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PONAŠANJE BRODA NA TALASIMA____________________________Sledi jednostavna, ali veoma važna relacijaω =2ngknčiji se fizički smisao još ne vidi...To je tzv. disperziona relacija talasa naslobodnoj površini tečnostiPrivremeno, to je uslov pod kojim jeemementarno rešenje problema...φ ( x , zt , )Poremećaj slobodne površine takođe se sastojiiz beskonačnog zbira elementarnih poremećaja∞ζ( x, t) = ∑ ζn( x, t)n=1pri čemu u za svaki od elementarnig e e poremećajaećajaslobodne površine važi1ζn( xt , ) =−g∂φ( x, 0t , )n∂tnNa osnovu∂φn∂tkz n=± B ω e sin( k x± ω t+ε )Sledi konačnoiligde jen n n n nζ ( xt , ) = Asin( kx± ω t+ε )n n n n nζn( xt , ) = An sin ⎡⎣kn( x± ctn) + εn⎤⎦cnωn=knAnBnωn= ∓gTo je elementarni, sinusni, pravilni iliregularni talas.c n – brzina prostiranja talasaA n – amplituda talasaTalas je harmonijska (sinusna)funkcija u prostoru i vremenu.PREDAVANJA 2009. 43
PONAŠANJE BRODA NA TALASIMA____________________________U određenom trenutku opisan je funkcijomζ ( x) = A sin( k x+ ε + const)n n n na na određenom mestu, funkcijomTalasna dužina i period povezani su stalasnim brojem i frekvencijom2π2λn= , Tn=kζn( t) = Ansin( ωnt + εn+ const)Pošto su talasni broj i frekvencija povezanidisperzionom relacijom 2ω = gkvažia takođe iTn2π2π = = ... = λnω gcnnn= = =n nnnπωω g gλnk k 2πnnω n – kružna frekvencija talasak n – talasni brojε n – fazni pomeraj.brzina prostiranja talasa zavisi od talasnedužine..!Talasi na površini vode su disperzioni...Duži talasi se prostiru brže...PREDAVANJA 2009. 44
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