Final answer:
For sinusoidal wave functions, y-values start to repeat after one complete cycle, which is 2π radians. The periods of the given functions y1 and y2 are fractions of 2π; however, since the question seeks a common repetition rate for both, the answer is 2π radians, which is the least common multiple of their periods. Option A is correct.
Step-by-step explanation:
The question is asking for the period of a trigonometric function, which is the length of one complete cycle of the wave before the y-values start to repeat. In radians, a full cycle of any sinusoidal function, like sine or cosine, is 2π radians. If we consider the general form of a sine function y = A sin(Bx + C), the period is given by 2π/B.
For the functions y1 (x, t) = 0.50 m sin(3.00 m-1x - 4.00 s-1t) and y2 (x, t) = 0.50 m sin(6.00 m-1x + 4.00 s-1t), the B values are 3.00 m-1 and 6.00 m-1 respectively.
This means the periods are 2π/3 and 2π/6, but since the question asks when the y-values start to repeat for both, we need to find a common multiple of the periods, which is 2π radians, the least common multiple of the individual periods.