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

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)=(1.97 cm)sin (k_1x+(0.313 rad /s)t+Phi_1) y_2(x,t)=(5.53 cm)sin (k_2x+(5.63 rad /s)t+Phi_2) If 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

here,

the maximum positive displacement , Amax = A1 + A2

Amax = 1.97 cm + 5.53 cm

Amax = 7.5 cm

the maximum positive displacement is 7.5 cm

at ( x,y) = (0 ,0) and t = 3 s

y1 = (1.97 cm) sin( k1x +( 0.313 rad/s)t + phi1)

0 = sin( 0 + 0.313* 3 + phi 1)

phi1 = - 0.939 rad

the unknown phase constant is ( - 0.939) rad

at ( x,y) = (0 ,0) and t = 3 s

y2 = (5.53 cm) sin( k2x - ( 5.63 rad/s)t + phi2)

0 = sin( 0 - 5.63* 3 + phi 2)

phi2 = 16.89 rad

the unknown phase constant is 16.89 rad

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