Vertical Sound Waves

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Spencer Francis
5 years ago
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1 Vral Sond Wavs On an drv h formla for hs avs by onsdrn drly h vral omonn of momnm qaon hrmodynam qaon and h onny qaon from 5 and hn follon h rrbaon mhod and assmn h snsodal solons. Effvly h frs ro and frs olmn of qaon 4 vanshs and. n For vral sond avs W 3 A ππ ππ L and L T T r L s h vral av lnh T s h rod and s r L s h vral av lnh T s h rod and s h has sd of h avs.

2 L s onsdr h rm n h las ro and h sond olmn of h drmnan. r L π h l l f h h F l d s h vral sal of h amoshr. For vral sond avs h rao of L and s small and hn an b nld. n h qaon 3 an b rrn as n h qaon 3 an b rrn as W 4 A 4 For nonrval solon h drmnan vanshs and hn } { } { Rmovn h ommon faor from all h l.h.s. rms 5 } {

3 s h qaon of sa RT and o RT RT Th las rm s small omard o h ohr o rms. Also hs rm s manary. n nln h las rm. ± RT RT 6 Th sam rlaon o n 7 for h vral sond avs. If or. f h rrbaon s assmd o b hydrosa or h nomrssblybl form of onny qaon s onsdrd hn hr s no vrally roaan sond avs. I may b nod ha h nomrssbly s rahr a dras lmaon.

4 oronal Sond Wavs Consdr h av roaaon alon -dron only. n and also vral vloy vanshs. Th vral momnm qaon n 5 s no mor vral momnm qaon n 5 s no mor onsdrd. n n 4 ll no nld h sond ro and sond olmn o ro and sond olmn o S 7 A 7 E h d d Eqan h drmnan o ro and sn } { } { 3 3 3

5 Whn sn { } h as la { RT } Ths n hs as hr solons. Th rval roo and h vlos of sond avs ± RT 9 If h omrssbly rm s omd by n Ths as s qvaln o non-dvrn flo and hs h sond avs ar flrd and only h rval solon rmans. 8

6 Srfa Gravy Wavs L s onsdr horonally roaan ravy avs hh L s onsdr horonally roaan ravy avs hh rm boh horonal and vral moon. No l s rr h lnarsd qaons of moon 9 and onny qaon as drvd bfor. Assm h amoshr o b nomrssbl. Ths an r srfa ss hh s rmd o b fr. Dron h rms h abov s of qaons bom ρ 3 ρ

7 Th hydrosa qaon for h ndsrbd flo s 3 ρ Inran h abov qaon from o hh ρ As bfor assm harmonsolons n h form As bfor assm harmon solons n h form 3 ψ 3 ρ S b 3 3 d lf Sbsn 3 n 3 and smlfyn an ψ 33 ψ ψ Elmnan from h frs o qaons n 33 ψ ψ

8 No lmnan bn h las qaon and h hrd ψ qaon n Allon h vral alraon Allon h vral alraon 35 a a Whn h rrbaons ar hydrosa Whn h rrbaons ar hydrosa n from b b Consans aab and b ar arbrary o b drmnd by bondary ondons.

9 Th lor bondary s assmd o b horonal and hr h vral vloy n l.b.. n 35 aa. a aa say n for Eandn For n for h onal alyn a B. C. o rm as 36 b or b b say srs a For h r bondary h oal rssr of a srfa arl hh ms rman a h srfa d d Sn nln rod of rrbaon W a 39 rms

10 sn 3 and 3 ρ ρ ρ 4 39 n n ρ ρ ρ 4 No ll aly boh h bondary ondon rsls and 4 o 33 n ordr o h solons for hydrosa and non-hydrosa amoshr. Cas non-hydrosa From h hrd qaon of 33 ψ From 37 a From 37 a 4 a ψ

11 Also from h frs qaon of 33 ψ a Sbsn 37 and 4 n 4 4 { a a n π L ± L π anh π L 43 Cas hydrosa From h hrd qaon of 33 Aan from 38 b ψ ψ b

12 Aan from h frs qaon of 33 Sbs n n ψ 4 on s b b { } b ± 44 Wavs ravln h h has vloy vn by 44 ar nrally rfrrd o as Shallo ar or Lon ravy avs. Whn h rao /L n 43 s rlavly lar abo.5 s sffn h has vloy boms aromaly L ± 45 π Ths avs ar alld D ar avs. Th fld arl Trajors ar narly rlar.

13 For small vals of.4 L h arl rajors n 43 ar vry lonad llss and hs narly horonal lns. If on assms a homonos amoshr h hydrosa qaon vs ρ RT and 44 may b rn as ± RT 46 Ths h sd of h lon ravy avs s narly h sd of h sond avs.

(heat loss divided by total enthalpy flux) is of the order of 8-16 times

(heat loss divided by total enthalpy flux) is of the order of 8-16 times 16.51, Rok Prolson Prof. Manl Marnz-Sanhz r 8: Convv Ha ransfr: Ohr Effs Ovrall Ha oss and Prforman Effs of Ha oss (1) Ovrall Ha oss h loal ha loss r n ara s q = ρ ( ) ngrad ha loss s a S, and sng m =