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Two traveling waves are generated on the same taut string. Individually. the two

ID: 1472638 • Letter: T

Question

Two traveling waves are generated on the same taut string. Individually. the two traveling waves can be described by the following two equations: y_1(x,t) = (2.93 cm)sin (k_1x+(0.208 rad/s)t+phi_1) y_2(x,t) = (4.78 cm)sin (k_2x+(5.13 rad/s)t + phi_2) both of the above traveling waves. exist on the string at the same time, what is the maximum positive displacement that a point on the string can ever have What are the smallest positive values of the unknown phase constants (in radians) such that the above displacement occurs at the origin (x = 0) at time t = 3.00 s?

Explanation / Answer

a) Maximum displacement = sum of indivisual amplitudes=2.93+ 4.78 = 7.71 cm

b) For that to happen at x=0 ,t=3.00

both 0.208*3 +Q1 =pi/2

Q1 = 0.946796 rad

Phase of y2 = (-5.13*3 + Q2)

        = -15.39+Q2

if min Q2 can be negative:

-15.39 +Q2 = -11*pi/2
       => Q2 = -1.888759 rad

else,

-15.39+Q2 = -7*pi/2

=> Q2= 4.394 rad