Phase comparison from zero crossings: One sine wave crosses zero (positive-going) at 15°, and a second sine wave crosses zero (positive-going) at 55°. What is the phase angle difference between the two waveforms?

Introduction / Context:Zero-crossing timing is a quick way to infer phase shift between two sinusoids of the same frequency. The positive-going zero crossing is a clean reference because amplitude differences do not affect the crossing instant, only phase does. This is fundamental in AC measurements, synchronization, and phasor analysis.

Given Data / Assumptions:

• Sine wave A: positive-going zero at 15°.
• Sine wave B: positive-going zero at 55°.
• Both have the same frequency and are measured within the same cycle reference.

Concept / Approach:For equal-frequency sinusoids, phase difference equals the angular separation between corresponding features (here, positive-going zeros). Subtract the angles, taking the smaller absolute separation modulo 360° if needed.

Step-by-Step Solution:

Verification / Alternative check:Plotting or imagining the sine waves confirms waveform B reaches zero later (at a higher angle), indicating a 40° lead relative to the 15° reference.

Why Other Options Are Wrong:

• 0°: Would require identical crossing angles.
• 45°: Not equal to the given separation.
• none of the above: Incorrect since 40° is directly obtained.

Common Pitfalls:

• Using negative-going zeros or mixing degree/radian units.
• Forgetting that only equal-frequency waves have a fixed phase difference.

Final Answer:40°