizes the similarities and distinctions in the pairs o the eects, enabling thus their exhaustive comparison. 1. The technical details o measuring equipment are plunged into the natural medium o the wave propagation. Some o these details can be moved in space. The continuous and ARC Page 8

2 Wave Eects Caused by Mechanical Motion conditionally resting medium, as the wave substratum, represents the most natural rame o reerence. Possible its own motion must be reerred to some implicit, external local rame. Separate motions o the particular elements, or o the equipment in the whole, determine the parameters o the emitted and received signals, including the propagating wave. The complete or ractional motion o the medium is also considered.. We here will restrict to the uniorm, mainly rectilinear, motion o the elements, in the direction o the wave motion, along the line generator-receiver, or at least in very small angle with respect to this line. Approximately or in the limiting process, the last case is reduced to the circular motion and propagation, along the circle perimeter. In one particular case, the longitudinal and transverse wave beams are compared. Out o the rame o the treated eects, the accelerated motion may be also considered. 3. As the variable and invariant physical quantities, the known wave parameters are here observed: oscillating period ( ) as the time o an oscillating cycle, phase ( t/ ) the observed time expressed in the cycles, requency ( 1/ ) the cycle number in a second, speed o wave propagation (c) and wave length ( c ) the path taken or a cycle. The oscillating process, expressed by the phase, is copied by the wave lengths along the path o propagation. The speed o propagation, determined by the medium eatures (elasticity and density), is naturally reerred to the medium itsel. 4. The historical development o this scientiic topic, expressed by the years o the eect registrations and denoted by their investigators, just accords to the logic o exposition. Though this need not be ever the case in the science, the simplest eect was primarily registered, described and explained. It was then successively ollowed by all the other eects, each succeeding or a little complicated than the preceding. The names o the investigators are here ollowed by the years o investigations: Doppler 184, Fizeau 1851, Michelson 1881/87 and Sagnac This act enables the logical exposition, so that the explanations sequentially and gradually develop. 3. SIMPLE DOPPLER S EFFECTS Wave propagation through a medium carries the alternating signal, rom the emitter to the receiver. However, its native requency can be changed by motion o each o these two technical elements. Though the two inal results may be similar in the range o their usual measurements, their wider unctions and respective physical processes are essentially distinct. In the aim to cover these distinctions by the sequence o ollowing explanations, we thus distinguish a ew Doppler s eects. Let us start by the moving emitter, as the wave generator. By its motion at a speed ( u ) in the direction o propagation, each ollowing signal phase starts rom the point a little displaced orward, with respect to the ormer phase start. This act causes some squeeze o the wave along the path, with respective diminution o the wave lengths. In act, the path covered by the emitter is thus subtracted rom that covered by the wave. This simple logic inally determines the new wave length: ' c u (c u) (c u)/ (1) The opposite motion stretches the wave and its length. At least in homogeneous nondispersive media, the speed o propagation is invariant. The requency is inversely proportional to the wave length, with their invariant product (c) : ' (c u)/ c, '/ c/(c u) () At the positive speed, the new requency is greater, and vice versa. I this speed tends toc, the emitter ollows its wave in space, and the requency tends to ininity. The wall o the dense energy is thus ormed in the emitter ront, obstructing its acceleration. By suicient orce, however, the emitter can break this wall. International Journal o Advanced Research in Physical Science (IJARPS) Page 9

