Waveform fundamentals: in signal analysis, what is the “period” of a repetitive waveform such as a sine wave or square wave?

Introduction / Context:
Time-domain descriptions of periodic signals use two key parameters: period (T) and frequency (f). Getting these definitions correct is vital for converting between time and frequency domains and for interpreting oscilloscope measurements and filter behavior.

Given Data / Assumptions:

• We consider a repetitive, periodic waveform (sine, square, triangle, etc.).
• We want the definition of period T.
• Standard relationships apply: f = 1 / T.

Concept / Approach:
The period T is the smallest time interval over which a periodic waveform exactly repeats itself. Equivalently, it is the duration of one complete cycle from any point back to the identical point in phase on the next cycle. Frequency is the reciprocal of period and has units of hertz (cycles per second).

Step-by-Step Solution:
Identify a full cycle on the waveform (e.g., peak to next peak for a sine wave).Measure the elapsed time between equivalent phase points.That elapsed time is the period T.Select the option defining period as “the time required to complete one full cycle.”

Verification / Alternative check:
If f = 50 Hz, then T = 1/50 = 0.02 s. Measuring 20 ms between repeating points on an oscilloscope confirms the relationship.

Why Other Options Are Wrong:
B defines frequency, not period. C describes rise time, a separate specification. D references 0.707 of peak (RMS of a sine), which is an amplitude measure, not time.

Common Pitfalls:
Confusing frequency with period; using rise time for non-slew-limited signals; mixing amplitude metrics (RMS) with time metrics.

Final Answer:
the time required to complete one full cycle