fig4 shows the the present invention in its general form ( its function is described above in detail ) with ring resonator 1 , two similar standing wave modes with two nodes each ( numerals 5 and 5a ), a perturbation 11 to separate the frequencies of these two modes and fix their locations , and wave source 7 ( located midway between adjacent maxima of the two modes to excite both modes equally ), driven with an oscillator 9 and alternate wave source locations and / or additional wave sources 7a , 7b , and 7c . the resulting traveling wave 12 is shown symbolically . fig5 illustrates the required frequency relationship of the two standing wave modes . numerals 13 and 14 indicate the resonance curves of the two standing wave modes with the perturbation in place ( these two modes being separated in frequency by the average of their bandwidths 15 and 16 ). the frequency f s of the oscillator ( and wave source ) differs in frequency by a half bandwidth from the peak of each resonance . the wave source should excite the two modes roughly equally as indicated in fig5 by the equal peak heights . for proper operation , all other modes of the resonator should be essentially non - overlapping in frequency with f s . numeral 17 illustrates such an essentially non - overlapping nearby resonance shown to be about five of its bandwidths from f s . fig6 indicates the phase relationship of the modes 13 , 14 and wave source . if the conditions of eq . 6 are met at the operating frequency f s , one standing wave mode will lead the wave source by 45 ° ( indicated by numeral 18a ) and the other will lag the wave source by 45 ° ( indicated by numeral 18b ). thus the two mode will differ in phase by 90 ° at the operating frequency f s . fig7 shows a general simply - connected cylindrical resonator 19 , with two ( similar ) m = 1 , n = 1 modes , ( their lines of nodes are indicated by numerals 20a and 20b , while the plus and minus signs ( numerals 2 and 3 ) indicate a maximum and minimum at one instant of time for the mode with node 20a ), with perturbation 11 to separate the frequencies of these two modes ( by the average of their bandwidths ) and fix their locations as shown , and wave source 7 located midway between two maxima of the two modes on the walls to excite both modes roughly equally . oscillator 9 drives the wave source . this setup will excite a rotating mode 12 ( shown symbolically ) in the resonator . for proper operation , all other modes of the resonator should be essentially non - overlapping with f s . fig8 shows a square cross section metal pipe bent around and joined to itself to form a ring resonator 1 . it has a perturbation 11 , a wave source 7 , and driving oscillator 9 . this setup can sustain traveling waves 12 ( shown symbolically ) in a ring resonator of either the electromagnetic type or the acoustic type , depending on the type of wave source 7 installed . note that electromagnetic ring resonators can also be constructed of dielectric materials [ see for example , richtmyer , j . appl . phys . 10 , pp . 391 - 398 , ( 1939 )] or from sections of transmission lines ( e . g . coaxial cables , twin lines , strip lines , etc .) bent around and joined to make loops . acoustic ring resonators can also be made of rings of solid material or a hollow pipe ( of almost any cross sectional geometry ) filled with a liquid or gas . fig9 shows a solid ring resonator 1 , with perturbation 11 , surface wave source or transducer 7 attached to the resonator surface at a location such a prescribed above and driven by oscillator 9 . this setup will sustain traveling surface waves 12 ( shown symbolically , also wave crests 21 shown ) such as required for surface wave motors as described more fully below . the electromagnetic , acoustical , and surface wave acoustical traveling wave ring resonators could be used in signal generation and processing . such devices can simultaneously serve to filter signals and generate output signals of several phases ( tapped out of the ring at any number of points ). alternatively , a movable tapping point out would allow an adjustable phase shift . another application would be an antenna based on ring resonators to couple to circularly polarized electromagnetic radiation . surface wave ring resonators also find use in surface wave motors as discussed below in connection with fig1 while acoustic ring resonators also find utility in thermoacoustic heat engines as discussed below in connection with fig1 . fig1 shows a ring shaped tank 23 of liquid with a free surface 24 which comprises a ring resonator . the tank has perturbation 11 and wave source 7 in its wall , driven by oscillator 9 . provided the perturbation and driving frequency are properly related as described above , this setup will sustain traveling waves 12 ( shown symbolically ) with wave crests 24a . free surface liquid traveling wave ring resonators could find use as recreational wave tanks that &# 34 ; recycle &# 34 ; their waves and thereby consume less power than conventional wave tanks and have phase velocities closer to those of natural water waves than the higher order modes often used in conventional wave tanks to conserve power . such water wave ring resonators would be very similar to the rotating mode resonator shown in fig1 and discussed below . fig1 shows a thin ring shaped disk 25 with a hole in its center to form a mechanical resonator designed to resonate in a flexure wave . numeral 27 indicates the crest of a traveling flexure wave , while numeral 12 symbolically indicates the whole traveling wave . the resonator has a perturbation 11 , and attached wave source 7 ( shown as an magnetic type transducer ) and driving oscillator 9 . fig1 shows an electronic ring resonator made of descrete components : inductors 28 and capacitors 29 to sustain traveling waves 12 ( shown symbolically ) in the voltage and currents in these components . the perturbation consists of one inductor 30 being of a different value than the rest ( a differently sized capacitor could also be used as a perturbation ). the wave source in this case is a coupling capacitor 31 attached to an oscillator 9 and the ring resonator at a point midway between the two standing wave maxima . this circuit could find use in generating properly phased signals which are simultaneously filtered or simply as a convenient phase shifter . fig1 shows a circular surface wave motor with rigid rotor 33 , surface wave ring resonator 1 having a perturbation 11 , wave source or transducer 7 , driving oscillator 9 , and resulting traveling wave 12 , shown symbolically . this would operate similar to other surface wave motors [ e . g . see u . s . pat . no . 