Final answer:
The period of x₁ is 416/π seconds and the period of x₂ is 784/π seconds.
Step-by-step explanation:
The period of a wave is the time it takes for one complete cycle to occur. To find the period of a wave, we need to determine the time it takes for the wave to complete one cycle. For the given signals, the period of x₁ can be found by identifying the smallest repeating pattern in the signal. In this case, the smallest repeating pattern is sin(π/416t), which completes one cycle every time t = 416/π seconds. Therefore, the period of x₁ is 416/π seconds. Similarly, the smallest repeating pattern in x₂ is sin(π/784t), which completes one cycle every time t = 784/π seconds. Therefore, the period of x₂ is 784/π seconds.