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,(x,») = (1.73 cm) sinlk.x+ (0.173 rad / s)t+ ylxd-16.03 cm] sinlk2x-(964 rad /s)1+2) s the maximum positive If both of the above traveling waves exist on the string at the same time, what is the maximum positive displan e ent that s paintion the sting can ever havn/ 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 = 1.68 s? Number Number rad rad

Explanation / Answer

a) From superposition;

the maximum amplitude is sqrt (A^2 + B^2 + 2AB cos(theta)) when theta is 1.

So maximum amplitude is (A+B) = 7.76  

b) The net difference is phase has to be zero at t = 1.68.

So, the phases are 16.48 /2 = 8.24 radians

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