Period from cycles over time: If a sine wave completes 10 cycles in 20 µs (microseconds), what is the period of one cycle?

Introduction / Context:Period and frequency calculations often start from counts of cycles over a measured time window. Converting counts to per-cycle period is straightforward division, but unit care (microseconds, milliseconds) matters to avoid scale errors.

Given Data / Assumptions:

• Total time window Δt = 20 µs.
• Number of cycles N = 10.
• Uniform sinusoid over the interval (no frequency drift).

Concept / Approach:

The period T is the time per cycle: T = Δt / N. Insert the given total time and the number of cycles completed.

Step-by-Step Solution:

Verification / Alternative check:

If each cycle is 2 µs, then 10 cycles take 20 µs, consistent. The reciprocal frequency calculation corroborates the period.

Why Other Options Are Wrong:

4 µs would yield only 5 cycles in 20 µs. 20 µs implies one cycle only. 100 µs is unrelated and would correspond to much lower frequency.

Common Pitfalls:

Dividing the wrong way (N/Δt); mixing µs with ms or s; failing to reduce fraction correctly.

Final Answer:

2 µs