3 Branko Mišković The breaking o (Mach s) sound wall is ollowed by a shot. Though the speed o light cannot be reached, Cherenkov realized the light wall break. Instead o the particle acceleration, the eect arises at sudden diminution o the speed o propagation, on the boundary o two media. O course, the particle speed must be between the speeds o propagation in the sparser and denser media. The negative speed dierence (b) is maniest by the light, discharging the kinetic energy excess. Though the detector speed () v does not inluence the propagating wave, it changes the received signal requency. This eect results rom the new mutual speed by which the wave approaches the detector. The ratio o the two requencies just accords to the ratio o the new and old mutual (wave-detector) speeds. "/ ' (c v)/c (3) At v c the detector escapes the wave signal, but the opposite motion causes the linear requency increase, without limitation. Though distinct in general, the corrections () and (3) are similar at small speeds o the elements. 4. COMPLEX DOPPLER S EFFECTS At simultaneous motion o more elements, respective simple eects are combined. In the case o the emitter and detector, the unctions () and (3) mutually multiply, thus expressing the ratio o the received and emitted signals: " " ' c v ' c u Nevertheless, the wave parameters on the path depend only on the emitter speed. At the same speed o these elements, the two eects inally cancel each other. The eect o the wave squeezing is inally annulled by its slower receiving. At the common speed vu c, the equation (4) is reduced to the undetermined ratio 0/0 : with the wave wall ormed on the emitter, the detector escapes the signal. Doppler s radar represents these two joined elements. It sends the waves through the space, and receives the signals relected rom the objects. At motion o this device, () and (3) are multiplied again, but with the opposite signs o the common speed with respect to the direction o reverse wave courses: " " ' c u ' c u Unlike mutually compensated eects (4), the increased denominator and decreased nominator give similar eects. At the positive speed, the requency increases twice: by the squeezing o direct wave, and the rapid signal receiving. The relecting object, as the third element, may also move, e.g. at a speed v. It thus plays the roles o the receiver o the direct, and transmitter o relected waves. The eect (5) is thus repeated, but with the opposite speed signs, as i v u. At the speed v c, the object escapes the wave and its relection, but at v c it relects the doubled requency, with the wave wall o the relected wave. At the simultaneous motion o the radar and its object, as the opposite elements, the respective eects in the orm (5) are mutually multiplied: "' "' " c v c u c(c u v) vu c v' " c v c u c(c u v) vu c v' (5) (4) (6) International Journal o Advanced Research in Physical Science (IJARPS) Page 10

4 Wave Eects Caused by Mechanical Motion O course, the relector plays its two opposite roles. There is inally some simpliication in (6). Neglecting the product uv o the two relatively small speeds, the mutual speed v' v u between the object and radar, is thus used. In the case o the common motion ( u v) o the two elements, the two pairs o eects mutually annul. O course, this is the inal ratio o the received and emitted signals, with the squeezed direct, and stretched reverse waves. 5. RELATIVISTIC EQUATION Under imperative o a direct empirical veriication, special relativity does not accept the wave propagation in the medium, but considers only the ormal ratios o the received and emitted requencies. Apart rom the denied medium, the temporal comparison o the distant events is avoided, on the pretext o the insolvable empirical limitations. By artiicial equaling in law o the radar and its object, the symmetry o the two eects (7a) is unoundedly postulated. The geometric average o the two apparently symmetric processes is inally applied (7b) to the simpliied result (6): r ''' '' '', r c v' c v' (7) At relatively small mechanical speeds, the square root o the value being close to unit is diicult to distinguish rom this value itsel. Moreover, the particular our eects in the beginning o (6), can be identiied by the additional detectors placed on the wave path and/or moving object, without relativistic mystiications. 6. FIZEAU EFFECT Possible motion o the complete medium, as the physical substratum and the rame o wave propagation, is equivalent with the opposite motion o the technical equipment (6), at u v. Depending on the motion course with respect to the direct and reverse waves, there appears the squeeze or stretch o the wave lengths. Nevertheless, the received one equals to emitted requency, as i being invariant. Instead o it, some o the variable parameters, as the phase, may be observed. In the resting or moving medium, the phase represents the ratio o a distance covered and the wave length: d/ or ' d / '. The inal phase variation can be obtained by comparison o such two phases. By convenient technical solution, Fizeau compared the phases o the two signals passing through the same running water, but in the opposite courses, with superposition o their eects (9): d d ' ' c v, d d " " c v ; (8) dv dv ' ". (9) c v c The opposite speed signs in (8) concern the two opposite beams. Neglecting the small speed square, (9) is the linear unction o v. However, the measurement gave less than a hal o this value. The result between the two extreme expectations resting rame and its ull draw by matter conused the physicist so that they rather orgot it. Our explanation relies on the moving media theory [1]. 7. NEW EXPLANATION The above consideration understood the motion o the complete medium, consisting o the vacuum and material layers. The corrective actor in dielectric media (j) equals to the ratio o respective two electric ields: International Journal o Advanced Research in Physical Science (IJARPS) Page 11

