i have to follow the class notes to solve this question on the white page thank you

countably infinite set # of elements of the set can be put in to a one on-one correspondence with the 2 / integers . Uncountabley infinite set : members of the sat . ( Pdz ) 2 24 = ( To 2 2 7 ) dz de = FV We have a traveling wave equation Correspond to ALL elements of TR . 22 2 / 1 = 41 ( 2 ) + ) + / 2 ( 2 , * ) Substitute the sum into the LDE @ string under tension : To 2 4 2 - 1 2 = 0 222 4 , 212 are solutions to the LDE assume a string has a uniform mass density = Ka = constant . 1 / weigh string 1 / 9 = in 2 2 2 2 22 2 . J D ; V = 1 / TTR ) = IT DV 222 / D = 2 R La] - M To in Hom in p = m . Traveling waves -salve Newtons and law for infinitesimal slice : d2 762 Earlier we naively close [ P] = kq when eAll waves are traveling waves for a limean system P = Ka - A ( 2 ) B ( 4 ) - 14 ( 2 , 1 ) = A ( 2 ) B ( * ) a little so eq . shape of stringy Recommended to use " separation of variables " to V ' = To salve the LDE . There is a characteristic speed for all 1 ( 2 , 4 ) = A (2 ) B ( X ) motion along 2 . B = B ( wt + 4 4 ) = cos ( wit + le ) ( choice ) -7 Z wave equ . says : 2B - - a sim ( wt + 6 ) PAZ = AM 2 B = - wo cos ( w+ + 6 ) T2 Cos Oz = T , Cost. Ensures no motion of AM - WV A ( 2 ) cos ( w* + 4 ) - V " cos ( wt + 4 ) 2 " A 2 22 20 along z . cos ( wt + 4 ) ( - WV A ( 2 ) - V 2 2 VA \\ = 0 2 2 2 / i coso, - TO 2 7 - vu jay - 0 ) Newton's and low for an ent ( limnar ) system . * AO 2 Cos Oz - To Suppose 4(2,t ) = 4 ( 2 + vx ) " A ( * + A ( 2 ) = 0 2 2 2 Fret = T 2 sin 02 - T , sim , (@ "A / 2) - 0/ Boundary conditions (2 ) f = 2 + Vx = 4 = 4 / f ) 2 22 distance B ( * )