sapling learning lo traveling waves are generated on the same taut string. Indiv

Question

sapling learning lo traveling waves are generated on the same taut string. Individually, the two traveling waves can be aescribed by the following two equations: y, (x,t)E (2.69 cm) sin kix+ (0.243 rad s t+ p y, (x,t (4.78 cm) sin kax- (4.45 rad s t+ p, f 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? Number cm 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 3.66 s? Number Number rad rad

Explanation / Answer

By superposition principle , y =y1+ y2.

y is max. when both y1 and y2 are max.

y1(max) = amplitude of y1 = 2.69 cm.,      y2(max) = amplitude of y = 4.78 cm.

So, y(max) = 2.69 +4.78 = 7.47cm......................answer(1).

This occurs when sin(k1x +0.243t + Q1)=1 and sin(k2x -4.45t + Q2)=1

                        or, k1x +0.243t + Q1= pi/2    and k2x -4.45t + Q2= pi/2

Put x = 0, t=3.66s ;   Q1=0.68 rad and Q2=17.86 rad......................answer(2)

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