Waveforms and time–frequency relationship: which statement best describes how the period of a waveform relates to its frequency in basic AC circuit theory?

Introduction / Context:
In alternating-current (AC) theory and signal analysis, time-domain and frequency-domain descriptions are linked by a simple inverse relationship. Recognizing how period and frequency relate is foundational for analyzing power systems, audio signals, and communication waveforms.

Given Data / Assumptions:

• Frequency f is measured in hertz (cycles per second).
• Period T is measured in seconds per cycle.
• Sine wave behavior is representative for illustrating the f–T relationship.

Concept / Approach:
The fundamental relationship is f = 1 / T. As the time for one cycle (T) increases, the number of cycles per second (f) decreases proportionally, and vice versa. Amplitude is independent of frequency; and 1.41 (square root of 2) relates RMS and peak of a sine wave’s amplitude, not its frequency. There is no default “assumed” frequency unless specified by a standard within a given context (e.g., regional mains frequency).

Step-by-Step Solution:

Verification / Alternative check:
Example: if T = 0.02 s, f = 1 / 0.02 = 50 Hz; if T doubles to 0.04 s, f halves to 25 Hz. This numerical check confirms the inverse relation.

Why Other Options Are Wrong:

Common Pitfalls:
Confusing amplitude–RMS relationships with frequency, or assuming regional mains frequency applies universally. Always rely on f = 1 / T to reason about time and frequency.

Final Answer:
A longer period corresponds to a lower frequency