Question

a) Two traveling waves are given by the expressions, yi(x,t) = 5.0cos(0.15x – 6.0t) and y2(x, t) = 5.0cos(0.15x – 6.0t + 1/4) What type of interference results when these waves are added together? Explain. b) Determine an expression for the superposition of these two waves. c) When these two waves are out of phase by a rad, what type of interference results? d) What type of wave does the summation of these two waves now represent? e) By how much has the frequency of this new wave changed? f) Sketch the waves y, and y, either as a function of position or time and indicate the nodes and antinodes. I

Answer 1

yg (2, t) = Solutiona) = 5 cos (0,15% -6t) Yg (0,t) = 5105 (0:15 2-67+74) fost constructive Interference phase difference 10) = 2nr inn → natural Number} Four destructive interference phone difference (0) = ma co { modd}. Here 0 = Thore Therefore Neither constructive.non destructive tot Interference will takes place. Solution by y = y + Y Amplitude of y = A = w 5 + 5 + 2x5?cos A =10 T 2 tana= 5 Sin T x = 22.50 5 + 5 COST 각

: y = 10 cos (0.154 – 67 +22.5°) y = 10 cos (0.15 4 – 67 + T 8 erence takes places Solution c) it phose difference 10) = 7 then Destructive interferer solutiond). The summation of these two waves now depresent the Resultant ware. solution e) Standing The frequency of the new ware to remains the same. Resultant solution of y > anthode. anthode antinode 370 ST slov 2 2 0 Node Node eti Node Node