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lecture8 - E'ELVIN WAKE Y K>’ La)k I 1:ng L-DLAL View...

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Unformatted text preview: E'ELVIN WAKE. Y ' K >’ ' La ' ) )k I 1:ng /// ' L-DLAL. View or KELVIN wmce I" ’L " cows‘ISTS APP<207<1HATEL7 oFA , {’LANE Paomesswa owwe Grzout’ ZPKDPAGATING IN DUEECTIoN 6”; As Norse Agave SURFACE WAVE SVS’I’EHS‘OF GENERAL FORM“ALUUA‘/5 CON€1$T OF CUMBINflT—ROMS OF PLANE PRDGJZESSWE WAVES 0F DWI—“EVENT Wane—“Nags AND DIPECTIG‘NS. Tm:— 5mm: MODEL OOILL APPU/ “TO THE SHIP KELV/IV WAKE. Remrme TO THE EARTH FRAME ,THE Loon— VLAME PEOGZESS‘NE WAuE TAKES Tr—H; ForaH: jg: 15A 8K2~LK(X6099+‘(51’n8)+{w-t SUBSTITWE; - X=w+0t Y= "2* %= 2 .._ RELATIVE ’TO THE $HzP FRAME: CF= iaA 8 k2 —£ kaw39+fow9) ~— (A) 'X 8-;(kucos9—Sw3t BUT RELATIVE TD'THE s HiP FRAME pol/was ARE STATIONARY) so we MUST HAVE :’ k0 0059‘ :00 fl:’\/ : 05033 K l’ @ THE PHASE VELOCtT‘f OFTHE wAVEs IN THE Keww wAiE Pkomch/Na w Drizgc'ncw 9 Hum“ BE ECQUAL To UCos3 , crrHerawyse THEY CANNOT BE$TATIONA12V 1&5ansz ’11) THE 3mg 0 RELATWE TO THE EA {2.714 9/3175»)! THE FRECDUENCV OF A LOCAL, $7 STEM PROPAGATINC w Queen/ow 3 lg GWEN BY THE: RELATION w: kUCOSS’ Keuwm: TO THE EARTH SVS’TEH THE DEEP wA'ree Dquazsnom RELATION STAY-55’: THIS is THE WMELENaTH 0F wA-VES (M A KELvmW/xge FPaPAGAT/MG m mega—now 9 AND BEINGSTATTIONAQY RELATIVE TO’Y’HE $HxP... AN cassava—2 StTTHUG ON AN EflfiTZ—l FIXED FKAME OBSEsz—ZS A LOCAL. wAUE SYSTEM Pmmcmnwa IN DtRECTION 9‘ TWUELl—wc AT ITS GROUP VELOCITY in}: By vzzrug ' dlc oF THE RAVLEIGH DEVICE OOHIC‘HS‘TATES THAT we NEED To Focus ON THE SPEED OF THE ENE—1261 DBVSI'TY (N WAVE AHPLtTqu) FATHER “THAN THE 59559 0? 1»sz CQESTS / So, RELATIVE TO THE EARTH 1;:pr INCLINED coozoywATE S‘YS’TEH (x270; ’ __ __ elm)" X/t’ V3 , CT— " I _, LOU .2 CL I; : So: KXrF‘WJC: kCICbsa-fi- 331M854. k1) wsa;w)’{; VT . “4 C) AND THE RA‘ILEHGH CONDITIOW Fm? THE VELocvrv OF TH'ECROU‘P ‘TA 1655’ THE POEM : J41: E kLB) C1cos§+gs£w9)1 =0 EV VIRTUE OF THE 1313956514») RELATION DERIVEO'ABOVE.‘ @ UL 60315“ kc93= \1’ Fouows FROM THE CHAIN EULE 0F D\FFE€EI\FT’M Tram TwAT {ZA’YLEIGH'S Commmw IS: (XCoSS + 75"W9)] =0 figfi UHCOSG comm N26 LOCALLY OBSE£vED BY AN OBSERvEIZ AT THE BEflCH , .930 THE \‘VISIBLE’IwAvES [N THE WAKE OF A $HIP A25 WAveaizchs wr-HCH MUCT‘ 'TFAVEL AT THE Loam, Giana? VELOCITY“ THES‘E CGMDITIO‘WS ‘TfPANSL/FFE INTO THE ABOUE Ecoumrzo-N vacH (you 86 SOLVED AND DQSCUSSED NEXT. MORE DISC‘USSION flux/D A M025 HA‘THEHA Tzcm, DEE?VATION BAS‘ED ON THE PZWQPLE o? STATzaNAfaY ‘PHAse HAY BE. FCNNO w MH. , THE 93meer OF THEABCVE ELQUH—T,ON WILL PfiOOUCE A RELfl'T'ZO’IU 857—00 SEN ly/x AND 9. $0 LOCALWA‘VES (N A {1'5va .WAICECAN 0N2)! PtcheAGATE MU ACERTAHU DHZEC‘TIO‘M 8 ) GIVEN ’j/X... $(H?‘LE ALCEBVA LE‘ADg TO? o Z/Xm) us szvvaMETezc ASNT 8:0 EACH PAEL'T CemEESPowps TO THE KELU/IU WAKE m THE PORT AND STAEBOARD SIDES OF THE VESSEL. . THE PHYSICS 0w EITHER '5on l3 TDE’I’UTICAL DUE To 97' HHETKY. H e (9: o WAVES P20 FAGAT/UC m THE SAME DHZECTICMJ AS THE S’HHP.’ THES‘E WAVES CAM ONLY EXIST AT Yco AS SEEN ABOVE o 9: If : WAVES PRoPAGAT/UG ATAqo" ANGLE QECA‘T’H/E “TO THE s” H1 P DHZEC'TIO‘N o1: FOEWARD TRANSLATION o 8': 35016,: WAVES PEOPA OAT/N4 AT AN ANGLE 33°16’ RELATn/ETO THE S’H‘P szs. THESE Aft": WAvEy SEEN AT THE CH USTIC OF THE {18-va WAKE. LET ”ME SOLUTION OF THE 79x09) BE 0F THE POEM, wHE/U IN veri'rE—D : THE CRESTS‘ OF THE wAue SYS'TEH TpAiuuc A S‘H-IP , THE tau/w WAKE) M25 cow/ego? CONSTA-LJ—r PHASE OR 3 IN KECMDN I 3 X C03 “(:1 [750+ 73"“ {Di-(y/x) C = SQ X COSZ'F1(Y/x) l< 4‘) IN EECtoN “II“? _ “X Q09 C x {W 1(y C _ “C2. 7/)+7’5 'F /)<) EGzQ/ZQ) Oust-F; (WK) ‘PLCSTT/w THECE Queues we org—mm A VIS‘uAL GRAPH O'FTHEL TRANS‘VEIZSE” AND “DIN/5245p?" wAve Sims—Ms IN THE KELVW WAKE. "YR/«muses; wAvES % ...
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