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What is the result when two sinusoids at 150 Hz with a peak amplitude of 2 are 180 degrees out of phase?

  1. 150 Hz sinusoid with a peak amplitude of 0.0

  2. 150 Hz sinusoid with a peak amplitude of 4.0

  3. 300 Hz sinusoid with a peak amplitude of 0.0

  4. 300 Hz sinusoid with a peak amplitude of 4.0

The correct answer is: 150 Hz sinusoid with a peak amplitude of 0.0

When two sinusoids are out of phase by 180 degrees, they effectively cancel each other out. In this scenario, both sinusoids have the same frequency of 150 Hz and a peak amplitude of 2. The 180-degree phase difference indicates that when one sinusoid reaches its positive peak, the other is at its negative peak of equal amplitude. As a result, when the two sinusoids combine, their contributions to the overall signal negate one another. Mathematically, this cancellation results in a composite signal with an amplitude of 0. Therefore, the outcome is a sinusoid at 150 Hz but with a peak amplitude of 0.0. This aligns with the concept that the superposition of two equal but opposite amplitudes leads to a net amplitude of zero. This analysis clarifies why the selected answer is indeed the correct interpretation of the situation.