4 , 504 , 760 ] with the difference that only one source or phase of electrical power need be provided for operation . the elimination of the circuitry to provide the second phase of power and the second transducer should make this invention less costly . note that the wave source 7 can be piezoelectric in nature , magnetic ( e . g . such as the pole pieces in conventional motors ), or mechanical ( e . g . fluid driven ). fig1 shows a thermoacoustic , traveling wave heat engine consisting of a regenerator section 40 ( which contains heat input and output 40a and 40b , acoustical input and output 43a and 43b , and a solid packing material 44 [ see u . s . pat . no . 4 , 114 , 380 ]) connected to the acoustic circuit 41 which returns part of the acoustic output of the regenerator section back into its input . a second regenerator section 42a is optional . this is also a correct alternate location for the regenerator section . the acoustic - to - electric transducer 45 represents one way to use the acoustical energy created in this device and , in this case , produce electrical power . the regenerator section 42 and feedback pipe 41 comprise a ring resonator which has perturbation 11 . this regenerator section powers the wave and is located midway between adjacent maxima of the two standing wave modes being used ( the 45 ° spacing from regenerator section to the perturbation as shown is appropriate for an n - 1 mode ). for pure traveling waves 12 ( shown symbolically ), the ring resonator ( including the perturbation ) should have a geometry such that the modes are separated in frequency by the average of their bandwidths and that there be no other standing wave resonances within a few bandwidths of f s . given this , the resonator section will amplify the traveling wave mode at a frequency f s = f 1 - 1 / 2δf 1 = f 2 + 1 / 2δf 2 . compared to the invention of u . s . pat . no . 4 , 114 , 380 , the present invention represents a new , unobvious , and simplified way to achieve the matching required and get the output of the regenerator section to power the ring resonator given their differences in acoustic impedance . one method of reducing losses in a traveling wave heat engine is to add in properly positioned standing waves [ see u . s . pat . no . 4 , 355 , 517 ] to increase the effective wave impedance at the regenerator site . if properly done the regenerator still experiences a pure traveling wave as it needs for proper operation , but at an increased impedance . ( elsewhere in the resonator , with the exception of one spot halfway around the ring , there is a mix of standing and traveling waves .) one can use the present invention to accomplish this proper addition of standing waves by simply reducing the perturbation 11 , such that the frequency split 46 between the modes ( 13 and 14 ) is less than the average of the bandwidths ( 15 and 16 , in fig1 ). in this case the phase difference ( numeral 47 , fig1 ) between the two standing wave modes is less than 90 °. as indicated in the phasor diagram , fig1 , one can decompose these standing waves ( 13 and 14 ) into waves in - phase ( numerals 50 and 51 ) and waves 90 °- out - of - phase ( numerals 52 and 53 ). the in - phase waves add up to a standing wave ( not shown , but 1 . 414 times either 50 or 51 . it is a factor of 0 . 707 smaller than a simple addition of 50 and 51 because of the λ / 4 offset of the two modes ) having a maxima at the wave source ( i . e . the regenerator &# 39 ; s site ) as is needed for the enhanced impedance traveling wave heat engine [ u . s . pat . no . 4 , 355 , 517 ]. the 90 °- out - of - phase waves add up to a pure traveling wave ( of amplitude equal to the magnitude of vector 52 or vector 53 but not shown in fig1 ) as we saw in eq . 4 and as is also needed for the proper operation of this device . the effective impedance at the regenerator site is determined by the ratio of standing to traveling wave amplitudes which is in turn set by the perturbation size and consequent resonance curve separation as shown in fig1 . numeral 42a in fig1 shows the correct location for a second optional regenerator section in this device , at opposition around the ring where pure traveling waves ( at enhanced impedances ) exist the same as in the first location 40 . this could also be considered an alternate location . note that while in a regular traveing wave heat engine , there may be a number of possible regenerator sites , in a resonant traveling wave heat engine there are only two correct sites . compared with the invention of u . s . pat . no . 4 , 355 , 517 , the present invention represents a new , unobvious , and simplified way to achieve both the required matching and the required mix of standing and traveling waves . fig1 shows an almost circular swimming pool 60 filled with water 24 , and made with a perturbation 11 ( this perturbation could be adjustable if desired by using a movable wall , piston , bladder , or float ) and wave source 7 ( with self contained oscillator ). if properly adjusted to meet eq . 6 , it will sustain rotating waves 12 ( shown symbolically and also wave crest 24a shown ) for use as a recreational wave pool . similar to a ring resonator wave pool , this setup should require less energy than the conventional recreational wave pool in that the waves are rotating ( being recycled ) as opposed to being created and traveling to a dissipation region . the phase velocity of these rotating waves should be closer to that of a normal water wave and slower than that the high order traveling wave modes sometimes used in regular wave tanks to conserve power . this should make the waves easier to ride on surf boards or floats . as noted for general rotating wave resonators , such a rotating mode wave tank need not be perfectly circular , but might be a shape of some regular polygon , or other roughly circular shape as long as the modes and operating frequencies can be adjusted to meet the conditions of eq . 6 and that other non - useful mode are several bandwidths removed from f s .