5 Branko Mišković P DoE 1 j 1 D D r (10) Here P is the polarization o matter, and D P εoe o the total medium, including vacuum. The corrective actor is thus the unction o relative electric constant. In water, as the dielectric medium, the reraction actor, electric constants and corrective actor are: n /3, r n 16/9, j19/16 7/ MICHELSON S EFFECT The resting vacuum medium at Fizeau eect was implicitly connected to the ground. In the absence o the complete explanation, this obvious act was not noticed at all. There aroused the question o its own dependence on the Earth and its orbital motion. The ormer such experiment also used Fizeau method, but instead o the medium, the technical device was moving with Earth. Instead o the medium draw by the Earth, it was expected to be at rest, irrespective o the Earth motion. The measurement consists in the two light beams, sent rom the common point, into two perpendicular directions, longitudinal and transverse, with respect to the orbital Earth motion. Ater relections rom equally distant mirrors, their phases are compared at the same point. The phases o the direct and reverse paths o the longitudinal beam are expressed by (8). There just ollows their sum: dc d l ' ", c v cg g 1 ( v/c) (11) The transverse beam phase was considered as invariant, thus used in the role o the comparative phase. However, no phase dierence was noticed. This negative result stimulated some urther considerations. Thus Lorentz noticed that the transverse beam phase was also variable. When the orbital motion covers the basis o the triangle ( vt ), the light covers its two legs, in the summary length o (c t ). Pythagoras theorem applied to the triangle hal gives: ct vt d t cg d, t d cg t, l t ; (1) d 1 g (13) c g The transverse beam phase is obtained in the value (13a). With respect to some its distinction rom the longitudinal phase, there is their dierence (13b). Irrespective o the new explanation and urther advanced device, the result again equals to zero. The additional device improvements during 0 th century gave some phase dierence, a ew percents o the expected value. Not only that its speculative explanation, in the orm o special relativity [], was already widely accepted, but nobody had any alternative explanation. With respect to above explanation, the stratiication o vacuum medium, amongst nearby celestial bodies [3], may be proposed. 9. SAGNAC EFFECT Fizeau eect is here applied to the perimeter o a polygon or circle, rotating in its own plain. Two beams sent in the opposite direction meet each other at the starting point. The phase dierence depends on the peripheral speed, in accord to (9). This device is applied to registration o angular speeds on airplanes. International Journal o Advanced Research in Physical Science (IJARPS) Page 1

6 Wave Eects Caused by Mechanical Motion In act, the explanation o this eect is in essence nothing new. However, not only that this device by itsel represents very eective technical solution, but it obviously and convincingly denies the invariance o the relative light propagation, as the main result or even postulate o special relativity. The phase dierence just results rom the two dierent speeds o propagation with respect to the rotating perimeter. In other words, these two speeds are in act equal in the medium o propagation, but the mechanical rotation causes the eects already described above. The relativistic objection, o restriction o special relativity to rectilinear motion, may be expected. However, this restriction was introduced in the classical mechanics, where centriugal orces disturb relativistic logic. Even i we let the action o such the orces on light, the two beams will be thus equally inluenced. 10. CONCLUSION A number o mutually similar wave eects are sequentially explained, by reasonable classical logic. These explanations are suicient and complete, without any use o the relativistic bases. Moreover, they convincingly deny the relativistic principles. In act, all the explanations are ounded on the mutual light-device speed, with the invariant speed o propagation through the medium. The explanations concern all the types o waves, without exception o light or EM waves in general. REFERENCES [1] Mišković B, Systematic Foundation o EM Theory, International Journal o Electromagnetics and Applications, Vol. 4, No. 1, 014, [] Mišković B, Boundary Questions o EM Theory, International Journal o Theoretical and Mathematical Physics, Vol. 4, No. 3, 014, [3] Mišković B, Medium o Natural Phenomena, International Journal o Theoretical and Mathematical Physics, Vol. 4, No. 4, 014. AUTHOR S BIOGRAPHY In the period studied Technical Physics at University o Beograd, ex-yugoslavia. Being unsatisied by engineering practice, tried to compose a consistent text-book on EM theory. Owing to a sequence o unexpected diiculties, this job has been prolonged up to 30 years. Not only that EM theory is now inally considerably elaborated, but its new consequences call in question the majority o modern physics. The above article is a typical example. International Journal o Advanced Research in Physical Science (IJARPS) Page 13