Question

Problem 1 [30 pts): Two waves travelling in opposite directions produce a standing wave. The individual wave functions are: b = 6sin(4x - 5t) 42 = 6sin(4x + 5t) where x and y are measured in m and t in s. a) (10 pts] Find the amplitude of the simple harmonic motion of the element of the medium located at x = 2.7 m. b) (20 pts) Find the positions of the first three nodes and antinodes if one end of the string is at x = 0.

Answer 1

Y, = 6556 ( 43-5+) We = 6 sin ( 4x+5+) V= 4 + 42 6 [ 2 » 43Có *] 12 sin 42 cosst. Qo) so Y = 12 sinua cost A(22) = 12 sin42 A(X=2.7) = 12 sonl 4x2.7) = -1)-77m Ano. b.) for nodes A(Z) = 0 & Sin 4x=0 +42=nT nt 4 -) = 0 3. A 4, 37 are positions of nodes. and Sin42 = 1 For antino des. 2 = 4x = 18+ (-1)"2 ht+ (HDMA 중중 2C 3Ā 50 8 Ans.