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OS OS OS OS OS os os w 0 X + 2 € + c Update : mail.google.com/mail/u/0/ffsearch/assignment+4/FMfcgzGmvfZXLmxkLkCgFgQmkHXKnfg?projector=18.messagePartid=0.1 YouTube Maps Images GO GoGoAnimo.com -... https://mycourses.f... B BS(Computer Scien... Prove $x^7+3x^5 -... M Gmail C Proble Relaunch to update Chrome € € of Assignment4_2022.pdf segment New tab Ctrl+T Ctrl+N New window New Incognito window CtrlShift+N + Compose Assignment History Downloads Inbox SATA Ctrl+ Starred Bookmarks Nitin Upadhyaya > Snoozed Zoom 7596 + Please find eached Sent Print. Ctrl+P There is also a good will also Drafts More (1) Finally, from the Open with Google Docs post general solution to the full second order PDE 012, 2. Ripples on a pond: Ripple waves on the surface of a deep pond, arise due to the interplay of gravity, surface tension and the density of water. If the waves are dom- inated by gravity, the ripples are called gravity waves, else if they are dominated by surface tension, they are called surface tension or capillary waves. In this problem, let us simply use dimensional analysis to explore some of the properties of these two waves. (a) Let us lise square brackets to denote the dimensions of a physical quantity. Our goal is to express all physical variables of interest in terms of mass, length and time denoted as M,L,7 respectively. For example, the dimensions of mass are M = M. length are L = L and time are T = 1. Using this notation, the dimensions of spexiare (c) = LT-I Using this notation, write down the dimensions for coloration, force and density (mass per unit volume). (b) Let us now use dimensional analysis to find out the speed of gravity waves. For gravity waves, we expect the important variables to be gravitational acceleration 9. Waverumter k and density of water Let the speed of gravitational wave be Cy = f(g, k,p). In order to obtain the functional form for f, let y = geklip where a,b,c are to be determined. Express cach of the variables y, k, pin terns of M, L,T and compare the exponents of M, L, T on the left-hand side and right-hand side to solve for a,b,c and thereby, show that (c) Repeat the analysis for capillary waves, where we will express the spood c. = SIS.k.p), where is the surface tension of the air-water interface. Show that S=Notice how waves with large k (or small wavelength) move faster for capillary waves, but the opposite is true for gravity waves! (d) For both gravity and capillary waves, write work. This is called the disper- sion relation. Obtain the ratio and find the wavemumber and the corresponding wavelength), where you expect to see a transition from gravity waves to capillary Cast.. Regards Ctrl+F Find... More tools Meet New meeting 2 Attachments Edit Cut Copy Paste My meetings Settings Ilelp langouts Shruta Assignment Exit Srinidh Ramanshnan . Reply (e) When would you expext gravity waves versus capillary waves to be excited in the pond. Try dropping a large object (big stone) versus small stone (or drops of water) and see which wave gets excited. As the circular ripples propagate, what happens to the distance between the circular ripples for each kind of wave? Page 2 12 - Q + 32"C Partly sunny ENG IN 17:44 01-04-2022